PR1ME Math PHP 1stEd_4A_CWM_SampleChapt_LR_watermarked

TM A world-class program based on top-performing 4A Singapore, Republic of Korea and Hong Kong Coursework Manual Philippine Edition

TM A world-class program based on top-performing 4A Singapore, Republic of Korea and Hong Kong Coursework Manual Scholastic Philippine EditionA Teacher’s Guide to Scholastic PR1ME Mathematics Coursework Book

Scholastic © 2017 Scholastic Education International (Singapore) Private Limited A division of Scholastic Inc. All rights reserved. No part of this publication may be reproduced in whole or in part, or stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the written permission of the publisher. For information regarding permission, write to: Scholastic Education International (Singapore) Pte Ltd 81 Ubi Avenue 4, #02-28 UB.ONE, Singapore 408830 Email: [email protected] For sales enquiries, write to: Scholastic Philippines Penthouse 1, Prestige Tower, F. Ortigas Jr. Road, Ortigas Center, Pasig City 1605 Email: [email protected] Phone: (+632) 944-7323 Visit our website: www.scholastic.com.sg Coursework Manual 4A (Philippine Edition) First edition 2017 ISBN 978-981-47-6955-6

Contents About TM T5 T6 Mathematics (Philippine Edition) T14 T25 Introduction to Print-based Program 1 Introduction to Blended Learning Program 4 Developmental Continuum 4 10 Chapter 1 Whole Numbers Scholastic 16 20 Scheme of Work 23 Chapter Overview and Note for Teachers 23 Lesson 1 Numbers 0 to 100 000 Lesson 2 Rounding Numbers 25 Lesson 3 Factors 27 Lesson 4 Multiples Lesson 5: Number Patterns 27 Chapter Wrap-up 29 30 Chapter 2 Mental Math 31 Scheme of Work 34 Chapter Overview and Note for Teachers 34 Lesson 1 Mental Multiplication 39 Lesson 2 Mental Division 44 Chapter Wrap-up 52 54 Chapter 3 Multiplication and Division of Whole Numbers 54 Scheme of Work Chapter Overview and Note for Teachers 56 Lesson 1 Multiplication by 1-digit Numbers and by 10 61 Lesson 2 Division by 1-digit Numbers and by 10 61 Lesson 3 Multiplication by 2-digit Whole Numbers 63 Lesson 4 Problem Solving 69 Chapter Wrap-up 72 75 Review 1 80 84 Chapter 4 Fractions 87 Scheme of Work Chapter Overview and Note for Teachers Lesson 1 Mixed Numbers Lesson 2 Improper Fractions Lesson 3 Addition of Fractions Lesson 4 Subtraction of Fractions Lesson 5 Product of a Fraction and a Whole Number Lesson 6 Conversion of Measurements Lesson 7 Problem Solving Chapter Wrap-up © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

ScholasticChapter 5 Tables and Graphs 88 90 Scheme of Work 90 Chapter Overview and Note for Teachers 98 Lesson 1 Presenting Data 99 Lesson 2 Problem Solving Chapter Wrap-up 99 Review 2 100 102 Chapter 6 Angles 102 107 Scheme of Work 111 Chapter Overview and Note for Teachers 112 Lesson 1 Angle Measures Lesson 2 Turns and 8-point Compass 113 Lesson 3 Problem Solving 114 Chapter Wrap-up 114 117 Chapter 7 Perpendicular and Parallel Line Segments 119 Scheme of Work 119 Chapter Overview and Note for Teachers Lesson 1 Drawing Perpendicular Line Segments 120 Lesson 2 Drawing Parallel Line Segments 121 Chapter Wrap-up 121 126 Review 3 127 Chapter 8 Squares and Rectangles 130 130 Scheme of Work 135 Chapter Overview and Note for Teachers 138 Lesson 1 Properties of Squares and Rectangles 142 Chapter Wrap-up 147 150 Chapter 9 Area and Perimeter 151 Scheme of Work 153 Chapter Overview and Note for Teachers 153 Lesson 1 Perimeter 155 Lesson 2 Area of a Rectangle 157 Lesson 3 Squares and Rectangles Lesson 4 Composite Figures 1 57 Lesson 5 Problem Solving Chapter Wrap-up 159 Chapter 10 Probability 177 Scheme of Work Chapter Overview and Note for Teachers Lesson 1 Recording Outcomes and Finding Probability Lesson 2 Problem Solving Chapter Wrap-up Review 4 Answers Teacher’s Resources © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

About TM Mathematics (Philippine Edition) Welcome to Scholastic TM Mathematics (Philippine Edition). The pedagogical approach and instructional design of Scholastic TM Mathematics (Philippine Edition) are based on the innovative and effective teaching and learning practices of nations that are global top-performers in mathematics. The approach and instructional design are proven to be effective in developing conceptual mastery and procedural fluency, and are crafted to enable the teacher and student to evaluate learning and identify areas of remediation, if needed. The content in Scholastic TM Mathematics (Philippine Edition) is presented under five strands of mathematics across six years/grades: Numbers and Number Sense, Measurement, Geometry, Statistics and Probability, and Patterns and Algebra. This program has been carefully designed to meet the objectives of the Philippine Department of Education Mathematics Curriculum. There are two instructional pathways for Scholastic TM Mathematics (Philippine Edition): 1. Print-based Program: This program consists of two Coursework Books with their accompanying Coursework Manuals for each year/grade. Together, they form a complete curriculum that caters to teaching and learning needs in the classroom and at home. The Coursework Books contain material for active learning, guided practice and independent practice. The lesson plans in the Coursework Manuals provide teachers with complete guidance in class. Scholastic 2. Blended Learning Program: This program consists of two Coursework Books with their accompanying Coursework Manuals and an Interactive Edition for each year/grade. The Interactive Edition is a digital resource that contains material for active learning and guided practice. The Coursework Books complement the Interactive Edition and contain material for home revision and independent practice. The lesson plans in the Coursework Manuals provide teachers with complete guidance in class. Scholastic TM Mathematics (Philippine Edition) Coursework Manuals provide clear instruction for both instructional pathways. TM Mathematics Coursework Book and Coursework Manual (Philippine Edition) TM Mathematics Interactive Edition T5 For users of the Print-based Program, go to p. T6. For users of the Blended Learning Program, go to p. T14. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6

Print-based Program T6 Instructional Design Scholastic TM Mathematics (Philippine Edition) is designed on a pedagogical model that ensures teaching and learning are effective, measurable and diagnostic. Each chapter of the Coursework Book involves three phases of learning: readiness, engagement and mastery. A simple model of the instructional design is presented below. ScPhase 1: Readiness Phase 2: Engageme Phase 3: Mas tery hLet's Remember nt oLet’s Remember Learn Practice ChapterWrap-up Review loffers an © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 aopportunity for Learn introduces new Chapter Wrap-up Reviews at the end of the provide systematic recall concepts and builds chapter summarizes summative on concepts and skills the key learning assessment sand assessment of learned previously. points of the and chapter. consolidation prior knowledge Practice after each of concepts in preparation for Learn provides and skills learned across ticnew learning. opportunities for formative and various topics. independent practice. Using the Coursework Manual • answers for tasks, with worked solutions for all word problems • photocopiables for class activities This Coursework Manual includes: • Developmental Continuum for all six years/grades • detailed Scheme of Work • lesson plans

Plan Print-based Program The Developmental Continuum (pp. T25–T36) offers the overall plan for learning outcomes over the six-year course. Teachers can refer to this to understand the scope of teaching that takes Developmental Continuumplace at each year/grade. Coursework Manual Year/Grade 1 Year/Grade 2 Year/Grade 3 NUMBERS AND NUMBER SENSE Whole Numbers / Count within 100. Count within 1000. Read and write a number Place Value within 10 000 — the numeral and the corresponding number word. Read and write a number Read and write a number Use number notation and from 0 to 100 — the numeral from 0 to 1000 — the numeral place values (thousands, and the corresponding and the corresponding hundreds, tens, ones). number word. number word. The Scheme of aWnodrktopprerceepCwdaoithuirnienngt1of0one0.raantced habaccchkhwianagrpdstienrdiisvptUedisldaneecsun,esouaivmngalebnlcsue)ee.hrsnda(ohptutaonttideoranersdas.ssn,idst in pCnuloammnbpenarrisenwgaitnhdtinho1er0de0c0r 0u. rriculum for the entire year Use number notation and Compare and order Find the number which is 1, place values (tens, ones). numbers within 1000. Each bo10o,k10s0poar n10s010 mseomre ethsatner Coursework Manual cinostmrupcrtisio(nionunrmgl.ebTsaesebrtahwoacitnuhh)tinea91rg0s0ivc0he0aon0.nuras dojfust SCTotrtahanladDp:uNratuetimornb:3e1:r4sAhan4d0ddmNiiuntmitEoohbsbtnaeijmernaSca1etn0tnse0sdinetohaSbeujgenbrcuottmusr.pabecorftoifoefwnewr ithfUoRsreecgtohrmeopsuyamprisbiononglso‘f>n’ uamnstindhcbdee‘h<riosv’d.iodulurcaInadautelimolncebtnlinfaesydrssobs.adeardssa.aenndddoetvnheenthpeace of Scholastic Compare the number of Find the number which is 1, Name a position using an Scheme of Work objects in two or more sets. 10 or 100 more than (or less ordinal number from 1st to Lesson Learning Outcomes Vocabulary BletnhdeadnLe)aarninggivPreognranmumber within 1Pr0in0t-btha.sed Program Mate1ria0ls00. Resources Materials Resources Let’s • Add within 1000 wCithoomut pare and order Read wh•olCeB np.u41mbers w•ith1 icnopy of ILdete’s ntify and use the pattern Remember wrehgoroleupbianrgmaonddeulnsteouarmepparberste-enrst within 100. 1000 on a number line. WReomrkeshmebeetor(Wf Sn3a.1)ming ordinal numbers (40 min) an addition situation per studenftrom 1st to 100th • Subtract within 1000 without Name a position using an Identify the position of an rwehgoroleupbianrgmaonddeulFsteoinaredpparterhst-eentnumber which is • aiSnovsluvoeblvtianrag1c-stsuitoebnptrsawitcuota1triohdtinooapnarrnon1bd)l0eammgoivreenthnaunm(boer rless ordinal number from 1st to object from a given point of tuosereapcreosmenptaarissounbwtbraiatcrhtmiionond1e0l 0. 20th. reference. situation Make a number story to Identify and use the pattern Lesson 1: Addition with Regroupingillustrate a number bond for of naming ordinal numbers 6h Adding with • Add within 1000 w5ithto 10. • Base ten bflroockms 1st to• 2C0B tphp. 42–44 • Base ten blocks • CWB pp. 36–37 regrouping regrouping in ones • PB pp. 31–32 in ones Write a number bond for 5 • CWB pp. 36–37 Adding with • Add within 1000 wtoith 10. • CB pp. 45–47 • CWB pp. 38–39 • PB pp. 33–34 regrouping regrouping in tens • CWB pp. 38–39 in tens Name a position using an Adding with • Add within 1000 woitrhdinal number from 1st to • CB pp. 48–51 • CWB pp. 40–42 regrouping in ten1s a0ntdhoanens d position words. • PB pp. 35–39 regrouping • CWB pp. 40–42 in tens and A listing Aodfdooniteibsonje/cStuivbterascationnd Use picture cutouts (or other Observe and apply the Associate the terms ‘sum’ mmatahnaekdnemispuseubalatnratiinvcgetsisotK)oenetf.oryamidllmusdsittariaottnheemaaaidtsdiecsdonaicttiitiloayn,ti.cveomprmoMupteaartttiiveeesrioaafnlsd aadnddit‘idoRinffeearsneodnucseurcb’ wteraistchltisiotn resources for each lesson list planning quick and easy. respecCtivWeBly:.Coursework Book © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 Make a number story Add or subtract within 1000. Add or subtract within for a given addition or Use a part-whole bar model 10 000. Each chapter begins with sNubotrtaectfioonrseTentaencche.ers. Thisotoriadrecpeorenmstepinfaiteriassonntahbdaedritmikoeondoyer lmathematical ideas of the subtraction situation. chapter. Coursework Manual Write a number sentence for Solve up to 2-step word Use a part-whole bar model a given situation involving problems involving adwACddhithiadtpiiRtoiteoegnnr r3aonudpiSnugostbourtrbaarcettricpoanorcemtsioepnnatsriaistuonaLALneedaaatd•rnrbiindnionggAadwdnOdiutrhi.twctromiteihmoginero:1onu00pd0inowgeitrihnrleognreosup(CinWg Binpo.n3e6s) addition or subtraction. and subtraction. Chapter Overview Materials: Let’s Remember • Base ten blocks Lesson 1: Addition with Regrouping Note for Teachers Lesson 2: Subtraction with Regrouping Stage: Concrete Experience Lesson 3: Problem Solving Begin by using base ten blocks to demonstrate the In this chapter, students will progress to addition Note for Teachers addition of 426 and 146. This allows students to have and subtraction of 3-digit numbers with In this chapter, students will progress to addition a concrete experience of the regrouping that takes regrouping. Students can draw part-whole or and subtraction of 3-digit numbers with regrouping. place in the ones place during the addition process. Students can draw part-whole or comparison bar It also reinforces the concept of addition as putting models to help them solve addition and subtraction together. Grouping the unit cubes together first, word problems. followed by the ten-rods and lastly the hundred- squares, introduces students to the process of adding Recall Prior Knowledge the ones first, followed by the tens and lastly the hundreds. comparison bar models to help them solve v Blended Learning Programv – Distribute base ten blocks to students and have T7 addition and subtraction word problems. them follow each step of your demonstration. From PR1ME Mathematics Interactive Edition: © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 Let’s Remember (CB p. 41) – Use 4 hundred-squares, 2 ten-rods and 6 unit Assign the tasks to students as classwork to cubes to represent 426. Use 1 hundred-square, © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 identify gaps in students’ understanding. Use the 4 ten-rods and 6 unit cubes to represent 146. objectives and chapter references given for each task in the corresponding lesson notes to address T23– Group the unit cubes together. Have students remediation needs. see that there are 12 unit cubes in all. Guide them to see that since 10 ones = 1 ten, we Distribute a copy of Let’s Remember Worksheet (WS3.1) combine 10 of the unit cubes to form a ten-rod to each student. Have students attempt the worksheet and place it together with the rest of the ten- to help them recall these previously acquired related rods. Have students see that there are 2 unit knowledge: cubes left after the regrouping exercise. – Group the ten-rods together and have students • Add within 1000 without regrouping and use a part-whole bar model to represent an addition see that there are 7 ten-rods in all. situation (CWB 2A Chapter 2) – Group the hundred-squares together and have • Subtract within 1000 without regrouping and students see that there are 5 hundred-squares use a part-whole bar model to represent a in all. subtraction situation (CWB 2A Chapter 2) – Lead students to see that 5 hundred-squares, 7 ten-rods and 2 unit cubes represent 572. • Solve a 1-step word problem involving Hence, the sum of 426 and 146 is 572. subtraction and use a comparison bar model to represent a subtraction situation (CWB 2A Stage: Pictorial Representation Chapter 2) Follow up by relating the base ten blocks activity to the tables of the base ten blocks on CWB p. 36. This For answers, go to CW Manual p. 126. helps students to transit from concrete experience to pictorial representation. The first row of blocks in the Lesson 1: Addition with Regrouping table represents the augend, the second row of blocks represents the addend and the final row represents the Duration: 6 h sum. This presentation parallels the addition of numbers in vertical form. It aids the transition from pictorial representation to abstract representation later on. v Blended Learning Programv – Refer students to the table of the base ten blocks on CWB p. 36. Draw their attention to From PR1ME Mathematics Interactive Edition: the columns with the unit cubes and highlight Let’s Learn (CB pp. 42–43) the regrouping of the unit cubes. Relate it Go through the teaching examples with students for back to the combining of 10 unit cubes to concept development. Use the detailed lesson plan form a ten-rod. Show students the final number of unit cubes in the last row and reiterate that

Chapter Overview Materials: Let’s Remember • Base ten blocks Lesson 1: Addition with Regrouping Teach Lesson 2: Subtraction with Regrouping Stage: Concrete Experience Lesson 3: Problem Solving Begin by using base ten blo addition of 426 and 146. This Print-based Program Note for Teachers a concrete experience of th Phase 1 Readiness In this chapter, students will progress to addition Checking for Prior Knowledge and subtraction of 3-digit numbers with regrouping. place in the ones place dur Students can draw part-whole or comparison bar It also reinforces the concep together. Grouping the unit sintuLdeet’nswmtsRooeraddemtplsrreiotsobmkhlebebmlepes.ftrohecrmeorsaroelvnceetalwyd,dcittieoonanaccnehdepsurtsbitsmraincattiroyonudsuecethfstdohqeelul.oaowrneeesd,sinfbirtysrtot,hdfoeulcltoeewnse-srtdouddbseyantnhts Let’s Remember is a recall feature to identify If students are not able to answer the tasks objective of each task to identify gaps in their undeRrestcaanll dPriinogr Kanonwdlerdegfeer to the chapter referenchuendreds. for remediation. v Blended Learning Programv – Distribute base ten b them follow each ste Coursework Manual From PR1ME Mathematics Interactive Edition: Let’s Remember (CB p. 41) – Use 4 hundred-squa Chapter 3 Learn Assign the tasks to students as classwork to cubes to represent 4 Addition and Subtraction Adding with regrouping in ones (CWB p. 36) identify gaps in students’ understanding. Use the 4 ten-rods and 6 unit with Regrouping objectives and chapter references given for each Learning Outcome: task in the corresponding lesson notes to address – Group the unit cube Chapter Overview • Add within 1000 with regrouping in ones remediation needs. see that there are 12 Let’s Remember them to see that sinc Lesson 1: Addition with Regrouping Materials: Distribute a copy of Let’s Remember Worksheet (WS3.1) combine 10 of the u Lesson 2: Subtraction with Regrouping • Base ten blocks to each student. Have students attempt the worksheet and place it togethe Lesson 3: Problem Solving to help them recall these previously acquired related rods. Have students Stage: Concrete Experience knowledge: cubes left after the r Note for Teachers Begin by using base ten blocks to demonstrate the In this chapter, students will progress to addition addition of 426 and 146. This allows students to have • Add within 1000 without regrouping and use a – Group the ten-rods t and subtraction of 3-digit numbers with regrouping. a concrete experience of the regrouping that takes part-whole bar model to represent an addition see that there are 7 Students can draw part-whole or comparison bar place in the ones place during the addition process. situation (CWB 2A Chapter 2) models to help them solve addition and subtraction It also reinforces the concept of addition as putting – Group the hundred- word problems. together. Grouping the unit cubes together first, • Subtract within 1000 without regrouping and students see that the followed by the ten-rods and lastly the hundred- use a part-whole bar model to represent a in all. Recall Prior Knowledge squares, introduces students to the process of adding subtraction situation (CWB 2A Chapter 2) the ones first, followed by the tens and lastly the – Lead students to see hundreds. • Solve a 1-step word problem involving 7 ten-rods and 2 unit subtraction and use a comparison bar model Hence, the sum of 4 v Blended Learning Programv – Distribute base ten blocks to students and have to represent a subtraction situation (CWB 2A them follow each step of your demonstration. Chapter 2) Stage: Pictorial Representat From PR1ME Mathematics Interactive Edition: Follow up by relating the ba Let’s Remember (CB p. 41) – Use 4 hundred-squares, 2 ten-rods and 6 unit For answers, go to CW Manual p. 126. the tables of the base ten b Assign the tasks to students as classwork to cubes to represent 426. Use 1 hundred-square, helps students to transit from identify gaps in students’ understanding. Use the 4 ten-rods and 6 unit cubes to represent 146. Lesson 1: Addition with Regrouping pictorial representation. The objectives and chapter references given for each table represents the augend task in the corresponding lesson notes to address – Group the unit cubes together. Have students Duration: 6 h represents the addend and remediation needs. see that there are 12 unit cubes in all. GuideScholastic sum. This presentation paral them to see that since 10 ones = 1 ten, we in vertical form. It aids the tr Distribute a copy of Let’s Remember Worksheet (WS3.1) combine 10 of the unit cubes to form a ten-rod representation to abstract re to each student. Have students attempt the worksheet and place it together with the rest of the ten- to help them recall these previously acquired related rods. Have students see that there are 2 unit knowledge: cubes left after the regrouping exercise. • Add within 1000 without regrouping and use a – Group the ten-rods together and have students part-whole bar model to represent an addition see that there are 7 ten-rods in all. situation (CWB 2A Chapter 2) – Group the hundred-squares together and have • Subtract within 1000 without regrouping and students see that there are 5 hundred-squares use a part-whole bar model to represent a in all. subtraction situation (CWB 2A Chapter 2) – Lead students to see that 5 hundred-squares, • Solve a 1-step word problem involving 7 ten-rods and 2 unit cubes represent 572. subtraction and use a comparison bar model Hence, the sum of 426 and 146 is 572. to represent a subtraction situation (CWB 2A Chapter 2) Stage: Pictorial Representation Follow up by relating the base ten blocks activity to For answers, go to CW Manual p. 126. the tables of the base ten blocks on CWB p. 36. This helps students to transit from concrete experience to Lesson 1: Addition with Regrouping pictorial representation. The first row of blocks in the table represents the augend, the second row of blocks Duration: 6 h represents the addend and the final row represents the sum. This presentation parallels the addition of numbers v Blended Learning Programv in vertical form. It aids the transition from pictorial representation to abstract representation later on. From PR1ME Mathematics Interactive Edition: Let’s Learn (CB pp. 42–43) – Refer students to the table of the base ten Go through the teaching examples with students for blocks on CWB p. 36. Draw their attention to concept development. Use the detailed lesson plan the columns with the unit cubes and highlight given in the corresponding lesson notes to carry out the regrouping of the unit cubes. Relate it the teaching. back to the combining of 10 unit cubes to form a ten-rod. Show students the final number of unit cubes in the last row and reiterate that after regrouping the ones, there are 2 ones left. 30 Chapter 3 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 v Blended Learning Programv – Refer students to the blocks on CWB p. 36 Coursework Manual From PR1ME Mathematics Interactive Edition: the columns with the WS3.1 Let’s Remember Worksheet Let’s Learn (CB pp. 42–43) the regrouping of th Go through the teaching examples with students for back to the combin concept development. Use the detailed lesson plan form a ten-rod. Show given in the corresponding lesson notes to carry out of unit cubes in the the teaching. after regrouping the left. 1. Add 123 and 326. 326 123 123 + 326 = ? First, add the ones. 123 +326 30 Chapter 3 © 2017 Scholastic Education Int 2. Subtract 435 from 947. 947 435 ? First, subtract 947 – 435 = the ones. 947 –435 3. Joe collects 99 baseball cards. Shelly collects 15 fewer baseball cards than Joe. How many baseball cards does Shelly collect? 99 99 Joe –15 Shelly ? 15 Shelly collects baseball cards. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 Teacher's Resources 143 T8 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Phase 2 Engagement Print-based Program Teaching Concepts and Skills –– Developing Conceptual Understanding Each chapter is taught over several lessons, with each lesson focusing on a concept or part of it. The lesson is designed with a two-part structure of concept introduction, and guided with practice and formative assessment. Each concept is taught using the three-stage Concrete-Pictorial-Abstract approach to develop deep conceptual understanding. Coursework Book Addition and Subtraction with Regrouping Lesson 1 Addition with Regrouping Learning Outcomes: • Add within 1000 with regrouping in the ones and tens places • Solve 1-step word problems Adding with regrouping in ones Learn Add 426 and 146. 426 146 572 1 Add the ones. 2 Add the tens. 3 Add the hundreds. H TO H TO H TO 1 1 1 42 6 42 6 42 6 +1 4 6 +1 4 6 +1 4 6 2 72 5 72 6 ones + 6 ones = 12 ones 10 ones = 1 ten 12 ones = 1 ten 2 ones We regroup 12 ones into 1 ten 2 ones. Begin a lesson by walking students through the ‘Learning Outcomes’ list to encourage self-directed learning. Scholastic 426 + 146 = 572 36 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6939-6 Coursework Manual Chapter 3 Learn – Next, have students look at the columns with v Blended Learning Pro Adding with regrouping in ones (CWB p. 36) the ten-rods. Relate it back to the grouping of Stage: ConcreAtdedEitxiopnearniednScuebtraction the ten-rods. Reiterate that there are 7 tens in From PR1ME Mathemati Learning Outcome: all. Let’s Do (CB p. 44) Start Learn witwhitah Rheagnrodusp-oinng • Add within 1000 with regrouping in ones Assign the tasks to stude – Lastly, have them look at the columns with formative assessment. U activity. This is tChheaptceroOnvecrvireewte Materials: the hundred-squares. Relate it back to the notes to identify the obj learning journey.Let’s Remember • Base ten blocks grouping of the hundred-squares. Reiterate address remediation ne stage of the Lesson 1: Addition with Regrouping that there are 5 hundreds in all. be required to workLesson 2: Subtraction with Regrouping Stage: Concrete Experience Exercise 1 (PB pp. 31–32 Students may Begin by using base ten blocks to demonstrate the Stage: Abstract Representation Assign the tasks to stude Lesson 3: Problem Solving addition of 426 and 146. This allows students to have Lastly, present the addition in vertical form. Having formative assessment. U a concrete experience of the regrouping that takes gone through the previous stages, students will notes to identify the obj individually or iNnotge froor Tueapchse.rsTeachers place in the ones place during the addition process. see how the algorithm relates to the pictorial address remediation ne are encouraged to verbalize theIn this chapter, students will progress to addition It also reinforces the concept of addition as putting representation. This association is important as it helps together. Grouping the unit cubes together first, students to visualize the addition. It allows them to From PR1ME Mathemati and subtraction of 3-digit numbers with regrouping. followed by the ten-rods and lastly the hundred- understand and interpret the vertical form, especially Coursework Book Practi squares, introduces students to the process of adding the writing of digits above the augend in the vertical Assign all tasks to studen content in the speech bubblesStudents can draw part-whole or comparison bar the ones first, followed by the tens and lastly the form when regrouping occurs. This is an anchor for following notes to identi in the CoursewwmooordrdkeplsrBotobohleemolpsk.thetmosoglveuaidddeition and subtraction hundreds. learning addition with regrouping in other place task and address remed values, as well as more advanced forms of regrouping students’ thougRehcatllpPrrioor Kcneowslesdegse. that involve more than one place value. The three- Practice 1 (CWB p. 3 step approach (add the ones, then the tens and lastly v Blended Learning Programv – Distribute base ten blocks to students and have the hundreds) guides students to add systematically, Class practice (For Print them follow each step of your demonstration. reducing the likelihood of careless mistakes when they From PR1ME Mathematics Interactive Edition: are performing the addition in vertical form. Task 1 requires students – Use 4 hundred-squares, 2 ten-rods and 6 unit a 1-digit, 2-digit or 3-dig Let’s Remember (CB p. 41) cubes to represent 426. Use 1 hundred-square, – Write the vertical form of ‘426 + 146’ on the ones. The place values 4 ten-rods and 6 unit cubes to represent 146. board. First, guide students to add the ones. form of addition to guid Assign the tasks to students as classwork to Have them look at the digits in the ones place – Group the unit cubes together. Have students in the vertical form of addition. Students should Remediation Stage: Pictorial Representationidentify gaps in students’ understanding. Use the see that there are 12 unit cubes in all. Guide be able to state that 6 ones + 6 ones = 12 ones. Task 1(a): Reteach add objectives and chapter references given for each them to see that since 10 ones = 1 ten, we a 2-digit number with re combine 10 of the unit cubes to form a ten-rod – Reiterate that 12 ones can be regrouped into through Task 1(a). Highli In the pictorial stage, task in the corresponding lesson notes to address and place it together with the rest of the ten- 1 ten 2 ones. Relate the regrouping back to 10 ones, which can be r remediation needs. rods. Have students see that there are 2 unit the pictorial representation on the page. Have 1 ten + 5 tens = 6 tens. T cubes left after the regrouping exercise. students look at the columns with the unit guide students to represent cubes. Write the addition of the ones in the Task 1(b): Reteach add – Group the ten-rods together and have students vertical form of addition on the board. 2-digit number with regr mathematical ideas visually.Distribute a copy of Let’s Remember Worksheet (WS3.1) see that there are 7 ten-rods in all. through Task 1(b). Highli to each student. Have students attempt the worksheet – Then, guide students to add the tens by having = 14 ones, which can be – Group the hundred-squares together and have them look at the digits in the tens place in the 1 ten + 4 tens + 3 tens = Ensure that each student hasto help them recall these previously acquired related students see that there are 5 hundred-squares vertical form of addition. Again, relate 1 ten 684. knowledge: in all. + 2 tens + 4 tens = 7 tens back to the pictorial progressed succ•esAsdfud wlliythinto1000thwiitshout regrouping and use a representation by having students look at the Task 1(c): Reteach add introducing abstractpart-whole bar model to represent an addition – Lead students to see that 5 hundred-squares, columns with the ten-rods. Write the addition 3-digit number with regr stage before situation (CWB 2A Chapter 2) 7 ten-rods and 2 unit cubes represent 572. of the tens in the vertical form of addition on numbers e.g. 119 + 123. This middle stage• Subtract within 1000 without regrouping and Hence, the sum of 426 and 146 is 572. the board. Highlight that 4 ones + 8 representation. use a part-whole bar model to represent a regrouped into 1 ten 2 o Stage: Pictorial Representation – Finally, guide students to add the hundreds by 4 hundreds + 1 hundred is a crucial link between thesubtraction situation (CWB 2A Chapter 2) Follow up by relating the base ten blocks activity to having them look at the digits in the hundreds 404 + 168 = 572. • Solve a 1-step word problem involving the tables of the base ten blocks on CWB p. 36. This place in the vertical form of addition. Again, helps students to transit from concrete experience to relate 4 hundreds + 1 hundred = 5 hundreds Teaching tips concrete experience and thesubtraction and use a comparison bar model pictorial representation. The first row of blocks in the back to the pictorial representation by having Task 1 to represent a subtraction situation (CWB 2A table represents the augend, the second row of blocks students look at the columns with the hundred- represents the addend and the final row represents the squares. Write the addition of the hundreds in ¾ When reteachin abstract representaChtaipotenr 2)and serves sum. This presentation parallels the addition of numbers the vertical form of addition on the board. as the example in vertical form. It aids the transition from pictorial base ten blocks to build a solidFofor aunswnedrs,agottiooCnW.Manual p. 126. representation to abstract representation later on. – To conclude, write the addition sentence regrouping. Then ‘426 + 146 = 572’ on the board. vertical form. Lesson 1: Addition with Regrouping – Refer students to the table of the base ten blocks on CWB p. 36. Draw their attention to – Reiterate that we add the ones first, followed Duration: 6 h the columns with the unit cubes and highlight by the tens, then the hundreds. the regrouping of the unit cubes. Relate it Stage: Abstracvt BRlenedpedrLeeasrneinng Ptraogtraiomvn back to the combining of 10 unit cubes to Once conceptual From PR1ME Mathematics Interactive Edition: form a ten-rod. Show students the final number of unit cubes in the last row and reiterate that Let’s Learn (CB pp. 42–43) after regrouping the ones, there are 2 ones left. understanding is developed,Go through the teaching examples with students for concept development. Use the detailed lesson plan progress to thetghivaeetnbeainsctthhrienagc.ocrretspsotnadigngeles.son notes to carry out The concept or skill is represented using only numbers and mathematical symbols. 30 Chapter 3 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T9

Teaching Concepts and Skills — Formative Assessment Print-based Program There are opportunities for formative assessment within each lesson. Practice tasks in the Coursework Book reinforce students’ learning through guided and systematically varied tasks. – Next, have students look at the columns with the ten-rods. Relate it back to the grouping of When necessary, refer to the teaching tips in the Coursework Manual to address remediationthe ten-rods. Reiterate that there are 7 tens in all. – Lastly, have them look at the columns with needs. the hundred-squares. Relate it back to the grouping of the hundred-squares. Reiterate that there are 5 hundreds in all. v Blended Learning Programv From PR1ME Mathematics Interactive Edition: Let’s Do (CB p. 44) Assign the tasks to students as classwork for formative assessment. Use the corresponding lesson notes to identify the objectives of each task and address remediation needs. The icon indicates class Stage: Abstract Representation Exercise 1 (PB pp. 31–32) practice. After a concept is taught Lastly, present the addition in vertical form. Having Assign the tasks to students as classwork for further in Learn, go through related gone through the previous stages, students will formative assessment. Use the corresponding lesson Practice tasks as class practice. notes to identify the objectives of each task and sreeCperoehosuewrnsttaehtewioanol.gTrohkriisthBamsosoroeclkaiatteiosntoistihmeppoirctatonrtiaal s it helps address remediation needs. students to visualize the addition. It allows them to understand and interpret the vertical form, especially From PR1ME Mathematics Coursework Book: Coursework Book Practice 1 (CWB p. 31) tfohermwPwrrithainecgntoriecf gderiogs1uitspainbgoovcectuhres. augend in the vertical Assign all tasks to students as homework. Use the This is an anchor for following notes to identify the skills needed for each task and address remediation needs. vleaalurneins,gaas1d.wdeitlAlioadnsdmw.iothrereagdrvoaunpcinegdinfoormthseor fprleagcreouping that involve more than one placeStvaartlubey. aThdeditnhgrethee- ones. step approach (add the ones, thReengtrhoeupteinf sneacnedsslaasrytl.y the hundreds) guides students to add systematically, Practice 1 (CWB p. 37) Discuss students’ responses and− Next, have students look at the columns with vareBrldeeunpcdeienrfgdortLmheeianlrgaink)eitnhlgiehoPaordoHddgoirtTaifomcOnavinrevleesrstimcaisltafbok)rems.whHenTthOey c) H T O the ten-rods. Relate it back to the grouping of LFAarideerssoemstsm’eingsestnDi––sdPfmyoRitah1tet(heMibiHbWRnConeetoeatEnBr.atoiiavhttUMaspneebereksbde.rajestaetvl4.ehehtttchet4Foedeehite)trrsiomtessvvtm.ittchee,usc+aalatrgsodoattltiuooecir3tfc1rieokfnade2sertal5estmsIohpafntosanaoct73totrehesutmnhfresdc6daatcloeaicdoadnanfstnisgdgik‘tsnve4siwitletase2bitsooon6s+Eeinnsrddk+ao6.rtienSdaft1hooitgod4deunnrr6nddeoofto’:ohrseutneo+eerpn=mesnstesos16statdno2phstheiel4oiv3anosen.ctuo68eelds. Class practic4e (0Fo4r Print-based Program): remediate if necessary.the ten-rods. Reiterate that there are 7 tens in AfnEaoxodsrestmdiergcrasen–isttseiotsvher1ieedt1scvThtha(meeu2tutPeeaserbn.dBtesnsnipteeeckdi,pfisssna2ycgia.sApattmltuWotso.)otdfhiion3loedroresdiier1antntemoue.–so+ltk.n3d.srbttoeR2eUaheu1jfepe)esetdnealcrdatte3eahsdtsttnsideh.veade58teedssincttshiitctotcooaieoolnolautfanirrsomoeredseonnwgandsfrpcosotoththnhowrhuekenepittbtfahbdhoiotn)esoiernntkg+hanfpgeuaesbrasdr2lnbateigu.hndycsnee17stkioh.htr Hatne59oavivneg +168 all. − Lastly, have them look at the columns with the Task 1 requires students to add a 3-digit number and hundred-squares. Relate it back to the a 1-digit, 2-digit or 3-digit number, with regrouping in grouping of the hundred-squares. Reiterate ones. The place values are provided in the vertical that there are 5 hundreds in all. form of addition to guide students. Assign the rest of the tasks asStage: Abstract Representation Remediation homework for independent practice.Lastly, present the addition in vertical form. Having aTthar2sok-du1cgig()hait)Tn:aRu+semkt431be(aea50rc)w.h66Hiatihgdhrdeliiggnhgrotauthp1ai-ndtg3iginoitnoneunsme+sb.7Tehorenanen,sdg=o 10 ones, which can be regrouped into 1 ten. gone through the previous stages, students will see 1 ten + 5 tens = 6 tens. Therefore, 353 + 7 = 360. how the algorithm relates to the pictorial representation. This association is important as it helps them look at the digits in the tens place in the students to visualize the addition. It allows them to From PR1MveErtMicaatlhfeomrmaoticf sadCdoiutirosne.wAogrkaiBno, orekla: te 1 ten understand and interpret the vertical form, especially Coursewo+r3k2.BteonoAskd+Pd4ra.tcetnics e= 17 (tCenWsBbpa.c3k1t)o the pictorial Task 1(b): Reteach adding a 2-digit number and a the writing of digits above the augend in the vertical form when regrouping occurs. This is an anchor for Assign all crnteaoopsltukreesmssteantoons)stwitadui4tetdih3one6nttnihfb+tyesyt5atheh5seanh=-vsorkionmildlgsesn.swteWuoedrridtkeee.nUdtthssfeelootraohekdeadacitthitohne 2-digit number with regrouping in ones. Then, go learning addition with regrouping in other place following values, as well as more advanced forms of regrouping b) 6=t7h1r+o4u6og1nh7eTs=a, wskh1ic(bh)c. Hainghbleighretgthroautp6eodniensto+ 8 ones ones. that involve more than one place value. The three-step 1 ten 4 approach (add the ones, then the tens and lastly the tCasok aunrdseatohfdwetdhobreeorstakserrndeMs.minaetdhnieautviaoenrltinceael fdosr.m of addition on hundreds) guides students to add systematically, 1 ten + 4 tens + 3 tens = 8 tens. Therefore, 646 + 38 = reducing the likelihood of careless mistakes when they 684. – Finally, guide students to add the hundreds by Practiceha1vin(Cg WthBemp.lo3o1k) at the digits in the hundreds Task 1(c): Reteach adding a 3-digit number and a place in the vertical form of addition. Again, 3-digit number with regrouping in ones, using smaller are performing the addition in vertical form.Scholastic Class prarbcetaliaccteke(t4oFohtrhuPenrdipnritec-bdtoasrs+iae1ldrhePuprnoredgsrreeandmta=):t5iohnubnydhreadvsing numbers e.g. 119 + 123. Then, go through Task 1(c). The objective of each task is stated− Write the vertical form of ‘426 + 146’ on the Highlight that 4 ones + 8 ones = 12 ones, which can be board. First, guide students to add the ones. students look at the columns with the hundred- regrouped into 1 ten 2 ones. 1 ten + 6 tens = 7 tens. in the Coursework Manual, enablingHave them look at the digits in the ones place T1a-dskig1it,re2q-dstuhqigieureiatvsoreescrrtstu3.i)cd-Wdae3irlgnitf5oteits8rntmth+ouemoa4af2dbad4deddr=a,ditwiio3tii-ontdhnoigrofeittnghnrteouhumehpubbinneodgraraerindnd.ds inad) 4 hundreds + 1 hundred = 5 hundreds. Therefore, in the vertical form of addition. Students should ones.–TheTpolaccoencvlaudluee,swarrietepthroeviaddedditiinonthseenvteernticceal 244094 ++ 156386==572. learning andbe able to state that 6 ones + 6 ones = 12 form of ad‘4d2i6tio+n1t4o6 g=u5id72e’sotundtehentbs.oard. teachers to check ones. Teaching tips address remediation needs.− Reiterate that 12 ones can be regrouped into – Reiterate that we add the ones first, followed Task 1 1 ten 2 ones. Relate the regrouping back to Remediatbioynthe tens, then the hundreds. Answers are provided for all tasks.the pictorial representation on the page. Have Task 1(a): Reteach adding a 1-digit number and a ¾ When reteaching, follow the same procedure students look at the columns with the unit 2-digit number with regrouping in ones. Then, go as the example in Learn (CWB p. 36). Use cubes. Write the addition of the ones in the through Task 1(a). Highlight that 3 ones + 7 ones = base ten blocks to introduce the concept of 10 ones, which can be regrouped into 1 ten. regrouping. Then, continue with the addition in vertical form of addition on the board. 1 ten + 5 tens = 6 tens. Therefore, 353 + 7 = 360. vertical form. − Then, guide students to add the tens by having them look at the digits in the tens place Task 1(b): Reteach adding a 2-digit number and a 372-digit number with regrouping in ones. Then, go© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6939-6 in the vertical form of addition. Again, relate 1 through Task 1(b). Highlight that 6 ones + 8 ones = ten + 2 tens + 4 tens = 7 tens back to the 14 ones, which can be regrouped into 1 ten 4 ones. pictorial representation by having students look at the columns with the ten-rods. Write the 1 ten + 4 tens + 3 tens = 8 tens. Therefore, 646 + 38 = Task 9 requires students to solve a 1-step subtraction addition of the tens in the vertical form of 684.© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 word problem involving the part-Cwhaphteor 3le 3c1oncept. Distribute a copy of Min addition on the board. student. Have them un Task 1(c): Reteach adding a 3-digit number and a This helps them to unde − Finally, guide students to add the hundreds by 3-digit number with regrouping in ones, using smaller For answers, go to CW Manual pp. 123–124. interpret it correctly. having them look at the digits in the hundreds numbers e.g. 119 + 123. Then, go through Task 1(c). 1. Understand the prob place in the vertical form of addition. Again, – Guide students relate 4 hundreds + 1 hundred = 5 hundWredSs2.2 CrHeigahtleighYtothuart O4 ownens W+ 8oorknessh=e1e2tones, which can be them to find the back to the pictorial representation by having regrouped into 1 ten 2 ones. 1 ten + 6 tens = 7 tens. the train. tssThqtoueudcavoerenenrctsts.ilcuWloadorleitfkoe, awrtmthritethoeeaftadhcdedodilatuiiotdRTSmiohnhdenenopiotsnwiolfoaw,tnncshyitooteeshheluveht‘nerhmutbweentoohnodhreaecrurker’enwddcwd.oslreiretidnhadr‘p-lyfer.owb14ele6rh’8muin=n. dt5hr7ee2d.ws o+r1dhpurondbrleemd .= 5 hundreds. Therefore, 404 + v Blended Learning Programv From PR1ME Mathematics Interactive 2. Plan what to do. Tstoudaedndtrsedssisccuosms, mcoomn mmuisncicoanctee,pretiaonsosnaannddejurrsotirfsyamnadthsetrmenagtitchaelnidmeaasthaenmdautnicdael rtshtainnkdiningg, huasinvge− – Point out to stud Teaching tips Edition: backwards to s ‘426 + 146 = 572’ on the board. Think About It (CB p. 38) 3. Work out the Answer scenarios found in the Think About It feature.− Assign the task to students as classwork. Have them – Highlight to stud Reiterate that we add thMe aodneasmfirSsitt,i fsoollldow2e45d floweTras syke1sterday. sequence of ev by the tens, then the hunSdhreedsos.ld 32 more flowers todaØy thWahneynerseteterdaachy.ing, follow the same procedure as shown on Mi How many flowers did she sell todaas yth?e example in Learn (CWB p. 30). Use base complete the task in groups. Facilitate discussions diagram on the ten blocks to introduce the concept of – Explain to stude Coursework Manual regrouping. Then, continue with the addition inCuosuinrgsetwheorckoMrraenspuoanl ding lesson notes. backwards star vertical form. passengers left – Write ‘_____ + 15 Have students form WS2.3 Think About It Worksheet Have students get into groups. Distribute a copy of students to see Think About It Worksheet (WS2.3) to each group. Have from 788 to find groups to discuss   Hari bought 15 marbles. them discuss the question presented. Ask a student before 156 pass 27 from each group to present their answers before student work ou the question. Ask a  © 2015 Scholastic Education International (S) Pte LHtdisISBfNri9e78n-9d81-0g9-a049v9e-9 him 10 marbles. Chapter 3 proceeding with the questions below. and conclude t How many marbles does Hari have altogether? ? (whole) on the train bef representative from – What are Sam and Yen trying to find? (The total – Write ‘_____ – 10 15 (part) 10 (part) 15 (part) number of marbles Hari has) students to see to 632 to find th each group to present ? (whole) 10 (part) – How many marbles did Hari buy? (15) the beginning. – How many marbles did his friend give him? (10) addition on the and justify the group’s – How can we find the total? (Add) were 732 passe – Does Sam’s model show that we can find the total response. Sam Yen 4. Check if your answer number of marbles by adding the parts? (Yes) – Have students u Who has drawn the bar model correctly? Why? – Does Yen’s model show that we can find the total passengers at t through the wo Lesson notes are number of marbles by adding the parts? (Yes) the number of p Get students to see that we can draw either bar model the train, respec provided to facilitate to help us solve the problem. Conclude that both Sam – Lead students t and Yen have drawn the bar models correctly. number of pass discussions and guide the problem, th v Blended Learning Programv students to arrive at the correct conclusion. 140 Teacher's Resources © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 From PR1ME Mathematics Interactive Edition: Mind stretcher (CB p. 40) Go through the problem with students. Use the detailed lesson plan given in the corresponding lesson notes to carry out the teaching. Learn Mind stretcher Learning Outcome: • Solve a non-routine problem on addition and subtraction within 1000 using the strategy of working backwards Reiterate the following – When we add z Materials: same number. • 1 copy of Mind stretcher (BM2.3) – We can add tw T10 and get the sam © 2017OSvcehrovileawstic Education International (S) Pte Ltd ISBN 978-981-47-6–955-6We can group n This problem requires students to know the inverse – We can add or relationship between addition and subtraction. without regroup The strategy of working backwards is used in word – We can use a p

Teaching Concepts and Skills — Developing Processes and Strategies A problem solving lessonv at the end ofBlended Learning Programv the chapter consolidates learning. FocusTask 4 requires students to solve a 1-step word problem on both the Print-based Program involving subtraction by drawing a part-whole bar CpUpnrroooducberelseressmtswasaonodrnkf-dPBaloanthoynek-leAfsovnterrsaawl toeedfgreLAAfnFaE-doerxiodssoCreettsstmdm’iiierggasfcrassehnnDfiPsttisieoRiottsvclehh1eerr1(ieeeMdCe1ucamedttEBaa(snPleqsMkssptteBkkdi.faysdssyiups6atttmh7t..ooptheiie)4oeress8mRnnttre)suuotaon.ddecbtdeUeeijcceesnnfrescdtteissIetpstniht.vaatreeeossstsrcccsitaoolloocaafrtsssreitnssevwwoaoestpcoohEolhorrdvkknetbiffftadeooiosirrnuktnfpg:huairltnletrehddhsoesorebnpglreopomobrommTimTinndaalvv-oooessbooskkdddllvvo56eeemlhiielllnnrr...eelggavqq-mssuusuuibiinbbrroeesttssrrig.aaltssvccttsuuttiCddiipooneefnnnnrogobbttossyyrnttddoocprrsssaaaeooriwwsllovvpiisnnteeggcespaaaae11npr--cpssootsattaeemlrstppay-.pgwwwachooeroaisrrhlddoenpppaibnbrraoopatrbbgrllleetymmhmethabetahecfomkuoar-ftsittcehapel CofuorrsmeawtioverkaBssoeosskment. Use the corresponding lesson Task 7 requires students to solve a 1-step word problem notes to identify the objectives of each task and involving subtraction by drawing a comparison bar Lessoandd3rePsrsorbelmemedSioaltviionng needs. 4 Checmk odel. a) 14 WordFprroomblemPRs1ME Mathematics Coursework Book: if your answer 1 5 13 2 is correct. Task 8 req–u1ir68e76s students to solve a 1-step word problem IALtehtaaaidlronr6CA7shfsooespwuigehrarsnbdee2alwt5s3.llonterackkstBikesso. otok Practice 8 (CWB pp. 48–49) students as homework. Use the involving sThuerbe atrrea67cfetwioer nbeltbs thyandrawing a part-whole bar neckties. a) HHoofwwommllaaonnwyy bnieencltgsktaiernes aothnetdereb?selttsoareidtheerne atiltfoygetthheer? skills needed for each model. My answer is correct. b) 1 task and address remediation needs. For answb) e–rs413 ,138 g9 o to CW Manual pp. 125–126. Understand There are 253 neckties. There are the problem. 67 fewer belts. I have to find the 6 number of belts and the total 2 53 number of neckties and belts. There are 253 neckties. Practice 8 (CWB pp. 54–55)Plan My answer is correct. 2 what to do. v Blended Learning Programv I can draw a bar model 1. Understand 2. Plan 3. Answer 4. Check to show the number of Class practicneeck(tiFesoarndPbreiltns. t-based Program): From PR1ME Mathematics Interactive Edition: 3 TWAanosrwkseokru.t1thereqau) irneecsktisestudents25t3o solve a 1-step word problSSPeohraolmvwcettyihcoeuesres9wwoPAorkrrdscaslpeicrgaorbtlnyilec. mtehs. eD2rat(waCbsBakrsmpto.od6el8ss tt)ouhdelep nyotus. as classwork for involving subtraction. The comparison bar model is summative assessment.Understand Use the corresponding lesson provided to bgeltus ide them. 1. 2. Plan 3. Answer 4. Check ? 253 – 67 = 186 67 1 14 13 1. A syrnupofatcetosrytmoaikdese46n1tbifoyttletshoef oroanbgejesycrutpivineasdaoy.f each task and 2 5 aIt )maHakoedws 1md9a8rnefeyswbseortrtbeleosmttolefesaopdfpaileappstylierouspynrduopne. es itemdakse. in a day? RemediatioTnhere are 186 belts. – 67 b) How many bottles of syrup does it make in a day in total? 186 Task 1: Highlight that we have to find the number a) 461 There are fewer bottles of sotfusdtuednetsntbth)sainnnecHkHtieaas llll B. Poi2n53t out that Hall B has fewer Lesson 3: Problem Solvingorange A, so we subtra? ct to find the number syrup apple apple syrup than orange syrup. I should subtract. of students inbelHts all B. syrup Duration: ? h= 198 186 1 2 253 253 + 186 = 439 +186 There are 439 neckties and Ivt maBkeles ndedboLtetleas ornf aipnpgle sPyrruop gin raadmay.v 439 Teaching tipbselts altogether. Task 1 56 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6939-6 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6939-6 57 ¾ Use the 4-step problem solving approach to From PR1ME Mathematics Interactive Edition: go through the word problem. Let’s Learn (CB pp. 69–70) ¾ Go through the comparison bar model with Go through the teaching example with students for students and highlight that we are finding a concept development. Use the detailed lesson plan Scholastic part of the whole. CgoivuernseinwthoerkcoMrreasnpuoandl ing lesson notes to carry out ¾ Go through the subtraction in vertical form the teaching. with students. Reiterate the importance of aligning the digits of each number in Learn the correct place value when writing the Word problems (CWB pp. 56–57) subtraction in vertical form. Independent practice (For Print-based Program): Learning Outcomes: • Solve a 2-step word problem involving addition Task 2 requires students to solve a 1-step word problem and subtraction involving subtraction by drawing a part-whole bar • Use a part-whole bar model or a comparison bar model to represent an addition or 1 model. subtraction situation Understand Have students read the wordTask 3 requires students to solve a 1-step word problem Materials: • 1 copy of Create Your Own Worksheet (WS3.2) involving subtraction by drawing a comparison bar per group problem tmhoedenl. articulate in their own words what information is Overview v Blended Learning Programv given and what is unknown. This word problem requires students to apply the skill Pose questions to direct of adding and subtracting numbers within 1000 with From PR1ME Mathematics Interactive Edition: students. regrouping. Go through the word problem using the Let’s Do (CB p. 71) 4-step Understand-Plan-Answer-Check process. Assign the tasks to students as classwork for 44 Chapter 3 formative assessment. Use the corresponding lesson Have st©u2d01e7nScthsorleasaticdEdtuhceatiownoInrtdernpatrioonballe(S)mPteoLntd CWB p. 56 notes to identify the objectives of each task and ISBN 978-981-47-6951-8 address remediation needs. and underline the key information. This helps them understand the word problem and interpret it correctly. 2 Plan 1. Understand the problem. Exercises 12–13 (PB pp. 49–53) – Explain to students that they need to find the Assign the tasks to students as classwork for further Have students plan how to number of belts first before finding the total formative assessment. Use the corresponding lesson solve the problem. Have them number of neckties and belts. notes to identify the objectives of each task and discuss the various strategies address remediation needs. they have learned and choose 2. Plan what to do. one. – Point out to students that they can draw a bar From PR1ME Mathematics Coursework Book: model to help them solve the word problem. Coursework Book Practice 9 (CWB pp. 51–54) 3 Answer Assign all tasks to students as homework. Use the 3. Work out the Answer. following notes to identify the skills needed for each Have students solve the (a) task and address remediation needs. problem using the chosen strategy. – Draw a comparison bar model as shown on Practice 9 (CWB pp. 57–60) CWB p. 56 for part (a). Explain to students that 4 Check the shorter bar represents the number of belts Class practice (For Print-based Program): Have students check their because there are fewer belts than neckties. answer for accuracy or Task 1 requires students to solve a 2-step word problem reasonableness. – Guide students to see that in order to find involving addition and subtraction. Comparison bar Explore other strategies if time the number of belts, they need to subtract. models are provided to guide them. permits. Write the subtraction sentence as well as the subtraction of 67 from 253 in vertical form Remediation © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 on the board. Have a student work out the Task 1(a): Highlight that the juice syrup factory makes difference in the vertical form on the board fewer bottles of apple syrup than orange syrup. Hence and conclude that there are 186 belts. we need to subtract to find the number of bottles of apple syrup it makes in a day. (b) – Draw a comparison bar model as shown on Task 1(b): Highlight that to find the total number of CWB p. 56 for part (b). Point out to students that bottles of syrup the factory makes in a day, we have they have to find the total number of neckties to add the number of bottles of orange syrup and and belts. the number of bottles of apple syrup. – Since the number of neckties and the number of belts are known, students should be able to Teaching tips see that they need to add the two parts to find Task 1 the whole. Write the addition sentence as well as the addition of 253 and 186 in the vertical ¾ Use the 4-step problem solving approach to form on the board. Have a student work out go through the word problem. the sum in the vertical form on the board and conclude that there are 439 neckties and belts ¾ Go through the comparison bar models altogether. with students and highlight that a longer bar means a greater number. 4. Check if your answer is correct. (a) ¾ When working out the answer, remind students to write the addition and subtraction – Guide students to check their answers by sentences clearly. Go through the addition subtracting the answer they get (i.e. 186) from and subtraction in vertical form with students. 253. Point out to students that the value should Reiterate the importance of aligning the digits be the number of fewer belts given in the word of each number in the correct place value problem. when writing the addition or subtraction in vertical form. (b) – Guide students to check their answers by T11 subtracting 186 from the answer they get (i.e. 439). Point out to students that the value should be the number of neckties given in the word problem.

involving addition of three numbers with regrouping in Learning Outcome: hundreds, tens and ones. They can draw a part-whole • Solve a non-routine problem on addition within bar model to help them. 1000 with regrouping using the strategies of guess and check and working backwards For answers, go to CW Manual p. 126. Teaching Concepts and Skills — Problem PosingMaterials: (BM3.1) per student • 1 copy of Mind stretcher Print-based Program Create Your Own tasks provide students wOitvhervaienw opportunity to pose word problems. This improves their uvndBleendrsetdaLenadrniinnggProogrfamwvord problems andrTehliasintpiorconbsuhleilpmcbareetqtwueeiresenspsatudoddseitiniottinsvtaoenkdnaosuwtbtttirhtaeucitndiovneerassendtowards problem solving. Tasks FarormePRc1MoEnMsatthreumcattiecsdIntewracittivhe Edsiptioen:cific confhosartmvre.aTahisnetrsottsnragtetugonidees trinsettarosndtduincsgetodufhdaedreedihntioetnlpsi’nstuvmderetincatastl hematical thinking and compCAresresihganteethYneosutiaroOsknwto.n (CB p. 72) students as classwork. Have them to interpret the information presented and work backwards to make guesses about the missing data complete the task in groups. Facilitate discussions before verifying the validity of their guesses. Go through the prCoobulersmewusoinrkgMthaenu4-asltep Understand-Plan- CuosiunrgsethweorckoMrreasnpuoanlding lesson notes. Have students get into groups. Distribute a copy of Answer-Check process. Create Your Own Worksheet (WS3.2) to each group. WS3.2 Create Your Own Worksheet Have them discuss the problem presented. Ask a student from each group to present the questions they Distribute a copy of Mind stretcher (BM3.1) to each came up with, as well as the answers. student. Have theUmse uthnedgeivrleinnewtohrdeskaenydinnufomrbmearsttioonw.rite This helps them toau) nodneersataddnidtiotnhweoprdropbrolebmlema.nd interpret it correcbtl)y. one subtraction word problem. Then, solve the word problems. – Students should be able to identify ‘Dia’, 1. Understand the problem. Julio ‘Julio’, ‘Andy’ and ‘Yara’ as subjects when – Guide students to sDeiae that thestraemaprse 3 digitgsive away left constructing the word problems, and ‘stamps’, 483 ‘stickers’, ‘game cards’ and ‘erasers’ as ninutmhebefirrsot fntuhmebveesrrttiacickneadrlsf2odrmighiotosfwianmdthdaenityiosenc. ond Andy erasers objects. Highlight to them tYhaarat theregaamree3cadridgsits altogether – The numbers ‘483’, ‘163’ and ‘342’ should be missing. used in the word problems as numerical values to be subtracted from or added to. – Remind students th1a6t3we add ab3u-ydigit numbe3r 42 and a 2-digit number by adding the ones, then – Guide students to see that ‘give away’ and ‘left’ can also be used to construct an addition the tens and lastly, the hundreds. word problem. Similarly, ‘altogether’ and ‘buy’ can be used to construct an addition word – Tell students that addition of the two numbers problem. may involve regrouping. Highlight to them that the digits in the tens place of both numbers are the same. For sample answers, go to CW Manual p. 126. 46 Chapter 3 Scholastic © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 Consolidate Phase 3 Mastery Summative Assessment –– Review Reviews appear after every two or three chapters. Systematic variation of tasks and consolidation of concepts and skills reinforce students’ understanding and assess their ability to interpret144 Teacher'sResources © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 knowledge gained and apply their understanding. Coursework Manual Coursework Manual Assign Reviews as class tests 1. Understand the problem. Review 1 for summative assessment or homework. – Guide students to see thaWt RSo2l.a3nRdehvaies wmo1re cards than David. The objective of each task Materials: is stated in the Coursework Manual, enabling teachers – Exp1.lainWtoritestuthdeennutms bthearst. they need to nd the • 1 copy of Review 1 (WS2.3) per student to identify and address areas of weakness. numbear )oftchraeredtshRoouslaanndd, fniveeehdusndtoregdivaendDtawveindtys-oseven that theby) heaigvhet tthhoeussaanmde, fonuurmhubnedrreodf acnadrdsisx. Task 1 requires students to write a 4-digit number given Answers are provided for all tasks and worked solutions its corresponding number word. are provided for all word problems. 2. Plan mPwooh2ind.atetoltouWato)trdittheoo4e.1tslh9pte8utdnhueemnmtbseutrhns aidntewtrhsoteradyns.cdathnbed) prar7ow0b3a2lebmar Task 1(b) requires students to use zeros as – placeholders when writing the number. and plan the steps to solve the problem. Task 2 requires students to read a 4-digit number and 3. Write the numbers. write the corresponding number word. 3. Work out thae) An20s0w0e+r.400 + 10 = _____ Task 3 requires students to identify the value of each – Guide sbt)ud5e9n03ts=to50d00ra+w90t0h+e_c__o_m_ parison bar model as shown on Mind stretcher (BM2.1) on digit in a 4-digit number and complete the expanded the4.boaFirlldin. the blanks. form of the number. – Explainat)o sIntu1d3e59n,ttshtehdaigt istin1 ciseinRthoela_n__d__hpalas cmeo. re cards thb)anInD6a4v0i7d, ,thReodlaignitd__w__il_l hisainvtehetotegnisvpelace. some ocf)hisInc9a8r2d0,stthoe Ddiagvitid8 hinasoardvealrufeoor fth__e_m__.to Task 4 requires students to identify the digit of a place value in each 4-digit number, and the value of that have the same number of cards. digit. – Gu5i.de sFtilul idn ethnetsctirocleses ewithha>toirn<o. rder for the both of thema)to2h1a73ve th2e20s4ame numb)be4r0o35f car4d3s5, Task 5 requires students to use the ‘<’ and ‘>’ symbols Rolandch) as67to35sha6re75h3is excessdc) ar8d29s2with8294 to compare two numbers. David equally. – Usi6n.g thAerracnogme pthaerinsuomnbbearsrinmoorddeerl.,Bheiggihnlwigihtht tthoe smallest. Task 6 requires students to compare and order four students that they need to rst nd how many 4-digit numbers. more car3d6s47Roland h37a4s6than Da3v46id7. Then, 3th67e4y have to halve the difference to nd how many Task 7 requires students to count on or back in steps ca7r.ds RCoolamnpdlestehothueldnugmivbeertopaDttaevrnids.. of 1, 10, 100 or 1000 to complete the number patterns. – Guide sat)ud2e2n45ts, _to___s_u,b_t_r_a__c,t5426456,962fr4o5m, 72446587 in the verbtic) a7l 7fo02rm, 7.70T1h,e_n__, _g_u, i_d_e__t_h,e7m698t,o76d9iv7ide Task 8 requires students to associate the term ‘sum’ the diffce)ren19c5e3,b1y9623,a1n97d3,c1o9n83c,lu__d_e__t,h__a_t__Roland with addition and the term ‘difference’ with needs tdo) g4iv6e019, _c__a_r_d, s48to01D, 4a9v01id, ._____, 5101 subtraction. 4. Check if your answer is correct. Task 9 requires students to add or subtract with or – Have students nd the number of cards without regrouping. Roland and David each has in the end. – Lead students to conclude that since 4687 – 9 Task 10 requires students to solve a 1-step word = 4678 and 4669 + 9 = 4678, both Roland and problem involving subtraction. David have the same number of cards.© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6953-2 So, the answer is correct. Answers 175 Task 11 requires students to solve a 1-step word problem involving addition. T12 Reiterate the following points: Task 12 requires students to solve a 2-step word – We add to nd the sum of two numbers. problem involving addition. – We subtract to nd the difference between two numbers. Task 13 requires students to solve a 2-step word – We regroup if necessary when adding to or problem involving addition and subtraction. subtracting from a 4-digit number. – We can draw part-whole or comparison bar Task 14 requires students to solve a 2-step word models to solve addition and subtraction problem. Depending on the method chosen, students word problems. © 2017mSacyhuosleasotinclyEsduubctraatciotinonInoter urnseatbioonthala(dS)dPittioenLatdndISBN 978-981-47-6955-6 subtraction to solve the word problem. For answers, go to CW Manual pp. 149–150.

Summative Assessment –– Extended Learning Print-based Program Mind stretcher tasks are non-routine and are designed to develop higher order thinking skills. New problem solving strategies are also introduced. Coursework Manual Coursework Manual BM3.1 Mind stretcher 2 LIonodkeaptethnedetennts.practice (For Print-based Program): 2. Plan what to do. – Point out to students that they can make a Learn 9–1=8 1+ + =9 v Blended Learning Programv guess for each of the missing digits before checking if the numbers add up to 990. Adele wants to add two numbers. 4Ta+s4k=28requires students to solve a 2-step word problem From PR1ME Mathematics Interactive Edition: Reiterate the following po The digits in the tens place are the same. ci+nov8molvp144iangri55soanddbiatior mn aonddelss.ubtraction by drawing Practice 3 (CB p. 72) 3. Work out the Answer. – We can add or su Fill in the missing digits and find the two numbers. 8 Assign the tasks to students as classwork for – Highlight to students that to add a 3-digit with regrouping. +5 summative assessment. Use the corresponding lesson number and a 2-digit number, they have to – We can use a par Tas9k 39re0quires students to solve a 2-step word problem notes to identify the objectives of each task and first add the ones, before adding the tens, and comparison bar m 990 involving addition and subtraction by drawing a part- address remediation needs. lastly the hundreds. addition and subt 3 Lwoohkoalet tbhaerhmunoddreedl.s. 1 Understand How many digits are there in each 4 Check v Blended Learning Programv Guess 1 the problem. of the two numbers? Did you answer TaL8es+tk’0s 4gisonreobtaqecuqkiurteoalsSttosetp9u.2d. ents to solve a 2-step word problem – Guide students to see that they cannot add How many digits are missing? the question? involving addition and subtraction by drawing a From PR1ME Mathematics Interactive Edition: 2 Plan what to do. How do I add a 3-digit number Is your answer comparison model. Mind stretcher (CB pp. 73–74) a number to 5 and get 0, but they can add 5 and a 2-digit number? correct? Go through the problem with students. Use the and 5 to get 10. Do I need to regroup? GueTasssk2 5 requires students to solve a 1-step word problem detailed lesson plan given in the corresponding – Write the digits and the regrouping of ones in 3 Work out the 2 Linovook lavtinthgeatednds.ition o1f+three+num=b9er7s with regrouping in lesson notes to carry out the teaching. the vertical form as shown. I can guess and check and Answer. 1t9en– s1a=n1d8 ones. – Guide students to add the tens next. Bring to work backwards. 9to+ h9e=lp18them. They1 +can d+raw a= 1p9a3rt-whole bar model Learn their attention that the digits in the tens place 4 Check Regroup the tens. Mind stretcher are the same. Since 4 and 4 make 8, the Did you answer 11 missing digits are 4 and 4. 3 Work out the the question? Learning Outcome: – Write the digits in the tens place of the vertical Answer. To add a 3-digit number and a Is your answer Tas8k 69re5quires students to solve a 2-step word problem • Solve a non-routine problem on addition within form as shown. 2-digit number, first add the ones. correct? i+nvolv9ing5addition and subtraction by drawing a 1000 with regrouping using the strategies of Then, add the tens. guess and check and working backwards 4. Check if your answer is correct. Lastly, add the hundreds. co9mp9ari0son model. – Guide students to look at the hundreds. Materials: Highlight to them that since 8 + 0 does not Guess 1 3 LToaoskka7t rtehequhuirnedsrsetdusd. ents to solve a 1-step word problem • 1 copy of Mind stretcher (BM3.1) per student equal 9, they have to go back to Step 2 and 1ihn+uvn8odlv=rien9dgsa, tdednistioanndofotnheres.eThneuymcbaenrsdwraithwreagproaurtp-winhgoilne make another guess. 1 Look at the ones. Thebtawromnuomdbeel rtsoahree8lp95thaendm9.5. 3. Work out the Answer. 5 + 5 = 10 +5=0 7 + 5 = 10 3 89F5o+r9a5 n= s9w90ers, go to CW Manual p. 126. 1 Regroup the ones. Both numbers have the same 85 digit in the tens place. My answer is correct. +5 990 v Blended Learning Programv Overview Guess 2 This problem requires students to know the inverse – Guide students to look at the tens. Remind 1. Understand 2. Plan F3.roAnmswePr R1M4E. MCheactkhematics Interactive Edition: relationship between addition and subtraction and have a strong understanding of addition in vertical them that 1 ten was regrouped from 10 ones. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 Teacher's Resources 141 142 Teacher's Resources Create Your Own (CB p. 72) form. The strategies introduced here help students Highlight to them that the second guess is that Assign the task to students as classwork. Have them© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 to interpret the information presented and work the values of the two missing digits and the digit backwards to make guesses about the missing data 1 from the ten that was regrouped add up to 1. Understanducsotinmhgeptlhepeteroctobhrerleetsampsok.nindginrgoulepsss.oFnancoilitteast.e discussions 19. Hence, the missing digits are 9 and 9. – Guide students to see that Roland has more befRoerevvieeriwfyin1g the validity of their guesses. Go – Write the digits and the regrouping of tens in the vertical form. Guide students through the cards tHhaavensDtuadevnidts.get into groups. Distribute a copy of through the problem using the 4-step Understand-Plan- addition and the regrouping of 19 tens into – ExplainCrteoatsetuYdouernOtws nthWaotrktshheeytn(WeSe3d.2)ttoo enacdhtghroeup. 1 hundred 9 tens. AnsMwaert-eCrhieaclsk:process. numbeHraovef tchaemrddsisRcouslsatnhedpnroebeledms ptoresgeinvteedD. Aasvk iad so that thscetauymdehenaut vpfreowmitthhe,eaacsshawgmerloleauspntthuoemparbenssewernetorstf.hecaqurdesst.ions they Distribut•e a c1opcyoopf yMiondf Rsterevtciehewr (1BM(W3.1S)2to.3e)apceh r student – Bring their attention to the hundreds and highlight that since 1 + 8 = 9, the two numbers student. Have them underline the key information. are 895 and 95. TinhtiesTrhaperselkpts1itthcreeomrqreutcoitrlueyn.sdsetrustdanedntthsetoprowbrleitme aand4-digit number given its corresponding number word. 4. Check if your answer is correct. Scholastic 2. Plan what to d– o.Students should be able to identify ‘Dia’, 1. UTnadsekrs1ta(nbd)trheeqpuroirbelesms.tudents to use zeros as – Have students add 895 and 95 using the – Point out thoesc‘‘lpJstotuuicnltdioskhte’ere,urns‘cmA’,ttnis‘ngdugtayhnt’mahdaeetenwcdtrhsao‘teYrraddaysnrp’acdar’oanabtdhnslese‘muedbrpsra,ajesraeocwnrtbsds’awla‘eshstbmaeamnrps’, p– lacGeuhidoeldstuedrsenwtshtoensewe trhitaint gthethreeanreu3mdbigeitsr. vertical form. Have a student work out the sum model to on the board. in the first number and 2 digits in the second – Guide them to see that 895 + 95 = 990. Highlight number of the vertical form of addition. and plan theobsjteecptss. to solve the problem. TaskH2ighreligqhut tiroetshestmudtheant tthsetroe arerea3ddaigit4s-digit number antdo them that since the digits in the tens place, 9, are the same, the answer is correct. – The numbers ‘483’, ‘163’ and ‘342’ should be writemitshsineg.corresponding number word. 3. Work out the Anstuwosebeder.insutbhterawcoterdd problems as numerical values – Remind students that we add a 3-digit number from or added to. – Guide stu–deGnutsidteostdudraewntstthoeseceothmatp‘gaivriesoanwabya’ ar nd Taskath3nedrteeanq2s-udaiinrgeditslnasusttmulydb, teehrenbthysuantdoddreiidndges.tnhteifoyntehs,ethveanlue of each model as sho‘lewftn’ coann aMlsoinbdesutsreedtctohceorn(sBtrMuc2t .a1n)aodndition d– igitTeinll staud4e-ndtsigthitant audmdbitioenr oafnthde ctwoomnupmlebteersthe expanded – Ethxeplbaoinatrod.stupwcdaroonerbdnblepetmsrou.tbsheledamtto.sSicnimocnilaestrrlyuR,co‘talaaltnongadedthdhieatiros’namwndoorr‘debuy’ cards than David, Roland will have to give formmoayf itnhveolvneuremgbroeupr.ing. Highlight to them that the digits in the tens place of both numbers are some oFforhsiasmcpalerdasnstwoeDrs,agvoidtoinCWorMdaenrufaol rp.th12e6m. to the same. Task 4 requires students to identify the digit of a place value in each 4-digit number, and the value of that have the same number of cards. digit. – Guide students to see that in order for the both of them to have the same number of cards, Task 5 requires students to use the ‘<’ and ‘>’ symbols Roland has to share his excess cards with to compare two numbers. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 David 4e6quCahlalypt.er 3 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 – Using the comparison bar model, highlight to Task 6 requires students to compare and order four students that they need to rst nd how many 4-digit numbers. Wrapping Up the Chapter more cards Roland has than David. Then, they Task 7 requires students to count on or back in steps have to halve the difference to nd how many of 1, 10, 100 or 1000 to complete the number patterns. cards Roland should give to David. – Guide students to subtract 4669 from 4687 in Ending the chapter by summarizing the key learning points helps students realize how muchthe vertical form. Then, guide them to divide the difference by 2 and conclude that Roland Task 8 requires students to associate the term ‘sum’ with addition and the term ‘difference’ with learning has taken place. This helpsneetdhs teo gmive 9organizecards to David. the informsubtaracttiioon.n into a meaningful context in their minds and ensures learning is solidified for future lessons. This is a crucial step to help4. Check if your answer is correct. students – Have students nd the number of cards Task 9 requires students to add or subtract with or without regrouping. remember and apply the information they have learned.Roland and David each has in the end. Task 10 requires students to solve a 1-step word – Lead students to conclude that since 4687 – 9 = 4678 and 4669 + 9 = 4678, both Roland and problem involving subtraction. David have the same number of cards. CoursewSoo, rtkheManasnwueraisl correct. Task 11 requires students to solve a 1-step word problem involving addition. Reiterate the following points: Task 12 requires students to solve a 2-step word – We add to nd the sum of two numbers. problem involving addition. – We subtract to nd the difference between two numbers. Task 13 requires students to solve a 2-step word – We regroup if necessary when adding to or problem involving addition and subtraction. subtracting from a 4-digit number. – We can draw part-whole or comparison bar Task 14 requires students to solve a 2-step word models to solve addition and subtraction problem. Depending on the method chosen, students word problems. may use only subtraction or use both addition and subtraction to solve the word problem. For answers, go to CW Manual pp. 149–150. ™ Blended Learning Program™ From PR1ME Mathematics Interactive Edition: Review 1 (PB pp. 35–40) Assign the tasks to students as classwork for summative assessment. Use the objectives and chapter references given for each task in the corresponding lesson notes to address remediation needs. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6953-2 Chapter 2 39 © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T13

Blended Learning Program T14 Instructional Design Scholastic TM Mathematics (Philippine Edition) is designed on a pedagogical model that ensures teaching and learning are effective, measurable and diagnostic. Each chapter of the Coursework Book involves three phases of learning: readiness, engagement and mastery. A simple model of the instructional design is presented below. ScholasticPhase 2: Engagement Phase 3: Mastery P hase 1: Readiness * * Let’s Remember (Coursebook) offers an Practice* * * Practice Book opportunity for * Practice Book Learn Practice ChapterWrap-up systematic recall Review and assessment of Exercises prior knowledge © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 in preparation for Let’s Learn introduces new concepts Coursework Book Coursebook Chapter Wrap-up Practice new learning. and builds on concepts and skills at the end of the Book Reviews learned previously. Learn and Practice Practice after chapter summarizes provide each lesson the key learning summative Let’s Do and Practice Book provide opportunities provides points of the assessment and Exercises provide formative for home revision and opportunities chapter. consolidation of assessment. independent practice. for summative concepts and assessment. skills learned across various topics. *Found in the Interactive Edition Using the Coursework Manual • answers for tasks, with worked solutions for all word problems • photocopiables for class activities This Coursework Manual includes: • Developmental Continuum for all six years/grades • detailed Scheme of Work • lesson plans

Plan Blended Learning Program The Developmental Continuum offers the overall plan for learning outcomes over the six-year course. Teachers can refer to this to understand the scope of teaching that takes place at each Developmental Continuumyear/grade. Coursework Manual Year/Grade 1 Year/Grade 2 Year/Grade 3 NUMBERS AND NUMBER SENSE Whole Numbers / Count within 100. Count within 1000. Read and write a number Place Value within 10 000 — the numeral and the corresponding number word. Read and write a number Read and write a number Use number notation and from 0 to 100 — the numeral from 0 to 1000 — the numeral place values (thousands, and the corresponding and the corresponding hundreds, tens, ones). number word. number word. Count on and backwards Use number notation and Compare and order The Scheme of Work preceding ewiathcin h100c. hapter is desiptgelanncs,eeovdnaelsut)e.os (ahusnsdisretdisn, plannunminbegrs wthithein 1c0u00rr0i.culum for the entire year and to prepare for teaching individual chapters. Use number notation and Compare and order Find the number which is 1, place values (tens, ones). numbers within 1000. 10, 100 or 1000 more than Each book(sopr leassntsha1n)sea mgiveenster Coursework Manual comprisingnaumbboeur wt i9th0inh10o0u0r0s. of Estimate the number of Use the symbols i‘n>’starnudc‘<ti’on. IdTeenatifcyhodedrsacndaenveandjust aSennsdetohbSajuencb1t0tsr0ianocabtjgeiorcotnus.pwoiftfhewReer grofuorpcionmgparison otfhneumdbuerrsa. tionnusmbbearss.ed on the Chapter 3: Addition school calendar and the pace Strand: Numbers and Number Total Duration: 14 h 40 min Scheme of Work Scholastic Compare the number of F1i0ndorth10e0nmumorbeetrhinwadnhic(ivohridilseu1ss,al coNlraadmisnseaelans.upmosbiteiornfruosming1statno of objects in two or more sets. than) a given number within 100th. Blended Learnin1g0P0ro0g.ram Print-based Program Lesson Learning Outcomes Vocabulary Compare and ordeMr aterials ReadReswouhrcoelse numbersMwateitrhiailns IdentiRfeysoaunrcdes use the pattern numbers within 100. 1•00C0B po. n41 a numb•e1r clionpey.of Let’s of naming ordinal numbers Let’s • Add within 1000 without Remember (40 min) regrouping and use a part- Remember from 1st to 100th Worksheet (WS3.1) whole bar model to represent an addition situation per student • Subtract within 1000 without Find the number which is Name a position using an Identify the position of an regrouping and use a part- 1 or 10 more than (or less whole bar model to represent ordinal number from 1st to object from a given point of a subtraction situation than) a given number 20th. reference. within 100. • Solve a 1-step word problem involving subtraction and use a comparison bar model to represent a subtraction Make a number story to Identify and use the pattern situation illustrate a number bond for of naming ordinal numbers Lesson 1: Addition with Regrouping 5 to 10. from 1st to 20th 6h Adding with • Add within 1000 with Write a numbe•r bBaosne dtenfoblroc5ks • CB pp. 42–44 • Base ten blocks • CWB pp. 36–37 to 10. • PB pp. 31–32 regrouping regrouping in ones • CWB pp. 36–37 in ones Adding with • Add within 1000 with Name a position using an • CB pp. 45–47 • CWB pp. 38–39 ordinal number from 1st to • PB pp. 33–34 regrouping regrouping in tens • CWB pp. 38–39 • CWB pp. 40–42 in tens Associate the terms ‘sum’ and ‘difference’ with Adding with • Add within 1000 with 10th and position words. • CB pp. 48–51 addition and subtraction respectively. regrouping regrouping in tens and ones • PB pp. 35–39 in tens andAddition / Subtraction ones Use picture cutouts (or other O• bCsWeBrvpep. 4a0n–4d2 apply the mthaenmipeualantiinvgess)Motfoaaidlltudesittrriaioatnels identity, commutative and A listing of objectives and list associative properties of resources for each lesson makes planning quick and easy. and subtraction. addition. Resources list Key mathematicalMake a number story CB: CoursebookAdd or subtract within 1000. Add or subtract within© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 Use a parPt-Bw:hPorlaecbtaicremBoodoekl 10 000. for a given addition or subtractetiormn sesntence. or a compCaWrisBo:nCboaurrmseowdoelrk Book to represent an addition or subtraction situation. Each chapter begins with Note fWorriteTaenaucmhbeer rsesn.teTnhcies foidr eSnotlvifeieups ttoh2e-stekpewyordmatheUsme aaptaicrt-awhl oidle ebaar ms oodfelthe chapter. a given situation involving problems involving addition or a comparison bar model addition or subtraction. and subtracCtioonu.rsework to represent an addition or Manual subtraction situation. Note for Teachers Chapter 3 Learn In this chapter, students will progress to addition Addition and Subtraction Adding with regrouping in ones (CWB p. 36) and subtraction of 3-digit numbers with with Regrouping regrouping. Students can draw part-whole or© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 Learning Outcome: comparison bar models to help them solve Chapter Overview • Add within 1000 with regrouping in ones addition and subtraction word problems. Let’s Remember Lesson 1: Addition with Regrouping Materials: © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 Lesson 2: Subtraction with Regrouping • Base ten blocks Lesson 3: Problem Solving Stage: Concrete Experience Note for Teachers Begin by using base ten blocks to demonstrate the In this chapter, students will progress to addition addition of 426 and 146. This allows students to have and subtraction of 3-digit numbers with regrouping. a concrete experience of the regrouping that takes Students can draw part-whole or comparison bar place in the ones place during the addition process. models to help them solve addition and subtraction It also reinforces the concept of addition as putting word problems. together. Grouping the unit cubes together first, followed by the ten-rods and lastly the hundred- Recall Prior Knowledge T23squares, introduces students to the process of adding the ones first, followed by the tens and lastly the hundreds. v Blended Learning Programv – Distribute base ten blocks to students and have T15 them follow each step of your demonstration. From PR1ME Mathematics Interactive Edition: Let’s Remember (CB p. 41) – Use 4 hundred-squares, 2 ten-rods and 6 unit Assign the tasks to students as classwork to cubes to represent 426. Use 1 hundred-square, identify gaps in students’ understanding. Use the 4 ten-rods and 6 unit cubes to represent 146. objectives and chapter references given for each task in the corresponding lesson notes to address – Group the unit cubes together. Have students remediation needs. see that there are 12 unit cubes in all. Guide them to see that since 10 ones = 1 ten, we Distribute a copy of Let’s Remember Worksheet (WS3.1) combine 10 of the unit cubes to form a ten-rod to each student. Have students attempt the worksheet and place it together with the rest of the ten- to help them recall these previously acquired related rods. Have students see that there are 2 unit knowledge: cubes left after the regrouping exercise. • Add within 1000 without regrouping and use a – Group the ten-rods together and have students part-whole bar model to represent an addition see that there are 7 ten-rods in all. situation (CWB 2A Chapter 2) – Group the hundred-squares together and have • Subtract within 1000 without regrouping and students see that there are 5 hundred-squares use a part-whole bar model to represent a in all. subtraction situation (CWB 2A Chapter 2) – Lead students to see that 5 hundred-squares, • Solve a 1-step word problem involving 7 ten-rods and 2 unit cubes represent 572. subtraction and use a comparison bar model Hence, the sum of 426 and 146 is 572. to represent a subtraction situation (CWB 2A Chapter 2) Stage: Pictorial Representation Follow up by relating the base ten blocks activity to For answers, go to CW Manual p. 126. the tables of the base ten blocks on CWB p. 36. This helps students to transit from concrete experience to Lesson 1: Addition with Regrouping pictorial representation. The first row of blocks in the table represents the augend, the second row of blocks Duration: 6 h represents the addend and the final row represents the sum. This presentation parallels the addition of numbers v Blended Learning Programv in vertical form. It aids the transition from pictorial representation to abstract representation later on. From PR1ME Mathematics Interactive Edition: Let’s Learn (CB pp. 42–43) – Refer students to the table of the base ten Go through the teaching examples with students for blocks on CWB p. 36. Draw their attention to the columns with the unit cubes and highlight the regrouping of the unit cubes. Relate it back to the combining of 10 unit cubes to form a ten-rod. Show students the final number

Teach Phase 1 Readiness Checking for Prior Knowledge Let’s Remember is a recall feature to identify students at risk before a new concept is introduced. If students are not able to answer the tasks in Let’s Remember correctly, teachers may use the objective of each task to identify gaps in their understanding and refer to the chapter reference for remediation. Coursework Manual Blended Learning Program Chapter 3 Learn Scholastic Addition and Subtraction Adding with regrouping in ones (CWB p. 36) with Regrouping Learning Outcome: Chapter Overview • Add within 1000 with regrouping in ones Let’s Remember Lesson 1: Addition with Regrouping Materials: Lesson 2: Subtraction with Regrouping • Base ten blocks Lesson 3: Problem Solving Stage: Concrete Experience Note for Teachers Begin by using base ten blocks to demonstrate the In this chapter, students will progress to addition addition of 426 and 146. This allows students to have and subtraction of 3-digit numbers with regrouping. a concrete experience of the regrouping that takes Students can draw part-whole or comparison bar place in the ones place during the addition process. models to help them solve addition and subtraction It also reinforces the concept of addition as putting word problems. together. Grouping the unit cubes together first, followed by the ten-rods and lastly the hundred- Recall Prior Knowledge squares, introduces students to the process of adding the ones first, followed by the tens and lastly the hundreds. Instructions in grey boxes v Blended Learning Programv – Distribute base ten blocks to students and have throughout the Coursework them follow each step of your demonstration. Manual are for teachers using From PR1ME Mathematics Interactive Edition: the Blended Learning Program. Let’s Remember (CB p. 41) – Use 4 hundred-squares, 2 ten-rods and 6 unit Assign the tasks to students as classwork to cubes to represent 426. Use 1 hundred-square, Interactive Edition identify gaps in students’ understanding. Use the 4 ten-rods and 6 unit cubes to represent 146. objectives and chapter references given for each task in the corresponding lesson notes to address – Group the unit cubes together. Have students remediation needs. see that there are 12 unit cubes in all. Guide them to see that since 10 ones = 1 ten, we Distribute a copy of Let’s Remember Worksheet (WS3.1) combine 10 of the unit cubes to form a ten-rod to each student. Have students attempt the worksheet and place it together with the rest of the ten- to help them recall these previously acquired related rods. Have students see that there are 2 unit knowledge: cubes left after the regrouping exercise. • Add within 1000 without regrouping and use a – Group the ten-rods together and have students part-whole bar model to represent an addition see that there are 7 ten-rods in all. situation (CWB 2A Chapter 2) – Group the hundred-squares together and have • Subtract within 1000 without regrouping and students see that there are 5 hundred-squares use a part-whole bar model to represent a in all. subtraction situation (CWB 2A Chapter 2) – Lead students to see that 5 hundred-squares, • Solve a 1-step word problem involving 7 ten-rods and 2 unit cubes represent 572. subtraction and use a comparison bar model Hence, the sum of 426 and 146 is 572. to represent a subtraction situation (CWB 2A Chapter 2) Stage: Pictorial Representation Follow up by relating the base ten blocks activity to For answers, go to CW Manual p. 126. the tables of the base ten blocks on CWB p. 36. This helps students to transit from concrete experience to Lesson 1: Addition with Regrouping pictorial representation. The first row of blocks in the table represents the augend, the second row of blocks Duration: 6 h represents the addend and the final row represents the sum. This presentation parallels the addition of numbers v Blended Learning Programv in vertical form. It aids the transition from pictorial representation to abstract representation later on. From PR1ME Mathematics Interactive Edition: Let’s Learn (CB pp. 42–43) – Refer students to the table of the base ten Go through the teaching examples with students for concept development. Use the detailed lesson plan Clicking on the ‘Lessonblocks on CWB p. 36. Draw their attention to given in the corresponding lesson notes to carry out the teaching. the columns with the unit cubes and highlight the regroNupoingteofsth’etuanitbcudbeisr.eReclattesitteachers to the corresponding pageback to the combining of 10 unit cubes to form a ten-rod. Show students the final number in the Teacher’s Guide.of unit cubes in the last row and reiterate that after regrouping the ones, there are 2 ones left. Teachers are 30 Chapter 3 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 directed to the corresponding page in the Interactive Edition of the Coursebook. T16 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Phase 2 Engagement Blended Learning Program Teaching Concepts and Skills –– Developing Conceptual Understanding Scholastic Each chapter is taught over several lessons, with each lesson focusing on a concept or part of it. The lesson is designed with a two-part structure of concept introduction, and guided with practice and formative assessment. Each concept is taught using the three-stage Concrete-Pictorial-Abstract approach to develop deep conceptual understanding. Interactive Edition Begin a lesson by walking students through the list of learning objectives in the ‘You will learn to…’ box to encourage self-directed learning. Start Let’s Learn with a hands-on activity. This is the concrete stage of the learning journey. Students may be required to work individually or in groups. Teachers are encouraged to verbalize the content in the speech bubbles in the Coursebook to guide students’ thought processes. In the pictorial stage, guide students to represent mathematical ideas visually. Ensure that each student has progressed successfully to this stage before introducing abstract representation. This middle stage is a crucial link between the concrete experience and the abstract representation and serves to build a solid foundation. Once conceptual understanding is developed, progress to the abstract stage. The concept or skill is represented using only numbers and mathematical symbols. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T17

Use the Coursework Book to complement the teaching in class. Examples presented for each Learn correspond to each Let’s Learn and provide students with further opportunities for home revision. Blended Learning Program Interactive Edition Coursework Book Scholastic Addition and Subtraction with Regrouping Lesson 1 Addition with Regrouping Learning Outcomes: • Add within 1000 with regrouping in the ones and tens places • Solve 1-step word problems Adding with regrouping in ones Learn Add 426 and 146. 426 146 572 1 Add the ones. 2 Add the tens. 3 Add the hundreds. H TO H TO H TO 1 1 1 42 6 42 6 42 6 +1 4 6 +1 4 6 +1 4 6 2 72 5 72 6 ones + 6 ones = 12 ones 10 ones = 1 ten 12 ones = 1 ten 2 ones We regroup 12 ones into 1 ten 2 ones. 426 + 146 = 572 36 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6939-6 Teaching Concepts and Skills — Formative Assessment There are opportunities for formative assessment within each lesson and across chapters. Let’s Do reinforces students’ learning through guided and systematically varied tasks. A link in the Interactive Edition leads students to the corresponding Exercises for more formative assessment. Interactive Edition After a concept is taught in Let’s Learn, assign Let’s Do tasks as class work. Discuss students’ responses and remediate if necessary. The objective of each Let’s Do task is stated in the Teacher’s Guide, enabling teachers to check learning. Answers are provided for all tasks. Interactive Edition To further reinforce and assess understanding, assign Exercises as homework. The objective and skills of each task are stated in the Lesson Notes enabling teachers to check learning and address remediation needs. T18 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

address remediation needs. Stage: Abstract Representation Exercise 1 (PB pp. 31–32) Lastly, present the addition in vertical form. Having Assign the tasks to students as classwork for further gone through the previous stages, students will formative assessment. Use the corresponding lesson see how the algorithm relates to the pictorial notes to identify the objectives of each task and representation. This association is important as it helps address remediation needs. students to visualize the addition. It allows them to understand and interpret the vertical form, especially the writing of digits above the augend in the vertical Practice in the Coursework Book provides students with further opportunities for home practice.form when regrouping occurs. This is an anchor for learning addition with regrouping in other place Assign all the tasks in Practice to students as homework.values, as well as more advanced forms of regrouping that involve more than one place value. The three- From PR1ME Mathematics Coursework Book: Blended Learning Program Coursework Book Practice 1 (CWB p. 31) Assign all tasks to students as homework. Use the following notes to identify the skills needed for each task and address remediation needs. step approach (add the ones, then the tens and lastly When necessary, the hundreds) guides students to add systematically, to address remediation refer to the teaching tips in the Coursework Manualreducing the likelihood of careless mistakes when they are performing the addition in vertical form. Practice 1 (CWB p. 37) needs. Class practice (For Print-based Program): – Write the vertical form of ‘426 + 146’ on the board. First, guide students to add the ones. Task 1 requires students to add a 3-digit number and Have them look at the digits in the ones place a 1-digit, 2-digit or 3-digit number, with regrouping in Coursework Book in the vertical form of addition. Students should ones. The place values are provided in the vertical be able to state that 6 ones + 6 ones = 12 ones. formCoofuardsdeitwionotrokgMuidaenstuuadel nts. – Reiterate that 12 ones can be regrouped into 1 ten 2 ones. Relate the regrouping back to Remediation Practices1 the pictorial representation on the page. Have Task 1(a): Reteach adding a 1-digit number and students look at the columns with the unit a 2-digit number with regrouping in ones. Then, go 1. Add. cubes. Write the addition of the ones in the through Task 1(a). Highlight that 3 ones + 7 ones = vertical form of addition on the board. 10 ones, which can be regrouped into 1 ten. Start by adding the on–es. Then, guide students to add the tens by having 1 ten + 5 tens = 6 tens. Therefore, 353 + 7 = 360. Regroup if necessary. them look at the digits in the tens place in the vertical form of addition. Again, relate 1 ten Task 1(b): Reteach adding a 2-digit number and a a) H T O b) H T O + 2 tecn)s + 4 HtenTs O= 7 tens back to the pictorial 2-digit number with regrouping in ones. Then, go croeofptluhremesentensnt+wasitti14nihontt60hhbee48yvteheanrt-vircionadgl sf.sotWurmdriteoenfttahs delodaoitkdiodanittiotohnne through Task 1(b). Highlight that 6 ones + 8 ones 353 646 = 14 ones, which can be regrouped into 1 ten 4 ones. +7 + 38 1 ten + 4 tens + 3 tens = 8 tens. Therefore, 646 + 38 = the board. 684. – Finally, guide students to add the hundreds by having them look at the digits in the hundreds Task 1(c): Reteach adding a 3-digit number and a 2. Add. place in the vertical form of addition. Again, 3-digit number with regrouping in ones, using smaller relate 4 hundreds + 1 hundred = 5 hundreds numbers e.g. 119 + 123. Then, go through Task 1(c). a) 1 3 8 b) 2 7 5 backct)o the 3pic0to6rial representation by having Highlight that 4 ones + 8 ones = 12 ones, which can be +5 + 19 students Wlo+orit4kea5tthte6headcdoiltuiomnnosfwthiteh the hundred- regrouped into 1 ten 2 ones. 1 ten + 6 tens = 7 tens. squares. hundreds in 4 hundreds + 1 hundred = 5 hundreds. Therefore, the vertical form of addition on the board. 404 + 168 = 572. – To conclude, write the addition sentence ‘426 + 146 = 572’ on the board. 3. Add. – Reiterate that we add the ones first, followed Teaching tips a) 436 + 55 = by the tens, then the hundreds. Task 1 b) 67 + 617 = ¾ When reteaching, follow the same procedure as the example in Learn (CWB p. 36). Use base ten blocks to introduce the concept of regrouping. Then, continue with the addition in vertical form. c) 358 + 424 = d) 249 + 536 = © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 Chapter 3 31 Scholastic To address common misconceptions and errors and strengthen mathematical thinking, have students discuss, communicate, reason and justify mathematical ideas and understanding using©2017ScholasticEducationInternational(S)PteLtd ISBN978-981-47-6939-6 37 scenarios found in the Think About It feature. Interactive Edition Have students form groups to discuss the question. Ask a representative from each group to present and justify the group’s response. Lesson notes are provided to facilitate discussions and guide students to arrive at the correct conclusion. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T19

Blended Learning ProgramTeaching Concepts and Skills –– Developing Processes and Strategies Scholastic A problem solving lesson at the end of the chapter consolidates learning. Focus on both the process and the strategies required to solve the problems. Consistently apply the four-step Understand-Plan-Answer-Check process to build good habits for approaching mathematical problems of any difficulty. Refer to the problem-solving process page at the back of the Coursework Book. Interactive Edition 1 Understand Have students read the word problem then articulate in their own words what information is given and what is unknown. Pose questions to direct students. 2 Plan Have students plan how to solve the problem. Have them discuss the various strategies they have learned and choose one. 3 Answer Have students solve the problem using the chosen strategy. 4 Check Have students check their answer for accuracy or reasonableness. Explore other strategies if time permits. Teaching Concepts and Skills — Problem Posing Create Your Own tasks provide students with an opportunity to pose word problems. This improves their understanding of word problems and inculcates positive attitudes towards problem solving. Tasks are constructed with specific constraints to test students’ mathematical thinking and comprehension. Interactive Edition T20 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Consolidate Blended Learning Program Phase 3 Mastery Summative Assessment –– Practice and Review Practice tasks at the end of each lesson consolidate the learning for the lesson. Tasks are systematically varied to reinforce students’ understanding. Interactive Edition Assign Practices as homework and summative assessment. The objective of each task is stated in the Lesson Notes, enabling teachers to check learning and address remediation needs. Answers are provided for Practice tasks in the Coursebook and Exercises in the Practice Book. Worked solutions are provided for all word problems. Scholastic Reviews appear after every two or three chapters. Systematic variation of tasks and consolidation of concepts and skills reinforce students’ understanding and assess their ability to interpret knowledge gained and apply their understanding. Interactive Edition Assign Reviews as class tests for summative assessment or homework. The objective of each task is stated in the Lesson Notes, enabling teachers to identify and address areas of weakness. Chapter references make it easy for teachers to access remediation resources. Answers are provided for all tasks and worked solutions are provided for all word problems. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T21

Summative Assessment –– Extended Learning Mind stretcher tasks are non-routine and are designed to develop higher order thinking skills. New problem solving strategies are also introduced. Interactive Edition Blended Learning Program Assign Mind stretcher Scholastictasks to on-level and above-level students. Help them see that the same four-step Understand- Plan-Answer-Check process can be applied to problems of any difficulty or context. 1. Understand the problem. Review 1 – Guide students to see that Roland has more cards than David. Materials: – Explain to students that they need to nd the • 1 copy of Review 1 (WS2.3) per student number of cards Roland needs to give David so that they have the same number of cards. Task 1 requires students to write a 4-digit number given its corresponding number word. 2. Plan what to do. Task 1(b) requires students to use zeros as – Point out to students that they can draw a bar placeholders when writing the number. model to help them understand the problem and plan the steps to solve the problem. Task 2 requires students to read a 4-digit number and write the corresponding number word. 3. Work out the Answer. – Guide students to draw the comparison bar Task 3 requires students to identify the value of each model as shown on Mind stretcher (BM2.1) on digit in a 4-digit number and complete the expanded the board. form of the number. – Explain to students that since Roland has more cards than David, Roland will have to give Task 4 requires students to identify the digit of a place some of his cards to David in order for them to value in each 4-digit number, and the value of that have the same number of cards. digit. – Guide students to see that in order for the both of them to have the same number of cards, Task 5 requires students to use the ‘<’ and ‘>’ symbols Roland has to share his excess cards with to compare two numbers. David equally. – Using the comparison bar model, highlight to Task 6 requires students to compare and order four Wrapping Up the Chapter students that they need to rst nd how many 4-digit numbers. more cards Roland has than David. Then, they Task 7 requires students to count on or back in steps have to halve the difference to nd how many cards Roland should give to David. of 1, 10, 100 or 1000 to complete the number patterns. Ending the chapter by summarizing the key learning points helps students realize how– Guide students to subtract 4669 from 4687 in much the vertical form. Then, guide them to divide Task 8 requires students to associate the term ‘sum’ learning has taken place. This helps them organize the information into a meaningfulthe difference by 2 and conclude that Roland context in needs to give 9 cards to David. with addition and the term ‘difference’ with subtraction. their minds and ensures learning is4.sCohelcidk ifiyfoiuer adnswfeor isrcofrruectt.ure lessons. This is a crucial step to helpTask 9 requires students to add or subtract with or students information they have learned.– Have students nd the number of cards remember and apply the Roland and David each has in the end. without regrouping. – Lead students to conclude that since 4687 – 9 Task 10 requires students to solve a 1-step word = 4678 and 4669 + 9 = 4678, both Roland and problem involving subtraction. David have the same number of cards. CourseSwo,othrke aMnsawneur ias cl orrect. Task 11 requires students to solve a 1-step word problem involving addition. Reiterate key learning Reiterate the following points: Task 12 requires students to solve a 2-step word points and provide – We add to nd the sum of two numbers. problem involving addition. examples where necessary. – We subtract to nd the difference between two numbers. Task 13 requires students to solve a 2-step word – We regroup if necessary when adding to or problem involving addition and subtraction. subtracting from a 4-digit number. – We can draw part-whole or comparison bar Task 14 requires students to solve a 2-step word models to solve addition and subtraction problem. Depending on the method chosen, students word problems. may use only subtraction or use both addition and subtraction to solve the word problem. For answers, go to CW Manual pp. 149–150. ™ Blended Learning Program™ From PR1ME Mathematics Interactive Edition: Review 1 (PB pp. 35–40) Assign the tasks to students as classwork for summative assessment. Use the objectives and chapter references given for each task in the corresponding lesson notes to address remediation needs. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6953-2 Chapter 2 39 T22 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Teaching Problem Solving — Mathematical Modeling Blended Learning Program Mathematical modeling is a way of connecting school mathematics with real-world problems. Students represent a real-world problem using mathematics and formulate a model which may describe, explain or predict the real-world problem. The formulated model is thereafter used to obtain a solution to the real-world problem. Mathematical modeling tasks are closely related, but different, from application tasks. Application tasks require one to use learned mathematics concepts and skills to solve a task crafted with a real-world context. Mathematical modeling tasks, on the other hand, require one to represent the real-world problem in a mathematical model involving negotiated variables from which the solution is derived. The five-phased modeling process undertaken in this book is referenced from Ng (2011) and Lehrer & Lesh (2003). Phase 1: Discuss Introduce the real-world problem to the students. The focal points for teaching are (i) to familiarize students with the real-world context, (ii) to explicate the problem so that students understand what is expected, and (iii) to make connections between the real-world problem and the related mathematical interpretation or representation. Phase 2: Manipulate Students create a suitable mathematical model or framework for the given real-world problem. They may be required to decide on the variables involved, make sense of data and define terms. The focal points for teaching are (i) to introduce useful organizational tools such as making a table, and thinking tools such as brainstorming, (ii) to monitor and tailor learning to varied individuals, and (iii) to impart required knowledge outside the domain of mathematics e.g. conducting a fair test in Science. As this phase is characterized largely with students’ argumentations, reasoning, analysis and sense-making discussions, teachers may need to prepare and equip students progressively on collaboration, communication and mediating skills. Scholastic Phase 3: Experiment and Verify Students carry out the plan of constructing the model. This phase usually involves the use of concrete materials (e.g. construction of box) or pictorial representations (e.g. graph). This hands-on approach is intentional to address the needs of elementary school students. Through the process of manipulating and experimenting, students will verify the feasibility and validity of their mathematical model. Teachers are advised to assess the appropriateness of students’ model or framework and demonstrate the manipulation process if needed. Phase 4: Present Students present their model and supporting evidence, findings and observations that support the appropriateness of the model in addressing the real-world problem. An accompanying by-product of the modeling process is often required here. It may come in the form of a prototype of the model, written documents or oral presentations. Such artefacts serve as one basis for evaluating the mathematical modeling progress and attainment of a student. Phase 5: Reflect This phase seeks to direct students to the limitations of the constructed model and extends the model to other similar real-world situations. The key teaching focus is to encourage students to reexamine how well the model formulated serves its purpose in the real-world situation. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T23

There are two tasks each for Years/Grades 4 to 6. Each task may incorporate one or more mathematical concepts taught in each semester. As such, teachers may use one task towards the end of that semester when all the required mathematical concepts have been covered. The teacher's guide is written according to the five phases detailed on the previous page. In addition, a generic rubric to evaluate students’ mathematical modeling process is provided to assist teachers in delivering the tasks and in assessing students’ performance. Interactive Edition Blended Learning Program Interactive Edition Scholastic T24 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Developmental Continuum Year/Grade 3 Year/Grade 4 Year/Grade 5 NUMBERS AND NUMBER SENSE Whole Numbers / ScholasticRead and write a number Read and write a number Read and write a number Place Value within 10 000 — the numeral within 100 000 — the numeral within 1 000 000 000 — and the corresponding and the corresponding the numeral and the Addition / Subtraction number word. number word. corresponding number word. Use number notation and Use number notation and Identify the values of digits in place values (thousands, place values (ten thousands, a number within hundreds, tens, ones). thousands, hundreds, tens, 1 000 000 000. ones). Compare and order Compare and order numbers Compare and order numbers within 10 000. within 100 000. numbers within 1 000 000. Find the number which Find the number which is 1, Round a whole number is 1, 10, 100 or 1000 more 10, 100, 1000 or 10 000 more to the nearest thousand, than (or less than) a given than (or less than) a given ten thousand, hundred number within 10 000. number within 100 000. thousand, million, ten million or hundred million. Identify odd and even Read a number line. To use the divisibility rules for numbers. 2 to 12. Name a position using an Round a whole number to Find the common factors ordinal number from 1st to the nearest ten or hundred. and greatest common 100th. factor of up to four numbers. Identify and use the pattern List all factors of a whole Find out if a number is a of naming ordinal numbers number up to 100. common factor of two given from 1st to 100th. numbers. Identify the position of an Find out if a 1-digit whole Find the common multiples object from a given point of number is a factor of a given and least common multiple reference. whole number. of up to four numbers. Differentiate prime numbers Find out if a number is a Associate the terms ‘sum’ from composite numbers. common multiple of two and ‘difference’ with given numbers. addition and subtraction Use prime factorization to Create and solve problems respectively. write a given number as a involving factors, multiples Add or subtract within product of its prime factors. and divisibility rules for 2 to 12. 10 000. List the multiples of a whole number up to 10. Estimate an answer in Use a part-whole bar model Relate factors and multiples. addition or subtraction. or a comparison bar model Find out if a whole number is to represent an addition or a multiple of a given whole Do mixed operations subtraction situation. number. involving addition and Identify multiples of 2, 5 and subtraction without Solve up to 2-step word 10. parentheses. problems involving addition Estimate an answer in Do mixed operations and subtraction. addition or subtraction. involving addition, subtraction, multiplication Check reasonableness of and division with or without an answer in addition or parentheses. subtraction. Solve multi-step word problems involving the four operations of whole numbers. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T25

Year/Grade 3 Year/Grade 4 Year/Grade 5 NUMBERS AND NUMBER SENSE (continued) Addition / Subtraction Mentally add two 2-digit (continued) whole numbers with Multiplication / Division regrouping. Fractions / Concepts Mentally subtract: - a 2-digit whole number from another 2-digit whole number with regrouping - a 2-digit or 3-digit whole number from hundreds Multiply a number by 0 and 1. Observe the associative Estimate an answer in property of multiplication. multiplication or division. Count by sixes, sevens, Apply the commutative and Multiply or divide a whole eights and nines. associative properties of number by 10, 100 or 1000. multiplication in computation. Observe the commutative Multiply or divide a 4-digit Multiply or divide a whole number by tens, hundreds or and distributive properties of whole number by a 1-digit thousands. multiplication. whole number. Build up the multiplication Multiply or divide a whole Do mixed operations tables of 6, 7, 8 and 9 and number up to 4 digits by 10. involving multiplication and commit the multiplication division without parentheses. facts to memory. Multiply or divide numbers Multiply a whole number up Do mixed operations within the multiplication to 3 digits by a 2-digit whole involving addition, tables of 6, 7, 8 and 9. number. subtraction, multiplication Scholastic and division with or without parentheses. Find the missing number in Multiply a whole number up Multiply a 4-digit whole a multiplication or division to 4 digits by tens. number by a 2-digit whole sentence. number. Associate the term Estimate an answer in Multiply a 3-digit or 4-digit whole number by a 3-digit ‘product’ with multiplication. multiplication or division. whole number. Associate the terms Check reasonableness of an Estimate an answer in ‘quotient’ and ‘remainder’ answer in multiplication or multiplication by 2-digit and with division. division. 3-digit whole numbers. Multiply or divide a whole Solve up to 3-step word Divide a whole number up number up to 3 digits by a problems involving to 4 digits by a 2-digit whole 1-digit number. multiplication and division. number. Use a part-whole bar model Mentally multiply up to a Solve multi-step word or a comparison bar model 2-digit whole number by a problems involving the to represent a multiplication 2-digit whole number. four operations of whole or division situation. numbers. Solve up to 2-step word Mentally divide up to a 3-digit problems involving whole number by a 1-digit multiplication and division. whole number. Mentally multiply: - tens or hundreds by a 1-digit whole number - a 2-digit whole number by a 1-digit whole number without regrouping with product up to 100 Mentally divide: - tens or hundreds by a 1-digit whole number - a 2-digit number by a 1-digit whole number without remainder Identify the numerator and Write the sum of a whole Associate a fraction with denominator of a fraction. number and a proper division. fraction as a mixed number. T26 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Year/Grade 3 Year/Grade 4 Year/Grade 5 NUMBERS AND NUMBER SENSE (continued) Fractions / Concepts Compare and order Read a number line involving Express an improper fraction (continued) fractions which have a fractions and mixed numbers. as a whole number, mixed Fractions / common numerator. Arithmetic Operations number or decimal. Decimals Recognize and name Interpret an improper fraction equivalent fractions of as a multiple of a unit a given fraction with fraction. denominator up to 12. Express a fraction in its Write a whole number or simplest form. a mixed number as an improper fraction, and vice versa. Compare and order like, related and unlike fractions, including comparing to 1 . fractions with respect 2 Add or subtract like and Add two or three like or Divide a whole number related fractions within 1 related fractions with a sum by another whole number whole. more than 1 whole. and write the quotient as a mixed number. Solve a 1-step word problem Subtract one or two fractions Add or subtract unlike fractions and mixed involving fractions. from a whole number. numbers. Scholastic Understand a fraction of a Multiply mentally proper group of objects. fractions with denominators up to 10. Find the value of a fractional Multiply fractions. part of a quantity. Multiply a fraction and a Understand that multiplying whole number. a fraction by its reciprocal equals to 1. Express a part of a quantity Multiply a whole number by as a fraction. a mixed number. Convert a measurement of Multiply a fraction or mixed length, mass, volume of liquid number by a mixed number. or time from a larger unit of measure involving a fraction or a mixed number to a smaller unit. Convert a measurement of Divide a fraction by a whole length, mass, volume of liquid number. or time from a larger unit of measure involving a mixed number to compound units. Express a measurement of Divide a whole number by a length, mass, volume of liquid fraction. or time in the smaller unit as a fraction of a measurement in the larger unit. Solve up to 2-step word Solve multi-step word problems involving fractions. problems involving fractions. Read and write a decimal up Read and write a decimal to 3 decimal places. up to 4 decimal places. Express a fraction or mixed Interpret a decimal up to 4 number whose denominator decimal places in terms of is a factor of 10, 100 or 1000 ones, tenths, hundredths, as a decimal. thousandths and ten thousandths. Interpret a decimal up to 3 Identify the values of digits in decimal places in terms of a decimal up to 4 decimal ones, tenths, hundredths and places. thousandths. Identify the values of digits in Compare and order a decimal up to 3 decimal decimals up to 4 decimal places. places. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T27

Year/Grade 3 Year/Grade 4 Year/Grade 5 NUMBERS AND NUMBER SENSE (continued) Decimals (continued) Express a decimal up to 3 Round a decimal to 3 decimal places as a fraction decimal places. Rate or mixed number in its Ratio simplest form. Read a number line involving Add or subtract decimals up decimals. to 3 decimal places. Find the number which is 0.1, Divide a decimal by a 1-digit 0.01 or 0.001 more than (or whole number and round less than) a given number. the quotient to 2 decimal places. Compare and order decimals Express a mixed number up to 3 decimal places. as a decimal correct to 2 decimal places. Compare and order whole Multiply or divide a decimal numbers, decimals and or a whole number by 10, fractions. 100 or 1000. Round a decimal to the Multiply or divide a decimal nearest whole number or to 1 or a whole number by tens, decimal place. hundreds or thousands. Add or subtract decimals up Multiply a decimal up to 2 to 2 decimal places. decimal places by a 2-digit whole number. Scholastic Multiply or divide decimals Multiply a decimal up to up to 2 decimal places by a 2 decimal places by a 1-digit whole number. decimal with 1 decimal place. Divide a whole number Estimate an answer in by a 1-digit whole number addition, subtraction and and give the quotient as a multiplication. decimal. Estimate an answer in Check reasonableness addition, subtraction, of an answer in addition, multiplication or division subtraction and involving decimals. multiplication. Check reasonableness Convert a measurement of of an answer in addition, length, mass or volume of subtraction, multiplication or liquid from a larger unit of division involving decimals. measure involving a decimal to a smaller unit, and vice versa. Solve up to 2-step word Convert a measurement of problems involving decimals. length, mass or volume of liquid from a larger unit of measure involving a decimal to compound units, and vice versa. Solve multi-step word problems involving the four operations of decimals. Find the rate by expressing one quantity per unit of another quantity. Find a quantity using the given rate. Solve up to 3-step word problems involving rate. Use a ratio to compare two or three quantities. Use a comparison bar model to show a ratio. Use a ratio to compare two quantities given in a comparison bar model. T28 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Year/Grade 3 Year/Grade 4 Year/Grade 5 NUMBERS AND NUMBER SENSE (continued) Write equivalent ratios. Ratio (continued) Write a ratio in its simplest form. Percent Find the missing term in a Scholastic pair of equivalent ratios. Solve multi-step word problems involving ratio. Read and interpret a percentage of a whole. Express a fraction as a percent, and vice versa. Express a decimal as a percent, and vice versa. Express a percent as a ratio in its simplest form. Express a part of a whole as a percent. Understand that 1 whole is 100%. Identify the base, percentage and rate. Find the value of a percentage of a quantity. Solve up to 2-step word problems involving percentage, interest, tax and discount. MEASUREMENT Length Understand that a kilometer Convert a measurement of Convert a measurement of Perimeter / Area is greater than a meter and length from a larger unit of length from a larger unit of that a millimeter is smaller measure involving a fraction measure involving a decimal than a centimeter. or a mixed number to a to a smaller unit, and vice smaller unit. versa. Measure and compare Convert a measurement of lengths in kilometers, meters, Convert a measurement of length from a larger unit of centimeters and millimeters. length from a larger unit of measure involving a decimal measure involving a mixed to compound units, and vice Convert a measurement of number to compound units. versa. length from compound units to a smaller unit, and vice Express a measurement of Identify the base and height versa. length in the smaller unit as a of a triangle. Add or subtract lengths in fraction of a measurement in compound units. the larger unit. Find the area of a triangle using formula. Solve up to 2-step word Multiply or divide a problems involving length. measurement of length in Find the area of a figure compound units. related to the area of a Estimate and measure area triangle. in non-standard units. Solve up to 2-step word problems involving length in Compare the areas of compound units. figures made up of unit squares and half squares. Find the perimeter of a figure Visualize the sizes of made up of 1-centimeter or 1 square centimeter and 1-meter squares. 1 square meter. Measure the perimeter of a figure. Compare the areas and perimeters of figures made up of 1-centimeter or 1-meter squares. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T29

Year/Grade 3 Year/Grade 4 Year/Grade 5 MEASUREMENT (continued) Perimeter / Area Find the area of a figure Find the perimeter of a Find the area of a (continued) made up of 1-centimeter or rectilinear figure given the parallelogram using formula. 1-meter squares and half- lengths of all its sides. Volume squares. Compare the areas Find the area and perimeter Find the area of a rhombus of figures made up of of a square given the length using formula. 1-centimeter or 1-meter of one side. squares. Find the area and perimeter Find the area of a trapezoid of a rectangle given its length using formula. and breadth. Convert a measurement in Estimate the area of a square centimeters to square triangle, a parallelogram, a meters, and vice versa. rhombus and a trapezoid. Find one side of a rectangle Find the area of a figure given the other side and its made up of triangles, area or perimeter. parallelograms, rhombuses and trapezoids. Find the length of one side of a square given its area or perimeter. Find the area and perimeter of a figure made up of squares and/or rectangles. Scholastic Solve word problems involving area and perimeter of figures made up of squares and/or rectangles. Understand the concept of Convert a measurement of Convert a measurement volume. volume of liquid from a larger of volume of liquid from unit of measure involving a a larger unit of measure fraction or a mixed number involving a decimal to a to a smaller unit. smaller unit, and vice versa. Compare volumes of liquid Convert a measurement of Convert a measurement in two or more containers in volume of liquid from a larger of volume of liquid from non-standard units. unit of measure involving a a larger unit of measure mixed number to compound involving a decimal to units. compound units, and vice versa. Measure a volume of liquid Express a measurement Differentiate solid figures in liters and milliliters. of volume of liquid in the from plane shapes and smaller unit as a fraction of recognize that solid figures a measurement in the larger have volume. unit. Compare volumes of liquid Multiply or divide a Visualize a solid that is made in liters and milliliters. measurement of volume of up of unit cubes and state its liquid in compound units. volume in cubic units. Tell the difference between Solve up to 2-step word Visualize the sizes of 1 cubic volume and capacity. problems involving volume of centimeter and 1 cubic liquid in compound units. meter. Find the capacity of a Find the volume of a solid container. made up of 1-centimeter or 1-meter cubes. Compare capacities of two Compare the volumes or more containers. of solids made up of 1-centimeter or 1-meter cubes. Convert liters and milliliters to Use appropriate units of milliliters, and vice versa. measure for volume. T30 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Year/Grade 3 Year/Grade 4 Year/Grade 5 MEASUREMENT (continued) Volume (continued) Add or subtract volumes in Find the volume of a cuboid iters and milliliters. given its length, breadth and height. Solve up to 2-step word problems involving volume Recognize the equivalence and capacity. of 1 liter, 1000 milliliters and 1000 cubic centimeters. Mass ScholasticMeasure mass in kilograms Convert a measurement of Time: Calendar and grams. mass from a larger unit of Convert from one unit measure involving a fraction of measure of volume to Convert kilograms and or a mixed number to a another. grams into grams, and vice smaller unit. versa. Find the volume of liquid Convert a measurement of in cubic or rectangular mass from a larger unit of containers. measure involving a mixed number to compound units. Find the capacity of cubic or rectangular containers. Find the length of one edge of a cube given its volume. Find the length of one edge of a cuboid given its volume and two other edges. Find the length of one edge of a cuboid given the area of one face and its volume. Solve word problems involving volume of water in a cubic or rectangular container. Convert a measurement of mass from a larger unit of measure involving a decimal to a smaller unit, and vice versa. Convert a measurement of mass from a larger unit of measure involving a decimal to compound units, and vice versa. Compare masses in Express a measurement of kilograms and grams. mass in the smaller unit as a fraction of a measurement in the larger unit. Add or subtract masses in Multiply or divide a kilograms and grams. measurement of mass in compound units. Solve up to 2-step word Solve up to 2-step word problems involving mass. problems involving mass in compound units. Express years and months in months, and vice versa. Express months and days in days, and vice versa. Express years and days in days, and vice versa. Express weeks and days in days, and vice versa. Express months and weeks in weeks, and vice versa. Express years and weeks in weeks, and vice versa. Express days and hours in hours, and vice versa. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T31

Year/Grade 3 Year/Grade 4 Year/Grade 5 MEASUREMENT (continued) Time: Clock Tell and write time to 1 Convert a measurement of minute. time from a larger unit of measure involving a fraction or a mixed number to a smaller unit. Find the duration of a Convert a measurement of time interval in hours and time from a larger unit of minutes. measure involving a mixed number to compound units. Convert hours and minutes Express a measurement of to minutes, and vice versa. time in the smaller unit as a fraction of a measurement in the larger unit. Add or subtract in hours and Tell time to the second. minutes. Solve word problems Estimate and find the involving time. duration of a time interval in minutes. Find the duration of a time interval in seconds. Convert minutes and seconds to seconds, and vice versa. Scholastic Tell time using the 24-hour clock notation. Calculate time in different world time zones in relation to the Philippines. Convert time between the 12-hour and 24-hour clock notations. Solve word problems involving time in the 24-hour clock notation. Solve word problems involving world time zones in relation to the Philippines. Money Recognize and name the thousand-peso bill. Count and tell the amount of money in a group of bills. Exchange money. Compare amounts of money in pesos and centavos. Add or subtract amounts of money in pesos and centavos. Solve up to 2-step word problems involving money. Temperature Read and measure temperature using a thermometer. Estimate temperature. Convert a unit of temperature from degrees Celsius to degrees Farenheit, and vice versa. Solve problems involving temperature in real-life situations. T32 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Year/Grade 3 Year/Grade 4 Year/Grade 5 GEOMETRY Understand the properties of Recognize that the sum of squares and rectangles. the angle measures in a Plane Shapes triangle is 180°. Use properties of squares and rectangles to find unknown Find an unknown angle angle measures. measure in a triangle given the other two angle Use properties of squares and measures. rectangles to find unknown lengths. Identify a right triangle. Identify a symmetric figure. Recognize that when one Cut out a symmetric figure angle of a triangle is a from a piece of folded right angle, the sum of the paper. measures of the other two angles is 90°. Determine whether a line is a line of symmetry of a figure. Recognize that the measure of the exterior angle of a Draw a line of symmetry. triangle is equal to the sum of the measures of its interior Complete a symmetric figure opposite angles. with respect to a given horizontal or vertical line of Find an unknown angle symmetry. measure in a triangle Make a symmetric pattern. involving an exterior angle. Scholastic Identify an isosceles triangle and an equilateral triangle. Recognize that the angles opposite the equal sides of a triangle have equal measures. Find an unknown angle measure involving isosceles and equilateral triangles. State and apply the properties of parallelograms, rhombuses and trapezoids. Find an unknown angle measure involving parallelograms, rhombuses and trapezoids. Draw a triangle, rectangle, square, parallelogram, rhombus or trapezoid, given the measurements. Identify the unit shape in a tessellation. Identify if a given shape can tessellate. Make different tessellations with a unit shape. Draw a tessellation on dot paper. Make a tessellation with two different shapes. Visualize, name, describe and draw polygons with 5 or more sides. Describe and compare properties of polygons. Visualize congruent polygons. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T33

Year/Grade 3 Year/Grade 4 Year/Grade 5 GEOMETRY (continued) Build a solid with unit cubes. Visualize a solid drawn on Solid Shapes dot paper and state the number of unit cubes used Line Segments Identify and draw line Draw perpendicular line to build the solid. Angles segments that intersect. segments with a protractor or Identify the front, top and a set square. side views of a solid. Identify perpendicular and Visualize and identify parallel line segments. Draw parallel line segments the new solid formed by Draw perpendicular and with a set square and a ruler. changing the number of unit parallel line segments on a cubes of a given solid drawn square grid.Scholastic Use notations such as ∠ABC on dot paper. Identify horizontal and and ∠x. vertical line segments. Recognize that the sum of Identify and draw Recognize that the measure the angle measures on a line congruent line segments. of a right angle is 90°. is 180°. Understand the terms Recognize that the sum of ‘point’, ‘line’, ‘line segment’, Estimate and measure the the angle measures at a ‘ray’ and ‘angle’. size of an angle in degrees. point is 360°. Compare sizes of angles. Recognize that vertically Recognize an acute and an opposite angles have equal Identify angles on an object. obtuse angle. measures. Find the unknown measure Identify angles in a shape. of an angle involving angles on a line, angles at a point Identify right angles. Draw an angle. and vertically opposite Relate turns to right angles. angles. Tell whether a given angle Recognize that the sum of is equal to, smaller than or the angle measures in a bigger than a right angle. triangle is 180°. Find an unknown angle Relate wait41h-t1u8r0n°,waith34 90°, a measure in a triangle -turn with given the other two angle 1 -turn measures. 2 Recognize that when one angle of a triangle is a 270° and a complete turn right angle, the sum of the measures of the other two with 360°. angles is 90°. Tell direction in relation to the Recognize that the measure 8-point compass. of the exterior angle of a triangle is equal to the Read a simple map. sum of the measures of the interior opposite angles. Understand the properties of Find an unknown angle squares and rectangles. measure in a triangle involving an exterior angle. Recognize that the angles opposite the equal sides of a triangle have equal measures. T34 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Year/Grade 3 Year/Grade 4 Year/Grade 5 GEOMETRY (continued) Use properties of squares and Find an unknown angle rectangles to find unknown measure involving isosceles Angles (continued) angle measures. and equilateral triangles. State and apply the properties of parallelograms, rhombuses and trapezoids. Find an unknown angle measure involving parallelograms, rhombuses and trapezoids. STATISTICS AND PROBABILITY Graphs Read and interpret a block Present data in a bar graph. graph. Tables Read and interpret a bar Solve problems using data Averages graph. presented in a bar graph. Solve problems using data presented in a bar graph. Make a line graph. Collect and present data Read, interpret and present using a table. data in a line graph. Solve problems using data presented in a line graph. Compare a bar graph and a line graph to understand the properties and uses of each type of graph. Present data in a table. Scholastic Read and interpret a table. Solve problems using data presented in a table. Find the average of a group of data. Find the average given the sum of data and the number of data. Find the sum of data given the average and the number of data. Solve up to 3-step word problems involving average. Probability Tell whether something is sure, Record outcomes in a simple Describe experimental likely, equally likely, unlikely or experiment. probability. impossible to happen. Express the outcomes in an Perform an experimental Describe real-life situations experiment in words, symbols, probability and record its using ‘sure’, ‘likely’, ‘equally tables or graphs. results. likely’, ‘unlikely’ and ‘impossible’. Record favorable outcomes Analyze data obtained from of an event. chance using experiments involving letter and number Find the probability of an cards. event. Solve and create problems Solve and create problems involving experimental involving a simple probability. experiment. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6955-6 T35

Year/Grade 3 Year/Grade 4 Year/Grade 5 PATTERNS AND ALGEBRA Patterns Determine the missing Determine the missing term(s) Write a rule in finding the Expressions term(s) in a given combination of continuous in a sequence of numbers. next term in a sequence of and repeating pattern. numbers. Use letters to represent unknown numbers. Write a simple algebraic expression in one variable. Find the value of a simple algebraic expression using substitution. Simplify an algebraic expression in one variable. Solve word problems by forming an algebraic expression. Scholastic T36 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Chapter 1: Whole Numbers Strand: Numbers and Number Sense Total Duration: 15 h Scheme of Work Let’s Blended Learning Program Print-based Program SRememberLessonLearning Outcomes Vocabulary ch(30 min) Materials Resources Materials Resources •• Identify the values of digits in •• CB pp. 7–8 •• 1 copy of Let’s a 4-digit number Remember Worksheet (WS1.1) per student •• Compare 4-digit numbers •• Give the number which is 1, 10, 100 or 1000 more than (or less than) a given number within 10 000 •• Complete number patterns oLesson 1: Numbers 0 to 100 000 lReading 4 h 30 min aand writing •• CWB pp. 1–3 numbers sIdentifying •• Base ten blocks •• CB pp. 9–11 •• Base ten blocks tvalues of •• Magnetic counters icdigits and •• Place value cards •• Read and write a number •• Magnetic counters •• PB pp. 7–8 within 100 000 — the numeral and the corresponding •• Place value cards •• CWB pp. 1–3 number word •• Identify the value of each •• CB pp. 12–13 •• CWB pp. 3–4 digit and place value in a •• PB pp. 9–10 5-digit number •• CWB pp. 3–4 place values Finding ‘more •• Find a number which is 1, 10, •• Magnetic counters •• CB pp. 14–15 •• Magnetic counters •• CWB pp. 5–6 than’ and 100, 1000 or 10 000 more than •• PB p. 11 ‘less than’ (or less than) a given number •• CWB pp. 5–6 within 100 000 Reading •• Read a number line •• increasing •• CB p. 16 •• CWB p. 7 number lines order •• PB p. 12 •• CWB p. 7 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Blended Learning Program Print-based Program Lesson Learning Outcomes Vocabulary Materials Resources Materials Resources Comparing •• Compare and order •• CB pp. 17–20 •• 1 copy of Think About •• CWB p. 8 It Worksheet (WS1.2) 3h and ordering numbers within 100 000 •• PB p. 13 per group •• CWB p. 9 numbers •• CWB p. 8 •• 1 copy of Think About •• CWB pp. 10–11 Snumbers to the It Worksheet (WS1.3) Lesson 2: Rounding Numbers per group •• CWB pp. 11–12 cRounding 3-digit •• 1 copy of Think About •• CWB p. 13 It Worksheet (WS1.4) •• CWB p. 14 and 4-digit per group hnumbers to the nearest ten Rounding 2-digit •• Round a 2-digit number to the •• approximately •• 1 copy of Number •• CB pp. 21–23 nearest ten •• round Lines A (TR1.1) •• CWB p. 9 nearest ten oRounding •• CB pp. 23–25 •• PB pp. 14–15 numbers to •• CWB pp. 10–11 lthe nearest ahundred •• Round a 3-digit or 4-digit number to the nearest ten •• Round a whole number to the •• 1 copy of Number •• CB pp. 25–27 nearest hundred Estimating sums •• Estimate an answer in Lines B (TR1.2) •• PB pp. 16–17 sand differences addition or subtraction •• CWB pp. 11–12 ticUsing •• estimate •• CB pp. 27–28 •• PB p. 18 •• CWB p. 13 •• Check reasonableness of •• reasonable •• CB p. 29 estimation to an answer in addition and •• PB p. 19 check sums subtraction •• CWB p. 14 and differences Lesson 3: Factors  3h Finding •• List all factors of a whole •• factor •• Unit cubes •• CB pp. 30–32 •• CWB pp. 15–16 factors of a number up to 100 •• PB pp. 20–21 whole number •• CWB pp. 15–16 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Blended Learning Program Print-based Program Lesson Learning Outcomes Vocabulary Materials Resources Materials Resources Finding out if •• Find out if a 1-digit number •• CB pp. 32–33 •• CWB pp.16–17 •• CWB p.18 a number is a is a factor of a given whole •• PB p. 22 •• CWB pp. 19–20 factor of number •• CWB pp. 16–17 3h •• CWB pp. 21–22 another numberSPrime •• CWB p. 22 cfactorization •• CWB pp. 23–24 Prime and •• Differentiate prime numbers •• composite composite from composite numbers number 1h numbers •• prime number •• prime factorization hFinding •• Use prime factorization to omultiples of write a given number as a product of its prime factors a whole Lesson 4: Multiplesnumber laRelating •• List the multiples of a whole •• multiple •• CB p. 34 number up to 10 •• PB p. 23 factors and •• CWB pp. 21–22 smultiples •• CB p. 35 tIdentifying •• CWB p. 22 icmultiples of •• Relate factors and multiples •• 1 copy of Hundred •• CB pp. 36–37 •• 1 copy of Hundred •• Find out if a whole number is Chart (BM1.1) Chart (TR1.3) •• PB p. 24 a multiple of a given whole number up to 10 •• Identify multiples of 2, 5 and 10 2, 5 and 10 •• Black marker •• CWB pp. 23–24 •• Red marker •• Reusable adhesive Lesson 5: Number Patterns Finding the •• Find the missing term(s) in a •• CWB p. 25 missing term number pattern in a number pattern © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Chapter 1 Lesson 1: Numbers 0 to 100 000 Whole Numbers Duration: 4 h 30 min Chapter Overview  Blended Learning Program Let’s Remember Lesson 1: Numbers 0 to 100 000 From PR1ME Mathematics Interactive Edition: Lesson 2: Rounding Numbers Let’s Learn (CB pp. 9–11) Lesson 3: Factors Go through the teaching examples with students for Lesson 4: Multiples concept development. Use the detailed lesson plan given in the corresponding lesson notes to carry out Note for Teachers the teaching. In this chapter, students use base ten blocks, unit cubes, place value charts and other manipulatives Learn to learn about numbers within 100 000. They are Reading and writing numbers (CWB pp. 1–2) introduced to number lines and learn how they can use them to round numbers to the nearest ten or Learning Outcome: hundred. Besides learning to represent approximation •• Read and write a number within 100 000 — the or estimation with the approximation symbol (≈), numeral and the corresponding number word students are also taught how estimation can help them check if the answers that they obtained from addition Materials: or subtraction are reasonable. In the second half of •• Base ten blocks the chapter, students are introduced to factors and •• Magnetic counters multiples and how they are related to each other. The •• Place value cards multiplication tables of 2 to 10 have to be committed to memory in order for students to learn about Stage: Concrete Experience factors and multiples effectively. Students are also Using base ten blocks to represent numbers helps introduced to prime and composite numbers and how students understand how a number is broken down to differentiate between both. They are also taught into thousands, hundreds, tens and ones. This will help how to carry out prime factorization. Students will learn students to read and write numbers in numerals and to complete number patterns by counting on and number words correctly. backwards, and listing the multiples of a number. Scholastic Recall Prior Knowledge –– Show students a thousand-block and tell them that it is made up of 1000 unit cubes.  Blended Learning Program –– Refer students to the picture of the first row From PR1ME Mathematics Interactive Edition: of thousand-blocks on CWB p. 1. Point out to Let’s Remember (CB pp. 7–8) students that there are 10 thousand-blocks. Assign the tasks to students as classwork to identify gaps in students’ understanding. Use the objectives –– Draw 10 cubes on the board and indicate that and chapter references given for each task in the each cube represents 1 thousand-block. Then corresponding lesson notes to address remediation guide students to count the total number of needs. unit cubes by counting on in thousands starting from 1000 to 10 000. Point to each thousand- Distribute a copy of Let’s Remember Worksheet (WS1.1) block as you count on. Conclude that there to each student. Have students attempt the worksheet are 10 000 unit cubes altogether in the first row to help them recall these previously acquired related of thousand-blocks on CWB p. 1. knowledge: –– Write ‘10 000’ on the board and get students to •• Identify the values of digits in a 4-digit number read it as ‘ten thousand’. (CWB 3A Chapter 1) –– Tell students that we leave a space between •• Compare 4-digit numbers (CWB 3A Chapter 1) ‘10’ and ‘000’ so that it is easier to read the •• Give the number which is 1, 10, 100 or 1000 number ‘10 000’. more than (or less than) a given number within –– Guide students to count on to find the 10 000 (CWB 3A Chapter 1) remaining number of unit cubes: 10 000, 11 000, •• Complete number patterns (CWB 3A Chapter 1) 12 000, 13 000, 14 000, 15 000, 15 100, 15 200, 15 210, 15 220, 15 230, 15 240, 15 250, 15 260, For answers, go to CW Manual p. 160. 15 261, 15 262, 15 263. –– Write ‘15 263’ on the board and get students to read it as ‘fifteen thousand, two hundred and sixty-three’. –– Highlight to students that the space between ‘15’ and ‘263’ separates the thousands part of the number from the hundreds, tens and ones. Stage: Pictorial Representation In this stage, students will transit from the concrete experience to the pictorial representation by relating 4 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

the concrete activity to the presentation of a Scholastic Practice 1 (CWB pp. 2–3) number in the form of a place value chart and place value cards. These are useful tools to help students Class practice (For Print-based Program): understand the place value of each digit in a number based on its position. Understanding place value will Task 1 requires students to read a number help students in learning to compare numbers, and within 100 000. to add, subtract, multiply and divide numbers in the later stages. Task 3 requires students to write a number within 100 000 in numerals, given the corresponding –– Copy the place value chart shown on CWB number word. p. 2 on the board. Stick magnetic counters in the respective columns to represent the digit Remediation in each place of the number. Task 1: Copy the place value chart shown on CWB p. 2 on the board without sticking the counters. Refer students –– Explain to students that 1 counter in the ten to the place value chart on the page and get them to thousands column represents 1 ten thousand count the number of counters in each column. Then write and so on. the number of counters in their respective columns on the board. Conclude that the number is 12 134. –– Stick the place value cards ‘10 000’, ‘5000’, ‘200’, ‘60’ and ‘3’ on the board next to the place value Task 3: Guide students to find the number of thousands, chart. Guide students to see that the 1 counter in hundreds, tens and ones that make up the number. the ten thousands column is represented by the Conclude that there are 2 thousands, 3 hundreds, place value card ‘10 000’, the 5 counters in the 6 tens and 0 ones and the number is 2360. thousands column are represented by the place value card ‘5000’ and so on. Teaching tips Task 1 –– Overlap the place value cards to show 15 263 and explain to students that 10 000, 5000, 200, ¾¾ Ensure that students understand the letters ‘O’, 60 and 3 make 15 263. ‘T’, ‘H’, ‘Th’ and ‘T Th’ represent the ones, tens, hundreds, thousands and ten thousands place. Stage: Abstract Representation In this stage, students learn to read or write a number Task 3 systematically as they transit from the pictorial ¾¾ Highlight the use of zero as a placeholder representation to the abstract representation. where there are 0 ones in the number. –– Write ‘10 000 + 5000 + 200 + 60 + 3’ on the Independent practice (For Print-based Program): board. Explain to students that this is the expanded form of 15 263. Task 2 requires students to read a number within 100 000. –– Reiterate to students that the number 15 263 Task 4 requires students to write a number within 100 000 has 1 ten thousand, 5 thousands, 2 hundreds, in numerals, given the corresponding number word. 6 tens and 3 ones. Guide students to write the number word as ‘fifteen thousand, two Task 5 requires students to write a number within 100 000 hundred and sixty-three’. Highlight the use of in words, given the corresponding numerals. the comma in the number word to separate the thousands part of the number from the For answers, go to CW Manual p. 159. hundreds, tens and ones part.  Blended Learning Program  Blended Learning Program From PR1ME Mathematics Interactive Edition: From PR1ME Mathematics Interactive Edition: Let’s Learn (CB pp. 12–13) Let’s Do (CB pp. 11) Go through the teaching examples with students for Assign the tasks to students as classwork for concept development. Use the detailed lesson plan formative assessment. Use the corresponding lesson given in the corresponding lesson notes to carry out notes to identify the objectives of each task and the teaching. address remediation needs. Learn Exercise 1 (PB pp. 7–8) Identifying values of digits and place values Assign the tasks to students as classwork for further (CWB p. 3) formative assessment. Use the corresponding lesson notes to identify the objectives of each task and Learning Outcome: address remediation needs. •• Identify the value of each digit and place value in a 5-digit number From PR1ME Mathematics Coursework Book: Coursework Book Practice 1 (CWB pp. 2–3) Assign all tasks to students as homework. Use the following notes to identify the skills needed for each task and address remediation needs. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 5

Stage: Pictorial Representation ScholasticExercise 2 (PB pp. 9–10) In this stage, we help students understand the value Assign the tasks to students as classwork for further of a digit in a number by using place value cards. formative assessment. Use the corresponding lesson Overlapping the place value cards shows the number, notes to identify the objectives of each task and while separating them shows the value of each digit address remediation needs. in the number. This pictorial representation will help students understand the value of each digit in a From PR1ME Mathematics Coursework Book: number and also helps them to transit easily to telling Coursework Book Practice 2 (CWB p. 4) the value of a digit using a place value table. Assign all tasks to students as homework. Use the following notes to identify the skills needed for each –– Overlap the place value cards ‘70 000’, ‘5000’, task and address remediation needs. ‘800’, ‘20’ and ‘1’to show the number 75 821 on the board. Then, show each place value Practice 2 (CWB p. 4) card separately and guide students to see that 70 000, 5000, 800, 20 and 1 make 75 821. Class practice (For Print-based Program): –– Copy the place value chart on CWB p. 3 on Task 1 requires students to identify the value of each the board. Explain to students that they can digit in a 5-digit number. write the number 75 821 in a place value chart by writing the digit 7 in the ten thousands place Task 3 requires students to identify the value of each to represent 70 000, the digit 5 in the thousands digit and its place value in a 5-digit number given the place to represent 5000, the digit 8 in the place value chart. hundreds place to represent 800, the digit 2 in the tens place to represent 20 and the digit 1 Remediation in the ones place to represent 1. Help students Task 1: Draw a place value chart on the board and see how the place value cards correspond to write each digit of the number in its respective column. each digit in the place value chart. Using the place value chart, guide students to find the number of ten thousands, thousands, hundreds, tens Stage: Abstract Representation and ones that make up the number. In this stage, students will be able to identify the value of each digit in a number by looking at its position. Task 3: Get students to associate each digit in the number with its place value to find the value of the –– Guide students to understand that the digit 1 digit. For example digit 2 is in the thousands place, stands for 1, the digit 2 stands for 20, the digit which means there are 2 thousands so its value is 2000. 8 stands for 800, the digit 5 stands for 5000 and the digit 7 stands for 70 000. Teaching tips Task 1 –– Have students look at the place value chart on the board and explain that they can identify ¾¾ Highlight the use of zero as a placeholder the value of each digit or its place value by where there is a 0 in a number. looking at the columns. Independent practice (For Print-based Program): –– Explain to students that in 75 821, the digit 7 is in the ten thousands place, which means Task 2 requires students to identify the values of digits there are 7 ten thousands, so its value is 70 000. that make up a 5-digit number. Similarly, the digit 5 is in the thousands place, which means there are 5 thousands, so its value Task 4 requires students to identify the values of digits is 5000. The digit 8 is in the hundreds place, and place values in a 5-digit number. which means there are 8 hundreds, so its value is 800. The digit 2 is in the tens place, which For answers, go to CW Manual p. 159. means there are 2 tens, so its value is 20. The digit 1 is in the ones place, which means there is 1 one, so its value is 1.  Blended Learning Program  Blended Learning Program From PR1ME Mathematics Interactive Edition: From PR1ME Mathematics Interactive Edition: Let’s Do (CB pp. 12–13) Let’s Learn (CB p. 14) Assign the tasks to students as classwork for Go through the teaching examples with students for formative assessment. Use the corresponding lesson concept development. Use the detailed lesson plan notes to identify the objectives of each task and given in the corresponding lesson notes to carry out address remediation needs. the teaching. 6 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

Learn Scholastic –– Then remove 1 counter from the ten thousands column and guide students to understand that Finding ‘more than’ and ‘less than’ (CWB p. 5) the new number represented by the number of counters is 1 ten thousand less than 31 679. Learning Outcome: •• Find a number which is 1, 10, 100, 1000 or Stage: Abstract Representation 10 000 more than (or less than) a given number Allow students to transit from the pictorial to the within 100 000 abstract representation by guiding them to understand that finding 10 000 less than a number is the same as Materials: subtracting 1 ten thousand from the number. •• Magnetic counters –– Guide students to understand that to find (a) 10 000 less than 31 679, we have to remove Stage: Pictorial Representation 1 ten thousand from 31 679. Explain to students In Grade 3, students learned to find 1, 10, 100 or that when we remove 1 ten thousand from 1000 more than or less than a given number using 3 ten thousands, we get 2 ten thousands. counters in place value charts. In this section, they So, 10 000 less than 31 679 is 21 679. extend their knowledge to numbers involving ten thousands. Using counters allows students to clearly –– Point out to students that finding 10 000 less see the number of ten thousands, thousands, than 31 679 is the same as subtracting 10 000 hundreds, tens or ones that are added or removed from 31679. Write ‘31 679 − 10 000 = 21 679’ on from a number. In this example, students recognize the board. that to find 1000 more than a number, they have to add 1 thousand to the number of thousands in the –– Highlight to students that the digits in the other given number, that is, they have to increase the digit places do not change. in the thousands place by 1. (c) –– Copy the place value chart shown on Stage: Pictorial Representation CWB p. 5 on the board without showing the In this example, place value chart and counters will counters. be used to help students recognize that to find 100 less than a number, they have to remove 1 hundred from –– Have a student stick counters in the chart the number of hundreds in the given number, to show the number 31 679. that is, they have to decrease the digit in the hundreds place by 1. –– Add 1 counter to the thousands column and guide students to understand that the new –– Replace 1 counter to the ten thousands column number represented by the number of in the setup to show the number 31 679 again. counters is 1 thousand more than 31 679. –– Then remove 1 counter from the hundreds Stage: Abstract Representation column and guide students to understand that Allow students to transit from the pictorial to the the new number represented by the number abstract representation by guiding them to understand of counters is 1 hundred less than 31 679. that finding 1000 more than a number is the same as adding 1 thousand to the number. Stage: Abstract Representation Allow students to transit from the pictorial to the –– Guide students to understand that to find 1000 abstract representation by guiding them to understand more than 31 679, we have to add 1 thousand that finding 100 less than a number is the same as to 31 679. Explain to students that when we add subtracting 1 hundred from the number. 1 thousand to 1 thousand, we get 2 thousands. So, 1000 more than 31 679 is 32 679. –– Guide students to understand that to find 100 less than 31 679, we have to remove 1 hundred –– Point out to students that finding 1000 more than from 31 679. Explain to students that when we 31 679 is the same as adding 1000 to 31 679. remove 1 hundred from 6 hundreds, we get Write ‘31 679 + 1000 = 32 679’ on the board. 5 hundreds. So, 100 less than 31 679 is 31 579. –– Highlight to students that the digits in the other –– Point out to students that finding 100 less than places do not change. 31 679 is the same as subtracting 100 from 31 679. Write ‘31 679 − 100 = 31 579’ on the board. (b) Stage: Pictorial Representation –– Highlight to students that the digits in the other In this example, place value chart and counters will be places do not change. used to help students recognize that to find 10 000 less than a number, they have to remove 1 ten thousand  Blended Learning Program from the number of ten thousands in the given number, that is, they have to decrease the digit in the ten From PR1ME Mathematics Interactive Edition: thousands place by 1. Let’s Do (CB p. 15) Assign the tasks to students as classwork for formative –– Remove 1 counter from the thousands column assessment. Use the corresponding lesson notes to from the setup to show the number 31 679 again. identify the objectives of each task and address remediation needs. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 7

Exercise 3 (PB p. 11) Scholastic Blended Learning Program Assign the tasks to students as classwork for further formative assessment. Use the corresponding lesson From PR1ME Mathematics Interactive Edition: notes to identify the objectives of each task and Let’s Learn (CB p. 16) address remediation needs. Go through the teaching examples with students for concept development. Use the detailed lesson plan From PR1ME Mathematics Coursework Book: given in the corresponding lesson notes to carry out Coursework Book Practice 3 (CWB p. 6) the teaching. Assign all tasks to students as homework. Use the following notes to identify the skills needed for each Learn task and address remediation needs. Reading number lines (CWB p. 7) Practice 3 (CWB p. 6) Learning Outcome: Class practice (For Print-based Program): •• Read a number line Task 1 requires students to find the number which is Vocabulary: 1000 more than a given number within 100 000. •• increasing order Task 4 requires students to complete a number pattern Stages: Pictorial Representation and Abstract by counting on in steps of 10 000. R­ epresentation In this section, students are introduced to number lines Remediation for the first time. It is, however, not an entirely new Task 1: Draw a place value chart on the board and concept to students as they have learned to read stick counters to represent each digit of the number in scales in the measurement chapters in earlier grades. its respective column. Using the place value chart and Learning to read a number line is useful in helping counters, guide students to understand that to find students to learn about rounding numbers in a later 1000 more than 16 235, they have to add 1 thousand stage as it allows them to easily see the position of a to 16 235. Highlight to students that only the digit in the number relative to other numbers. thousands place changes. –– Copy the number line shown on CWB p. 7 on Task 4: Guide students to compare each digit of the the board. Highlight that the numbers on the numbers and recognize that only the digits in the ten number line become greater as they move thousands place are different, and that each number along the number line from left to right. is greater than the number before it, hence they have to add 10 000 to find the next number in the pattern. –– Guide students to understand that we can use a number line to show the order of numbers Teaching tips where the numbers are arranged in increasing Task 1 order from left to right. ¾¾ Highlight to students that the digits in the other –– Get students to count the number of intervals places do not change. between 10 000 and 20 000 and conclude that there are 10 equal intervals. Task 4 ¾¾ Highlight to students that they have to first –– Then guide students to find what each interval determine the place in which the digits are stands for. Lead students to see that since the different in the numbers – ones, tens, hundreds, 10 equal intervals represent a value of 10 000, thousands or ten thousands. Then identify if each interval stands for 1000. the numbers are increasing or decreasing to determine the rule of the number pattern. –– Get students to count in steps of 1000 from 10 000 to 25 000, and find the values Independent practice (For Print-based Program): represented by W, X, Y and Z. Task 2 requires students to find the number which is  Blended Learning Program 1, 10, 100, 1000 or 10 000 more than or less than a given number within 100 000. From PR1ME Mathematics Interactive Edition: Let’s Do (CB p. 16) Task 3 requires students to find how much more the first Assign the tasks to students as classwork for formative number is than the second number. assessment. Use the corresponding lesson notes to identify the objectives of each task and address Task 5 requires students to complete a number pattern remediation needs. by counting on or backwards in steps of 1, 10, 100, 1000 or 10 000. Exercise 4 (PB p. 12) Assign the tasks to students as classwork for further For answers, go to CW Manual p. 159. formative assessment. Use the corresponding lesson notes to identify the objectives of each task and address remediation needs. 8 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

From PR1ME Mathematics Coursework Book: Scholastic –– Have three students fill in the table to show the Coursework Book Practice 4 (CWB p. 7) numbers 53 843, 53 840 and 39 964. Assign all tasks to students as homework. Use the following notes to identify the skills needed for each –– Guide students to compare the numbers task and address remediation needs. starting from the greatest place value. Lead students to understand that they have to start Practice 4 (CWB p. 7) comparing from the left column of the place value chart. Class practice (For Print-based Program): –– Guide students to compare the digits in the ten Task 1 requires students to find the numbers that are thousands place and conclude that since 3 ten represented on each number line. thousands is smaller than 5 ten thousands, 39 964 is the smallest number. Remediation Task 1: Draw the number line on the board. Highlight –– Next, have students compare the remaining that there are 5 equal intervals between 40 100 and two numbers, 53 843 and 53 840. Since the digits 40 150, so each interval stands for 10. Guide students to in the thousands, hundreds and tens places are count in steps of 10 from 40 100 to 40 200 and fill in the the same, point out to students that they have missing numbers. to compare the digits in the ones place. Teaching tips –– Guide students to compare the digits in the Task 1 ones place of 53 843 and 53 840 and conclude that since 3 ones is greater than 0 ones, 53 843 ¾¾ Highlight to students that they only need to is greater than 53 840. look at the first two numbers from the left and the number of intervals between them –– Conclude that the smallest number is 39 964, to find the value represented by each interval. followed by 53 840 and the greatest number is 53 843. Independent practice (For Print-based Program): –– Guide students to arrange the numbers in order Task 2 requires students to find the numbers that are from the greatest number: represented on each number line. 53 843, 53 840, 39 964 For answers, go to CW Manual p. 159.  Blended Learning Program  Blended Learning Program From PR1ME Mathematics Interactive Edition: Let’s Do (CB pp. 18–19) From PR1ME Mathematics Interactive Edition: Assign the tasks to students as classwork for formative Let’s Learn (CB pp. 17–18) assessment. Use the corresponding lesson notes to Go through the teaching examples with students for identify the objectives of each task and address concept development. Use the detailed lesson plan remediation needs. given in the corresponding lesson notes to carry out the teaching. Exercise 5 (PB p. 13) Assign the tasks to students as classwork for further Learn formative assessment. Use the corresponding lesson Comparing and ordering numbers (CWB p. 8) notes to identify the objectives of each task and address remediation needs. Learning Outcome: •• Compare and order numbers within 100 000 From PR1ME Mathematics Coursework Book: Coursework Book Practice 5 (CWB p. 8) Materials: Assign all tasks to students as homework. Use the •• 1 copy of Think About It Worksheet (WS1.2) following notes to identify the skills needed for each per group task and address remediation needs. Stage: Abstract Representation Practice 5 (CWB p. 8) Students have learned to compare numbers using a place value chart in the earlier grades. In this stage, Class practice (For Print-based Program): they will be comparing 5-digit numbers involving the ten thousands place. Task 1 requires students to compare two numbers within 100 000. –– On the board, copy the place value table on CWB p. 8 without filling in the numbers. Remediation Task 1: Draw a place value chart on the board and guide students to fill in each digit of the numbers into their respective place value column. Then compare the digits from the left to the right. Point out that since the first digit in both numbers in Task 1(a) and 1(b) are the same, students have to compare the second digit. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 9

Teaching tips  Blended Learning Program Task 1 From PR1ME Mathematics Interactive Edition: ¾¾ Reiterate to students that they have to Practice 1 (CB pp. 19–20) compare the digits of the numbers from the Assign the tasks to students as classwork for greatest to the smallest place, that is, from left summative assessment. Use the corresponding lesson to right. Highlight that they only need to go on notes to identify the objectives of each task and to compare the digits in the next place if the address remediation needs. digits in the greater place are the same. Independent practice (For Print-based Program): Lesson 2: Rounding Numbers Duration: 3 h Task 2 requires students to arrange four numbers in order from the smallest.  Blended Learning Program Task 3 requires students to form the greatest and smallest 5-digit number using the given digits. For answers, go to CW Manual p. 159. From PR1ME Mathematics Interactive Edition: Let’s Learn (CB pp. 21–22) ThinkAbout It Go through the teaching examples with students for  Blended Learning Program concept development. Use the detailed lesson plan given in the corresponding lesson notes to carry out the teaching. From PR1ME Mathematics Interactive Edition: ScholasticLearn Think About It (CB p. 19) Assign the task to students as classwork. Have them Rounding 2-digit numbers to the nearest ten complet e the task in groups. Facilitate discussions (CWB p. 9) using the corresponding lesson notes. Learning Outcome: Have students get into groups. Distribute a copy of •• Round a 2-digit number to the nearest ten Think About It Worksheet (WS1.2) to each group. Have them discuss the question presented. Ask a student Vocabulary: from each group to present their answers before •• approximately proceeding with the questions below. •• round –– What is Yen trying to find? (The greatest number (a) among a set of three numbers) Stage: Pictorial Representation Students are introduced to rounding numbers for the –– Why does Yen think that 9876 is the greatest first time. In this example, students learn to round down number? (The first digit of the number, 9, is the a number to the nearest ten. In this stage, a number greatest among the first digits of the three numbers) line will be used to allow students to easily see the position of a number relative to other numbers. –– What is the place value of the digit 9 in 9876? (Thousands) –– Draw a number line from 40 to 50 with 10 equal intervals on the board. Guide students to see –– What is the place value of the digit 7 in 76 543? that there are 10 equal intervals in the number (Ten thousands) line and each interval stands for 1. –– What is the place value of the digit 8 in 87 654? –– Have a student point out where 43 lies on the (Ten thousands) number line and mark the spot. Get students to see that 43 is between 40 and 50. –– Which is greater, thousands or ten thousands? (Ten thousands) –– Lead students to see that there are 3 intervals between 40 and 43 and 7 intervals between 43 Conclude that Yen is wrong. Lead students to see that and 50, and 43 is less than halfway between 40 when comparing numbers, they should look at the and 50, hence 43 is nearer to 40 than to 50. digits in the greatest place value first. In this case, Yen should look at the digits in the ten thousands place. Stage: Abstract Representation She should not just look at the first digit of the numbers In this stage, students will associate the position of as the digits that are being compared may not be numbers on a number line to the concept of rounding from the same place value. Guide students to see to the nearest ten. that they can use a place value chart to help them compare and find the greatest number. –– Guide students to conclude that since 43 is nearer to 40 than to 50 on the number line, when we round 43 to the nearest ten, we get 40. 10 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

–– Write ‘43 ≈ 40’ on the board and get students to  Blended Learning Program read the statement as ‘43 is approximately 40’. From PR1ME Mathematics Interactive Edition: –– Highlight to students that ‘≈’ is the approximate Let’s Learn (CB pp. 23–24) sign and it means ‘approximately’. Go through the teaching examples with students for concept development. Use the detailed lesson plan (b) given in the corresponding lesson notes to carry out Stages: Pictorial Representation and Abstract the teaching. Representation In this example, students learn to round up a number to Learn the nearest ten. Rounding 3-digit and 4-digit numbers to the nearest ten (CWB p. 10) –– Draw a number line from 40 to 50 with 10 equal intervals on the board. Guide students to see Learning Outcome: that there are 10 equal intervals in the number •• Round a 3-digit or 4-digit number to the line and each interval stands for 1. nearest ten –– Have a student point out where 49 lies on the (a) number line and mark the spot. Get students to Stages: Pictorial Representation and Abstract see that 49 is between 40 and 50. Representation Using the same teaching procedure as the earlier –– Lead students to see that there are 9 intervals Learn on CWB p. 9, students will now learn to round between 40 and 49 and 1 interval between 49 3-digit or 4-digit numbers to the nearest ten. In this and 50, and 49 is more than halfway between example, students learn to round up a 3-digit number 40 and 50, hence 49 is nearer to 50 than to 40. to the nearest ten. –– Guide students to conclude that since 49 is nearer to 50 than to 40 on the number line, when we round 49 to the nearest ten, we get 50. –– Have a student write the statement ‘49 is approximately 50’ using the symbol ‘≈’ on the board. Scholastic (c) –– Draw a number line from 190 to 200 with 10 equal Stages: Pictorial Representation and Abstract intervals on the board. Guide students to see Representation that there are 10 equal intervals in the number In this example, students learn to round up a number line and each interval stands for 1. that is halfway between two tens to the greater ten. –– Have a student point out where 197 lies on the –– Draw a number line from 50 to 60 with 10 equal number line and mark the spot. Get students to intervals on the board. Guide students to see see that 197 is between 190 and 200. that there are 10 equal intervals in the number line and each interval stands for 1. –– Lead students to see that there are 7 intervals between 190 and 197 and 3 intervals between –– Have a student point out where 55 lies on the 197 and 200, and 197 is more than halfway number line and mark the spot. Get students to between 190 and 200, hence 197 is nearer to see that 55 is between 50 and 60. 200 than to 190. –– Lead students to see that there are 5 intervals –– Guide students to conclude that since 197 is between 50 and 55 and 5 intervals between 55 nearer to 200 than to 190 on the number line, and 60, hence 55 is halfway between 50 and 60. when we round 197 to the nearest ten, we get 200. –– Point out to students that when a number is –– Write ‘197 ≈ 200’ on the board and conclude halfway between two tens, we take the greater that ‘197 is approximately 200 when rounded to ten as the nearest ten to the number. In this case, the nearest ten’. the greater ten is 60. So, the nearest ten to 55 is 60. (b) –– Guide students to conclude that when we Stages: Pictorial Representation and Abstract round 55 to the nearest ten, we get 60. Representation In this example, students learn to round down a 4-digit –– Have a student write the statement ‘55 is number to the nearest ten. approximately 60’ using the symbol ‘≈ ’ on the board. –– Draw a number line from 7360 to 7370 with 10 equal intervals on the board. Guide students  Blended Learning Program to see that there are 10 equal intervals in the number line and each interval stands for 1. From PR1ME Mathematics Interactive Edition: Let’s Do (CB p. 23) –– Have a student point out where 7361 lies on the Assign the tasks to students as classwork for formative number line and mark the spot. Get students to assessment. Use the corresponding lesson notes to see that 7361 is between 7360 and 7370. identify the objectives of each task and address remediation needs. –– Lead students to see that there is 1 interval between 7360 and 7361 and 9 intervals between 7361 and 7370, and 7361 is less than halfway between 7360 and 7370, hence 7361 is nearer to 7360 than to 7370. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 11

–– Guide students to conclude that since 7361 is Practice 6 (CWB p. 11) nearer to 7360 than to 7370 on the number line, when we round 7361 to the nearest ten, Class practice (For Print-based Program): we get 7360. Task 1 requires students to round a whole number to –– Have a student write the statement ‘7361 is the nearest ten with the help of a number line. approximately 7360’ using the symbol ‘≈’ on the board. Remediation Task 1(a): Draw the number line on the board and (c) guide students to mark the position of 24 on the Stages: Pictorial Representation and Abstract number line. Guide students to conclude that 24 is Representation nearer to 20 than to 30, so 24 is approximately 20 In this example, students learn to round up a 4-digit when rounded to the nearest ten. number that is halfway between two tens to the greater ten. –– Draw a number line from 3800 to 3810 with Task 1(b): Draw the number line on the board and 10 equal intervals on the board. Guide students guide students to mark the position of 1275 on the to see that there are 10 equal intervals in the number line. Guide students to conclude that 1275 is number line and each interval stands for 1. halfway between 1270 and 1280, so 1275 is approximately 1280 when rounded to the nearest ten. –– Have a student point out where 3805 lies on the number line and mark the spot. Get students to Teaching tips see that 3805 is between 3800 and 3810. Task 1 –– Lead students to see that there are 5 intervals ¾¾ Reiterate to students that when a number is between 3800 and 3805 and 5 intervals between halfway between two tens, we take the greater 3805 and 3810, hence 3805 is halfway between ten as the nearest ten to the number. 3800 and 3810. Independent practice (For Print-based Program): –– Reiterate to students that when a number is halfway between two tens, we take the greater Task 2 requires students to round a whole number to ten as the nearest ten to the number. In this case, the nearest ten. the greater ten is 3810. So, the nearest ten to 3805 is 3810. For answers, go to CW Manual p. 159. –– Guide students to conclude that when we  Blended Learning Program round 3805 to the nearest ten, we get 3810. –– Have a student write the statement ‘3805 is approximately 3810’ using the symbol ‘≈’ on the board. Scholastic  Blended Learning Program From PR1ME Mathematics Interactive Edition: Let’s Learn (CB pp. 25–26) From PR1ME Mathematics Interactive Edition: Go through the teaching examples with students for Let’s Do (CB pp. 18–19) concept development. Use the detailed lesson plan Assign the tasks to students as classwork for given in the corresponding lesson notes to carry out formative assessment. Use the corresponding lesson the teaching. notes to identify the objectives of each task and address remediation needs. Learn Exercise 6 (PB pp. 14–15) Rounding numbers to the nearest hundred Assign the tasks to students as classwork for further (CWB pp. 11–12) formative assessment. Use the corresponding lesson notes to identify the objectives of each task and Learning Outcome: address remediation needs. •• Round a whole number to the nearest hundred From PR1ME Mathematics Coursework Book: Materials: Coursework Book Practice 6 (CWB p. 11) •• 1 copy of Think About It Worksheet (WS1.3) per Assign all tasks to students as homework. Use the group following notes to identify the skills needed for each task and address remediation needs. (a) Stages: Pictorial Representation and Abstract Representation Using the same teaching procedure as the earlier Learn on CWB p. 10, students will now learn to round numbers to the nearest hundred. In this example, students learn to round up a 4-digit number to the nearest hundred. 12 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6

–– Draw a number line from 6600 to 6700 with Scholastic –– Guide students to conclude that when we round 10 equal intervals on the board. Guide 84 450 to the nearest hundred, we get 84 500. students to see that there are 10 equal intervals in the number line and each interval –– Have a student write the statement ‘84 450 is stands for 10. approximately 84 500’ using the symbol ‘≈’ on the board. –– Have a student point out where 6680 lies on the number line and mark the spot. Get students to ThinkAbout It see that 6680 is between 6600 and 6700.  Blended Learning Program –– Lead students to see that 6680 is more than halfway between 6600 and 6700, hence 6680 is From PR1ME Mathematics Interactive Edition: nearer to 6700 than to 6600. Think About It (CB p. 26) Assign the task to students as classwork. Have them –– Guide students to conclude that since 6680 is complete the task in groups. Facilitate discussions nearer to 6700 than to 6600 on the number line, using the corresponding lesson notes. when we round 6680 to the nearest hundred, we get 6700. Have students get into groups. Distribute a copy of Think About It Worksheet (WS1.3) to each group. Have –– Write ‘6680 ≈ 6700’ on the board and conclude them discuss the question presented. Ask a student that ‘6680 is approximately 6700 when rounded from each group to present their answers before to the nearest hundred’. proceeding with the questions below. (b) –– What is the question asking the children to do? Stages: Pictorial Representation and Abstract (Round 3462 to the nearest hundred) Representation In this example, students learn to round down a 5-digit –– How can we round a number to the nearest number to the nearest hundred. hundred? (Use a number line to see which hundred the number is nearer to) –– Draw a number line from 15 300 to 15 400 with 10 equal intervals on the board. Guide students –– What two hundreds is 3462 between? (3400 to see that there are 10 equal intervals in the and 3500) number line and each interval stands for 10. –– What is the number that is halfway between –– Have a student point out where 15 327 lies on 3400 and 3500? (3450) the number line and mark the spot. Get students to see that 15 327 is between 15 300 and 15 400. –– Is 3462 less than halfway or more than halfway between 3400 and 3500? (More than halfway) –– Lead students to see that 15 327 is less than halfway between 15 300 and 15 400, hence –– What is the nearest hundred to 3462? (3500) 15 327 is nearer to 15 300 than to 15 400. Conclude that Sam is correct and Yen is wrong. Lead –– Guide students to conclude that since 15 327 students to see that Yen should not have looked at is nearer to 15 300 than to 15 400 on the number the digit in the hundreds place as the hundred to line, when we round 15 327 to the nearest round 3462 to. hundred, we get 15 300.  Blended Learning Program –– Write ‘15 327 ≈ 15 300’ on the board and conclude that ‘15 327 is approximately 15 300 From PR1ME Mathematics Interactive Edition: when rounded to the nearest hundred’. Let’s Do (CB p. 27) Assign the tasks to students as classwork for formative (c) assessment. Use the corresponding lesson notes to Stages: Pictorial Representation and Abstract identify the objectives of each task and address Representation remediation needs. In this example, students learn to round up a 5-digit number that is halfway between two hundreds to the Exercise 7 (PB pp. 16–17) greater hundred. Assign the tasks to students as classwork for further formative assessment. Use the corresponding lesson –– Draw a number line from 84 400 to 84 500 with notes to identify the objectives of each task and 10 equal intervals on the board. Guide students address remediation needs. to see that there are 10 equal intervals in the number line and each interval stands for 10. From PR1ME Mathematics Coursework Book: Coursework Book Practice 7 (CWB p. 12) –– Have a student point out where 84 450 lies on Assign all tasks to students as homework. Use the the number line and mark the spot. Get students following notes to identify the skills needed for each to see that 84 450 is between 84 400 and 84 500. task and address remediation needs. –– Lead students to see that 84 450 is halfway between 84 400 and 84 500. –– Reiterate to students that when a number is halfway between two hundreds, we take the greater hundred as the nearest hundred to the number. In this case, the greater hundred is 84 500. So, the nearest hundred to 84 450 is 84 500. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6955-6 Chapter 1 13