PR1ME Math PHP 1stEd_6A_CWM_SampleChapt_LR_watermarked

TM A world-class program based on top-performing 6A Singapore, Republic of Korea and Hong Kong Coursework Manual Philippine Edition

TM A world-class program based on top-performing 6A Singapore, Republic of Korea and Hong Kong Coursework Manual Scholastic Philippine Edition

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 6A (Philippine Edition) First edition 2017 ISBN 978-981-47-6959-4

Contents About TM T5 T6 Mathematics (Philippine Edition) T14 T25 Introduction to Print-based Program 1 Introduction to Blended Learning Program 2 2 Developmental Continuum 4 5 Chapter 1 Exponents 6 Scheme of Work 8 Chapter Overview and Note for Teachers 8 Lesson 1 Exponential Notation 18 Lesson 2 Mixed Operations 22 Chapter Wrap-up 23 Chapter 2 Algebra Scholastic 25 25 Scheme of Work 28 Chapter Overview and Note for Teachers 31 Lesson 1 Algebraic Equations 32 Lesson 2 Problem Solving Chapter Wrap-up 32 Chapter 3 Fractions 33 Scheme of Work 35 Chapter Overview and Note for Teachers 39 Lesson 1 Division of Fractions by Fractions 39 Lesson 2 Division of Mixed Numbers 41 Lesson 3 Problem Solving 44 Chapter Wrap-up 45 Review 1 Review A Chapter 4 Decimals Scheme of Work Chapter Overview and Note for Teachers Lesson 1 Addition and Substraction of Decimals Lesson 2 Multiplication of Decimals Lesson 3 Terminating and Non-terminating Decimals Lesson 4 Division of Decimals © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

Lesson 5 Mixed Calculations with Fractions and Decimals Scholastic 55 Lesson 6 Mixed Operations on Decimals 59 Lesson 7 Problem Solving 61 Chapter Wrap-up 63 Chapter 5 Solid Shapes 64 Scheme of Work 68 68 Chapter Overview and Note for Teachers 76 Lesson 1 Prisms and Pyramids 79 Lesson 2 Cylinders, Cones and Spheres 83 Lesson 3 Nets 83 Lesson 4 Problem Solving Chapter Wrap-up 84 87 Chapter 6 Ratio 87 96 Scheme of Work 100 Chapter Overview and Note for Teachers 107 Lesson 1 Ratio and Fraction Lesson 2 Proportion 108 Lesson 3 Problem Solving 109 Chapter Wrap-up 109 110 Chapter 7 Patterns 110 Scheme of Work Chapter Overview and Note for Teachers 111 Lesson 1 Writing the Rule for a Number Pattern Chapter Wrap-up 113 Review 2 124 Review B Answers Teacher’s Resources © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

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 978-981-47-6959-4

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 and Coursework Manual 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 978-981-47-6959-4 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 various topics. formative and 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–T35) 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 year/grade. Coursework Manual The Scheme of Work preceding each chapter is designed to assist in planning the curriculum for the entire year and to prepare for teaching individual chapters. Coursework Manual Each book spans 1 semester comprising about 75 hours of instruction. Teachers can adjust the durations based on the school calendar and the pace of individual classes. Scholastic A listing of objectives and Key mathematical Materials list Resources list resources for each lesson makes terms planning quick and easy. CWB: Coursework Book Each chapter begins with Note for Teachers. This identifies the key mathematical ideas of the chapter. Coursework Manual Note for Teachers In this chapter, students will progress to addition and subtraction of 3-digit numbers with regrouping. Students can draw part-whole or comparison bar models to help them solve addition and subtraction word problems. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6959-4 T7

Print-based Program 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 Coursework Manual Scholastic T8 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

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 Begin a lesson by walking students ScholasticCoursework Manual through the ‘Learning Outcomes’ list to encourage self-directed learning. Stage: Concrete Experience Start 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 Coursework Book to guide students’ thought processes. Stage: Pictorial Representation 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. Stage: Abstract Representation T9 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 978-981-47-6959-4

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 v Blended Learning Programv When necessary, refer to the teaching tips in the Coursework Manual to address remediationthe ten-rods. Relate it back to the grouping of the ten-rods. Reiterate that there are 7 tens in From PR1ME Mathematics Interactive Edition: needs. all. Let’s Do (CB p. 44) − Lastly, have them look at the columns with the Assign the tasks to students as classwork for formative hundred-squares. Relate it back to the assessment. Use the corresponding lesson notes to grouping of the hundred-squares. Reiterate identify the objectives of each task and address that there are 5 hundreds in all. 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 see formative assessment. Use the corresponding lesson hreCopworetusheernstaealgtwioonroit.hTrmhkisrBealsoastooecskiatotiothneispimicptoorriatal nt as it helps notes to identify the objectives of each task and address remediation needs. The icon indicates class students to visualize the addition. It allows them to From PR1ME Mathematics Coursework Book: understand and interpret the vertical form, especially practice. After a concept is taught the writing of digits above the augend in the vertical Coursework Book Practice 1 (CWB p. 31) form when regrouping occurs. This is an anchor for Assign all tasks to students as homework. Use the in Learn, go through related learning addition with regrouping in other place following notes to identify the skills needed for each values, as well as more advanced forms of regrouping task and address remediation needs. Practice tasks as class practice. that involve more than one place value. The three-step Practice 1 (CWB p. 31) approach (add the ones, then the tens and lastly the Discuss students’ responses and− Next, have students look at the columns with hundreds) guides students to add systematically, Class practice (For Print-based Program): the ten-rods. Relate it back to the grouping of vrBeldeuncdiendg LtheearlinkienlgihoPorodgorafmcavreless mistakes when they are performing the addition in vertical form. Task 1 requires students to add a 3-digit number and a remediate if necessary.the ten-rods. Reiterate that there are 7 tens in 1-digit, 2-digit or 3-digit number, with regrouping in all. From DP−oR1(MCWEBrMipte.a4tthh4ee) mvearttiiccsaIlnftoerrmacotfiv‘e42E6d+iti1o4n6: ’ on the ones. The place values are provided in the vertical − Lastly, have them look at the columns with the Let’s form of addition to guide students. hundred-squares. Relate it back to the Assign thebtaosakrsdt.oFisrstut,dgeunidtseasstucdlaesnstws otorkafodrdfothrme aotnivees. grouping of the hundred-squares. Reiterate assessmenHt.aUvseetthheemcloororeksaptotnhdeindgigleitsssionnthneootensetsoplace Remediation that there are 5 hundreds in all. identify theinothbejevcetirvteicsaol ffoeramcohftaadskdaitinodn.aSdtuddreesnsts should Task 1(a): Reteach adding a 1-digit number and a remediatiobnenaebeledst.o state that 6 ones + 6 ones = 12 2-digit number with regrouping in ones. Then, go Assign the rest of the tasks asStage: Abstract Representation ones. through Task 1(a). Highlight that 3 ones + 7 ones = homework for independent practice.Lastly, present the addition in vertical form. Having 10 ones, which can be regrouped into 1 ten. fAnEaoxodsrestmdiergcrasenis−ttseiotsvher1ieedR1scvta(methtPeeauustneBeseribsdtttekdeniippeefcssyriisspana2actm.tot.tltthWosioef3oeeosnlr1orntntiierau–thomotens3d.labk.2reUettoeRjahe)esn1fepeetcdt2alrsattestahidoh.vatsededneeesdeisncttcchiistootolaoaiecofnlurtsanreirsmoeoewnaonsngnpcofbrostohorthekhnwuneterfapidtetohbhsioignrnekontgrfghoauapeerburlnastedphadigus.neescneortdki.htnHteinoatove 1 ten + 5 tens = 6 tens. Therefore, 353 + 7 = 360. gone through the previous stages, students will see how the algorithm relates to the pictorial AtfCFCoarsoolsslookmuigwrausnPein−nrRawdsg1lleoManttliThpranodwekoEhaisocdntetBkMvehoktrnsoio+esenaa,torrsgto2tigkvtsakoheutttsrelPheheitiMrdrdmurteeenmaiecdepsmaccaneaer+sttoetditlnilniccouf4slfiutyoaesedosutmrnttCekeamih1aotnnnosaaen(sstlouhtCtssiw=nrfootktWsheaoimine7tlelheBsdwabtededndtpodywhensii.grtd.ehokise3oiatrbtd1tsBnkhev)ae.o.ieninnUAcdo-gttskrkgehfoe:oatsendottrisuhnstet.debe,haWnreyeecsnrlihapttsetlaetch1ee Task 1(b): Reteach adding a 2-digit number and a representation. This association is important as it helps addition of the tens in the vertical form of 2-digit number with regrouping in ones. Then, go students to visualize the addition. It allows them to through Task 1(b). Highlight that 6 ones + 8 ones = understand and interpret the vertical form, especially addition on the board. 14 ones, which can be regrouped into 1 ten 4 ones. the writing of digits above the augend in the vertical Prac−ticeFin1a(llCy,WgBuidpe. 3st1u)dents to add the hundreds by 1 ten + 4 tens + 3 tens = 8 tens. Therefore, 646 + 38 = form when regrouping occurs. This is an anchor for 684. learning addition with regrouping in other place values, as well as more advanced forms of regrouping Task 1(c): Reteach adding a 3-digit number and a that involve more than one place value. The three-step 3-digit number with regrouping in ones, using smaller approach (add the ones, then the tens and lastly the numbers e.g. 119 + 123. Then, go through Task 1(c). hundreds) guides students to add systematically, Highlight that 4 ones + 8 ones = 12 ones, which can be reducing the likelihood of careless mistakes when they regrouped into 1 ten 2 ones. 1 ten + 6 tens = 7 tens. are performing the addition in vertical form. 4 hundreds + 1 hundred = 5 hundreds. Therefore, 404 + Scholastic having them look at the digits in the hundreds 168 = 572. The objective of each task is stated− Write the vertical form of ‘426 + 146’ on the Class pracptilcaece(FionrtPhreinvt-ebrtaicseadl foPrrmogoraf mad):dition. Again, Teaching tips board. First, guide students to add the ones. relate 4 hundreds + 1 hundred = 5 hundreds Task 1 in the Coursework Manual, enablingHave them look at the digits in the ones place T1ofoa-ndrsemkigs1.iotT−,rfhe2aeq-dduptbssTdihqtogilaruaieeuittdccicsoavookeesnrerenntturvo3tctstosda.i-lctduWlelhogaudigenouerleititfkistpsdoe, naawitrectomurthrtesmioteatthoeuprdbieafadrtdeoadhlecrvrdeda,noeidwditlpatu3siieo.tird-mtieddohndsningeiroitsneiinofotwgtttnnnhahritouetetshhiumeovehtpnnhbeuitbenreebntgoinrdyhcaacuriahnerenndalddd.vsrianeingd- Ø When reteaching, follow the same procedure in the vertical form of addition. Students should as the example in Learn (CWB p. 30). Use base learning andbe able to state that 6 ones + 6 ones = 12 ten blocks to introduce the concept of teachers to check ones. TR2a-edsmkige1it(d−aniau):tmiRRb‘o4ebeyn2teit6teehra+erwac1ittthe4eh6natrshe=d,agdt5htri7onew2gun’epoatiahnn1edgt-ddhhineiutghnobitednonreoaeusndrm.desT.b.shefeirrnsat,,gnfodolloawed regrouping. Then, continue with the addition in address remediation needs.− Reiterate that 12 ones can be regrouped into vertical form. 1 ten 2 ones. Relate the regrouping back to Answers are provided for all tasks.the pictorial representation on the page. Have students look at the columns with the unit through Task 1(a). Highlight that 3 ones + 7 ones = cubes. Write the addition of the ones in the 10 ones, which can be regrouped into 1 ten. vertical form of addition on the board. 1 ten + 5 tens = 6 tens. Therefore, 353 + 7 = 360. − Then, guide students to add the tens by Task 1(b): Reteach adding a 2-digit number and a having them look at the digits in the tens place in the vertical form of addition. Again, relate 1 2-digit number with regrouping in ones. Then, go ten + 2 tens + 4 tens = 7 tens back to the pictorial representation by having students through Task 1(b). Highlight that 6 ones + 8 ones = look at the columns with the ten-rods. Write the addition of the tens in the vertical form of 114teonn e +s4, which can be regrouped into 1 ten 4 ones. Chapter 3 27 addition on the board. tens + 3 tens = 8 tens. Therefore, 646 + 38 = thinking, − Finally, guide students to add the hundreds by 684.© 2015 Scholastic Education International (S) Pte Ltd ISBN 978-981-09-0499-9 having them look at the digits in the hundreds place in the vertical form of addition. Again,   relate 4 hundreds + 1 hundred = 5 hundreds Task 1(c): Reteach adding a 3-digit number and a back to the pictorial representation by having 3-digit number with regrouping in ones, using smaller common misconceptions andstudents look at the columns with the hundred- squares. Write the addition of the hundreds in numbers e.g. 119 + 123. Then, go through Task 1(c). Highlight that 4 ones + 8 ones = 12 ones, which can be regrouped into 1 ten 2 ones. 1 ten + 6 tens = 7 tens. To address errors and strengthen4 hundreds + 1 hundred = 5 hundreds. Therefore, 404 + mathematical have 168 = 572. students discuss, communicate, reason andthe vertical form of addition on the board. justify mathematical ideas and understanding using − To conclude, write the addition sentence Teaching tips scenarios found in the Think About It feature.‘426 + 146 = 572’ on the board. Task 1 − Reiterate that we add the ones first, followed by the tens, then the hundreds. Ø When reteaching, follow the same procedure as the example in Learn (CWB p. 30). Use base ten blocks to introduce the concept of Coursework Manual regrouping. Then, continue with the addition inCoursework Manual vertical form. Have students form WS2.2 Think About it Worksheet groups to discuss   Hari bought 15 marbles. 27 the question. Ask a© 2015 Scholastic Education International (S) Pte LtHd isISBfNr9ie78-n98d1-09g-04a99v-9e him 10 marbles. Chapter 3   How many marbles does Hari have altogether? representative from 15 (part) 10 (part) 15 (part) ? (whole) each group to present ? (whole) 10 (part) and justify the group’s response. Sam Yen Who has drawn the bar model correctly? Why? Lesson notes are provided to facilitate discussions and guide students to arrive at the correct conclusion. 106 Teacher's Resources © 2015 Scholastic Education International (S) Pte Ltd ISBN 978-981-09-0499-9 T10 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

Teaching Concepts and Skills — Developing Processes and Strategies Print-based Program 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 level of difficulty. Refer to the problem-solving process page at the back of the Coursework Book for a detailed description of the problem-solving process. Coursework Book Scholastic Coursework Manual T11 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. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6959-4

Print-based Program 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. Coursework Manual Coursework Manual WS3.2 Create Your Own Worksheet Use the given words and numbers to write a) one addition word problem. b) one subtraction word problem. Dia stamps give away Julio stickers how many Andy left game cards 483 Yara altogether erasers 163 buy 342 Consolidate Scholastic 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 interpret knowledge gained and apply their understanding. © 2014 Scholastic Education International (Singapore) Pte Ltd, A Division Of Scholastic Inc. 121 Coursework Manual Coursework Manual Assign Reviews as class tests WS3.3 Review 1 for summative assessment or homework. 1. Write the numbers. a) one hundred and thirty-seven The objective of each task b) six hundred and four is stated in the Coursework c) nine hundred and eighty Manual, enabling teachers to identify and address areas 2. Write the numbers in words. b) 520 of weakness. a) 358 d) 813 c) 709 Answers are provided for all tasks and worked solutions 3. Write the numbers. are provided for all word a) 1 hundred 2 tens 4 ones = problems. b) 8 hundreds 5 tens = 4. Write the numbers. b) 900 + 3 = a) 200 + 90 + 1 = ________ 5. Write the amount of money in the purse. 6. Fill in the circles with > or <. b) 533 473 a) 98 203 d) 915 916 c) 648 652 © 2015 Scholastic Education International (S) Pte Ltd ISBN 978-981-09-0499-9 Teacher's Resources 1 2A_TG Review 1_C3_2P_24Dec14.indd 1 24/12/14 1:42 PM T12 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

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 Look at the tens. Learn 8 9–1=8 1+ + =9 Adele wants to add two numbers. +5 4+4=8 The digits in the tens place are the same. Fill in the missing digits and find the two numbers. 990 1 845 + 45 1 Understand How many digits are there in each 990 the problem. of the two numbers? How many digits are missing? 4 Check 3 Look at the hundreds. 2 Plan what to do. How do I add a 3-digit number Did you answer and a 2-digit number? the question? 8 + 0 is not equal to 9. Do I need to regroup? Is your answer Let’s go back to Step 2. correct? I can guess and check and Guess 2 work backwards. 3 Work out the 2 Look at the tens. Answer. 3 Work out the To add a 3-digit number and a 19 – 1 = 18 1+ + =9 7 Answer. 2-digit number, first add the ones. 4 Check 9 + 9 = 18 1 + + = 19 3 Then, add the tens. Did you answer Regroup the tens. Lastly, add the hundreds. the question? 11 Is your answer 895 Guess 1 correct? + 95 990 1 Look at the ones. 3 Look at the hundreds. 1+8 =9 5 + 5 = 10 +5=0 7 + 5 = 10 3 The two numbers are 895 and 95. 1 Regroup the ones. 85 895 + 95 = 990 Both numbers have the same +5 digit in the tens place. My answer is correct. 990 100 Teacher's Resources © 2014 Scholastic Education International (Singapore) Pte Ltd, A Division Of Scholastic Inc. © 2014 Scholastic Education International (Singapore) Pte Ltd, A Division Of Scholastic Inc. Teacher's Resources 101 number, and the digit in the ones place of the 100 less than 307, they have to subtract 1 hundred number decreases by 1. Hence, ’1 less than’ from 307. 516 is 515. − Similarly, guide students to understand that to Task 1(f): Refer students to the picture of the base ten find ’10 less than’ 516, we have to decrease blocks on the page. Guide students to see that to find the digit in the tens place of 516 by 1. Hence, 100 more than 593, they have to add 1 hundred to 593. ’10 less than’ 516 is 506. − Finally, guide students to understand that to Teaching tips find ‘100 less than’ 516, we have to decrease Task 1 the digit in the hundreds place of 516 by 1. Hence, ’100 less than’ 516 is 416. Ø Highlight to students that when they find 1 more than or 1 less than a number, only the v Blended Learning Programv ones place of the number changes; when they find 10 more than or 10 less than a From PR1ME Mathematics Interactive Edition: number, only the tens place of the number Let’s Do (CB p. 23) changes; and when they find 100 more than Assign the tasks to students as classwork for formative or 100 less than a number, only the hundreds assessment. Use the corresponding lesson notes to place of the number changes. Reiterate to identify the objectives of each task and address students that the digits in the other places of remediation needs. the number remain unchanged. Independent practice (For Print-based Program): Scholastic Exercise 8 (PB pp. 19–20) Tasks 2–4 requires students to add or subtract 1, 10 or Assign the tasks to students as classwork for further 100 to find 1, 10 or 100 more than or less than the given Wrapping Up the Chapterformative assessment. Use the corresponding lesson numbers without pictorial guidance. notes to identify the objectives of each task and address remediation needs. For answers, go to CW Manual p. 112. Ending the chapter byFrom PR1ME Mathematics Coursework Book: summarizing the key learning points helps students realize how much learning has taken place.Coursework Book Practice 6 (CWB pp. 13–15) This helpsv Blended LetahrneingmProgroamrvg anize the information into a meaningful context in Assign all tasks to students as homework. Use the following notes to identify the skills needed for each lessons. This is a crucial step to help students their minds and ensures learning is solidified for futuretask and address remediation needs. From PR1ME Mathematics Interactive Edition: Practice 2 (CB p. 24) remember and apply the information they have learned.Assign the tasks to students as classwork for summative assessment. Use the corresponding lesson notes to Practice 6 (CWB pp. 13–15) identify the objectives of each task and address remediation needs. Coursework Manual Class practice (for Print-based Program): Task 1 requires students to add or subtract 1, 10 or 100 v Blended Learning Programv to find 1, 10 or 100 more than or less than the given numbers. Go through the following points with students to summarize the key learning points in this chapter. Remediation Task 1(a): Refer students to the picture of the base ten Reiterate the following points: blocks on CWB p. 14. Guide them to see that to find − We read and write 3-digit numbers in terms of 1 more than 211, they have to add 1 one to 211. hundreds, tens and ones. − We use the symbols ‘>’ and ‘<’ to compare Task 1(b): Refer students to the picture of the base ten numbers. ‘>’ means ‘greater than’ and ‘<’ blocks on the page. Guide them to see that to find means ‘smaller than’. 10 less than 342, they have to subtract 1 ten from 342. − When comparing numbers, we start from the digits with the greatest place value. Task 1(c): Refer students to the picture of the base ten − We add to find a number which is 1, 10 or 100 blocks on the page. Guide them to see that to find more than a given number. 1 less than 451, they have to subtract 1 one from 451. − We subtract to find a number which is 1, 10 or Task 1(d): Refer students to the picture of the base ten 100 less than a given number.   blocks on the page. Guide them to see that to find 10 more than 532, they have to add 1 ten to 532. Task 1(e): Refer students to the picture of the base ten blocks on the page. Guide students to see that to find 12 Chapter 1 © 2015 Scholastic Education International (S) Pte Ltd ISBN 978-981-09-0499-9   © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6959-4 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 and Coursework Manual 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 978-981-47-6959-4 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 year/grade. Interactive Edition The Scheme of Work preceding each chapter is designed to assist in planning the curriculum for the entire year and to prepare for teaching individual chapters. Coursework Manual Each book spans 1 semester comprising about 90 hours of instruction. Teachers can adjust the durations based on the school calendar and the pace of individual classes. Scholastic A listing of objectives and Materials list Resources list resources for each lesson makes planning quick and easy. Key mathematical CB: Coursebook terms PB: Practice Book CWB: Coursework Book Each chapter begins with Note for Teachers. This identifies the key mathematical ideas of the chapter. Coursework Manual Note for Teachers In this chapter, students will progress to addition and subtraction of 3-digit numbers with regrouping. Students can draw part-whole or comparison bar models to help them solve addition and subtraction word problems. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6959-4 T15

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 Instructions in grey boxes Clicking on the ‘Lesson Scholasticthroughout the Coursework Notes’ tab directs teachers Manual are for teachers using to the corresponding page the Blended Learning Program. in the Teacher’s Guide. Interactive Edition Teachers are directed to the corresponding page in the Interactive Edition of the Coursebook. T16 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

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 978-981-47-6959-4 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 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 978-981-47-6959-4

Practice in the Coursework Book provides students with further opportunities for home practice. Blended Learning Program Assign all the tasks in Practice to students as homework. When necessary, refer to the teaching tips in the Coursework Manual to address remediation needs. Coursework Book Coursework Manual Scholastic To address common misconceptions and errors and strengthen mathematical thinking, have students discuss, communicate, reason and justify mathematical ideas and understanding using 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 978-981-47-6959-4 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 978-981-47-6959-4

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 978-981-47-6959-4 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. number, and the digit in the ones place of the 100 less than 307, they have to subtract 1 hundred number decreases by 1. Hence, ’1 less than’ from 307. 516 is 515. − Similarly, guide students to understand that to Task 1(f): Refer students to the picture of the base ten find ’10 less than’ 516, we have to decrease blocks on the page. Guide students to see that to find the digit in the tens place of 516 by 1. Hence, 100 more than 593, they have to add 1 hundred to 593. ’10 less than’ 516 is 506. − Finally, guide students to understand that to Teaching tips find ‘100 less than’ 516, we have to decrease Task 1 the digit in the hundreds place of 516 by 1. Hence, ’100 less than’ 516 is 416. Ø Highlight to students that when they find 1 more than or 1 less than a number, only the v Blended Learning Programv ones place of the number changes; when they find 10 more than or 10 less than a From PR1ME Mathematics Interactive Edition: number, only the tens place of the number Let’s Do (CB p. 23) changes; and when they find 100 more than Assign the tasks to students as classwork for formative or 100 less than a number, only the hundreds assessment. Use the corresponding lesson notes to place of the number changes. Reiterate to identify the objectives of each task and address students that the digits in the other places of remediation needs. the number remain unchanged. Independent practice (For Print-based Program): Exercise 8 (PB pp. 19–20) Tasks 2–4 requires students to add or subtract 1, 10 or 100 to find 1, 10 or 100 more than or less than the given Wrapping Up the ChapterAssign the tasks to students as classwork for further numbers without pictorial guidance. formative assessment. Use the corresponding lesson notes to identify the objectives of each task and Endingaddrtehss reemecdiahtioan npeedtse. r by summariFzoirnangswerst, hgoeto CkWeMaynuallep. a112r. ning points helps students realize how much ltreehaemrirnemimntfAFCoarsooglsislokmbunigwrasnPedinenhRawdg1llosrMaantradkoEasadtsBkMersoesannotsttotsokhadsrdePeitdmurmaekdacneaeetettdiniiccfityasnpesnttCaih6osospen(uhuCpsnroklWseimyerllleBsweaednpowtesprsc.okeh.rdB1kleee.o3eU–do1s.kafe5:oi)nTtrhrehenfaociihsnrmhgeaivAPFslrrsopatsBmsicigleotsoninPcdRtenhl1teie2Mdhdt(EtaLCeeMishBkfaasiprmentet.hoin2ey4sgdmt)uPoadrhtoeifcrgnosagrtasInmratvaesvfrceaunlcatsitisvlzwueeoeErradkeiftoitorrhnnsl:ueemesmdsaintoi.vefnosr.mThaistioisnainctroucaiaml seteapnitnoghfuellpcostnutdeextnitns Practice 6 (CWB pp. 13–15) assessment. Use the corresponding lesson notes to identify the objectives of each task and address remediation needs. Coursework Manual Class practice (for Print-based Program): Reiterate key learningTask 1 requires students to add or subtract 1, 10 or 100 v Blended Learning Programv to find 1, 10 or 100 more than or less than the given Go through the following points with students to poinnutmsbaersn. d provide summarize the key learning points in this chapter. examples where necessary.Remediation Reiterate the following points: Task 1(a): Refer students to the picture of the base ten − We read and write 3-digit numbers in terms of blocks on CWB p. 14. Guide them to see that to find hundreds, tens and ones. 1 more than 211, they have to add 1 one to 211. − We use the symbols ‘>’ and ‘<’ to compare numbers. ‘>’ means ‘greater than’ and ‘<’ Task 1(b): Refer students to the picture of the base ten means ‘smaller than’. blocks on the page. Guide them to see that to find − When comparing numbers, we start from the 10 less than 342, they have to subtract 1 ten from 342. digits with the greatest place value. − We add to find a number which is 1, 10 or 100 Task 1(c): Refer students to the picture of the base ten more than a given number. blocks on the page. Guide them to see that to find 1 less than 451, they have to subtract 1 one from 451. − We subtract to find a number which is 1, 10 or 100 less than a given number.   Task 1(d): Refer students to the picture of the base ten blocks on the page. Guide them to see that to find 10 more than 532, they have to add 1 ten to 532. Task 1(e): Refer students to the picture of the base ten blocks on the page. Guide students to see that to find 12 Chapter 1 © 2015 Scholastic Education International (S) Pte Ltd ISBN 978-981-09-0499-9   T22 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

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 978-981-47-6959-4 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 978-981-47-6959-4

Developmental Continuum Year/Grade 4 Year/Grade 5 Year/Grade 6 NUMBERS AND NUMBER SENSE Whole Numbers / ScholasticRead and write a Read and write a number Express a number in Place Value number within 100 000 within 1 000 000 000 — exponential notation. — the numeral and the the numeral and the Addition / Subtraction corresponding number corresponding number word. Describe the exponent word. and the base in a number Use number notation Identify the values of expressed in exponential and place values (ten digits in a number within notation. thousands, thousands, 1 000 000 000. Find the value of a number hundreds, tens, ones). expressed in exponential Compare and order Compare and order numbers notation. numbers within 100 000. within 1 000 000. Understand and apply the Grouping, Exponent, Find the number which is 1, Round a whole number to Multiplication, Division, 10, 100, 1000 or 10 000 more the nearest thousand, ten Addition and Subtraction than (or less than) a given thousand, hundred thousand, (GEMDAS) rule to do mixed number within 100 000. million, ten million or hundred operations. million. Identify real-life situations Read a number line. that make use of integers. To use the divisibility rules for Describe integers. Round a whole number to 2 to 12. the nearest ten or hundred. Find the common factors Represent integers on a and greatest common factor number line. List all factors of a whole of up to four numbers. number up to 100. Find out if a number is a Compare and order integers common factor of two given with whole numbers, Find out if a 1-digit whole numbers. fractions and decimals. number is a factor of a Find the common multiples Add, subtract, multiply and given whole number. and least common multiple divide integers. Differentiate prime numbers of up to four numbers. from composite numbers. Find out if a number is a Do mixed operations common multiple of two involving integers. Use prime factorization to given numbers. write a given number as a Create and solve problems Solve word problems product of its prime factors. involving factors, multiples involving the basic List the multiples of a whole and divisibility rules for 2 to 12. operations of integers. number up to 10. Estimate an answer in Solve challenging word Relate factors and multiples. addition or subtraction. problems involving whole Find out if a whole number is numbers. a multiple of a given whole Do mixed operations number. involving addition and Identify multiples of 2, 5 and subtraction without 10. parentheses. Estimate an answer in Do mixed operations 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 978-981-47-6959-4 T25

Year/Grade 4 Year/Grade 5 Year/Grade 6 NUMBERS AND NUMBER SENSE (continued) Multiplication / Observe the associative Estimate an answer in Solve challenging word Division property of multiplication. multiplication or division. problems involving whole numbers. Apply the commutative Multiply or divide a whole and associative properties number by 10, 100 or 1000. of multiplication in computation. Multiply or divide a 4-digit Multiply or divide a whole whole number by a 1-digit number by tens, hundreds or whole number. thousands. Multiply or divide a whole Do mixed operations number up to 4 digits by 10. involving multiplication and division without parentheses. Multiply a whole number up Do mixed operations to 3 digits by a 2-digit whole involving addition, number. subtraction, multiplication and division with or without parentheses. Multiply a whole number up Multiply a 4-digit whole to 4 digits by tens. number by a 2-digit whole number. Estimate an answer in Multiply a 3-digit or 4-digit multiplication or division. whole number by a 3-digit whole number. Scholastic Check reasonableness of an Estimate an answer in answer in multiplication or multiplication by 2-digit and division. 3-digit whole numbers. Solve up to 3-step word Divide a whole number up problems involving to 4 digits by a 2-digit whole multiplication and division. number. Mentally multiply up to a Solve multi-step word 2-digit whole number by a problems involving the four 2-digit whole number. operations of whole numbers. Mentally divide up to a 3-digit whole number by a 1-digit whole number. Fractions / Concepts Write the sum of a whole Associate a fraction with number and a proper division. fraction as a mixed number. Read a number line Express an improper fraction involving fractions and as a whole number, mixed mixed numbers. number or decimal. Interpret an improper fraction as a multiple of a unit fraction. Write a whole number or a mixed number as an improper fraction, and vice versa. Fractions / Add two or three like or Divide a whole number by Divide a proper fraction by a Arithmetic Operations related fractions with a sum another whole number and proper fraction. more than 1 whole. write the quotient as a mixed number. Subtract one or two Add or subtract unlike Divide a mixed number by fractions from a whole number. fractions and mixed numbers. a fraction, whole number or another mixed number. Understand a fraction of a Multiply mentally proper Divide a whole number by a group of objects. fractions with denominators mixed number. up to 10. Find the value of a Multiply fractions. Solve a 1-step word problem involving division of proper fractional part of a quantity. fractions and mixed numbers. Multiply a fraction and a Understand that multiplying Add a fraction or mixed whole number. a fraction by its reciprocal number and a decimal. equals to 1. T26 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

Year/Grade 4 Year/Grade 5 Year/Grade 6 NUMBERS AND NUMBER SENSE (continued) Fractions / Express a part of a quantity Multiply a whole number by a Subtract a fraction or mixed Arithmetic Operations as a fraction. (continued) mixed number. number from a decimal, and vice versa. Convert a measurement Multiply a fraction or mixed Multiply a fraction or mixed of length, mass, volume of number by a mixed number. number and a decimal. liquid or time from a larger unit of measure involving a fraction or a mixed number to a smaller unit. Convert a measurement Divide a fraction by a whole Divide a fraction by a of length, mass, volume number. decimal, and vice versa. of liquid 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 Solve challenging word length, mass, volume of liquid fraction. problems involving fractions. 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. Decimals Read and write a decimal Read and write a decimal up Add or subtract decimals up up to 3 decimal places. Scholastic to 4 decimal places. to 4 decimal places. Express a fraction or mixed Interpret a decimal up to 4 Multiply a decimal by 0.1 number whose denominator decimal places in terms of and 0.01 mentally. is a factor of 10, 100 or 1000 ones, tenths, hundredths, as a decimal. thousandths and ten thousandths. Interpret a decimal up to Identify the values of digits in Multiply a decimal up to 3 decimal places in terms a decimal up to 4 decimal 2 decimal places by a of ones, tenths, hundredths places. decimal with 2 decimal and thousandths. places. Identify the values of digits in Compare and order Identify terminating and non-terminating decimals. a decimal up to 3 decimal decimals up to 4 decimal places. places. Express a decimal up to 3 Round a decimal to 3 Estimate a quotient. decimal places as a fraction decimal places. or mixed number in its simplest form. Read a number line Add or subtract decimals up Divide a decimal by a 2-digit involving decimals. to 3 decimal places. whole number. Find the number which is 0.1, Divide a decimal by a 1-digit Divide a whole number by 0.01 or 0.001 more than (or whole number and round the a decimal up to 2 decimal less than) a given number. quotient to 2 decimal places. places. Compare and order Express a mixed number as a Divide a decimal up to 4 decimals up to 3 decimal places. decimal correct to 2 decimal decimal places by 0.1, 0.01, places. 0.001 mentally. Compare and order whole Multiply or divide a decimal Divide a decimal up to numbers, decimals and or a whole number by 10, 100 2 decimal places by a fractions. or 1000. decimal up to 2 decimal places. Round a decimal to the Multiply or divide a decimal Add a fraction or mixed nearest whole number or to or a whole number by tens, number and a decimal. 1 decimal place. hundreds or thousands. Add or subtract decimals up Multiply a decimal up to 2 Subtract a fraction or mixed number from a decimal, and to 2 decimal places. decimal places by a 2-digit vice versa. whole number. Multiply or divide decimals Multiply a decimal up to 2 Multiply a fraction or mixed up to 2 decimal places by a decimal places by a decimal number and a decimal. 1-digit whole number. with 1 decimal place. Divide a whole number Estimate an answer in Divide a fraction by a by a 1-digit whole number addition, subtraction and decimal, and vice versa. and give the quotient as a multiplication. decimal. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6959-4 T27

Year/Grade 4 Year/Grade 5 Year/Grade 6 NUMBERS AND NUMBER SENSE (continued) Decimals (continued) Estimate an answer in Check reasonableness of an Perform mixed operations addition, subtraction, multiplication or division answer in addition, subtraction with or without parentheses involving decimals. and multiplication. involving decimals. Check reasonableness Convert a measurement of Solve multi-step and of an answer in addition, length, mass or volume of liquid challenging word problems subtraction, multiplication or from a larger unit of measure involving decimals. division involving decimals. involving a decimal to a smaller unit, and vice versa. Solve up to 2-step word Convert a measurement of problems involving length, mass or volume of decimals. 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. Rate Find the rate by expressing one quantity per unit of another quantity. Find a quantity using the given rate. Scholastic Solve up to 3-step word problems involving rate. Ratio Use a ratio to compare two Express one quantity as a or three quantities. fraction of another given their ratio. Use a comparison bar model Find how many times one to show a ratio. quantity is as large as another given their ratio. Use a ratio to compare Solve word problems two quantities given in a involving ratio and fraction. comparison bar model. Write equivalent ratios. Identify situations of direct and inverse proportion. Write a ratio in its simplest Write a ratio to compare form. quantities that are in proportion. Find the missing term in a pair Solve word problems of equivalent ratios. involving ratio and proportion. Solve multi-step word Solve multi-step and problems involving ratio. challenging word problems involving ratio. Percent Read and interpret a Express a fraction as a percentage of a whole. percent. Express a fraction as a Express a decimal as a percent, and vice versa. percent, and vice versa. Express a decimal as a Express one quantity as a percent, and vice versa. percentage of another. Express a percent as a ratio in Find the whole given a part its simplest form. and the percentage. Express a part of a whole as Solve word problems a percent. involving percentage. Understand that 1 whole is 100%. Solve challenging word problems involving percentage. 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. T28 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

Year/Grade 4 Year/Grade 5 Year/Grade 6 MEASUREMENT Length Convert a measurement of Convert a measurement of length from a larger unit of length from a larger unit of measure involving a fraction measure involving a decimal or a mixed number to a to a smaller unit, and vice smaller unit. versa. Convert a measurement of Convert a measurement of length from a larger unit of length from a larger unit of measure involving a mixed measure involving a decimal number to compound units. to compound units, and vice versa. Express a measurement of length in the smaller unit as a fraction of a measurement in the larger unit. Multiply or divide a measurement of length in compound units. Solve up to 2-step word problems involving length in compound units. Perimeter / Area Find the perimeter of a figure Identify the base and height Draw a circle with a given made up of 1-centimeter or of a triangle. radius or diameter. 1-meter squares. Scholastic Identify and measure the Measure the perimeter of a Find the area of a triangle radius and diameter of a circle. figure. using formula. Find the diameter of a circle Compare the areas and Find the area of a figure given its radius, and vice perimeters of figures made related to the area of a versa. up of 1-centimeter or triangle. 1-meter squares. Relate the circumference of a circle to its diameter. Find the perimeter of a Find the area of a rectilinear figure given the parallelogram using formula. Understand the concept of lengths of all its sides. pi (π). Find the area and perimeter Find the area of a rhombus Relate the area of a circle to of a square given the length using formula. its radius. of one side. Find the circumference and Find the area and perimeter Find the area of a trapezoid area of a circle given its radius or diameter. of a rectangle given its using formula. Find the perimeter and length and breadth. area of a semicircle or a quadrant. Convert a measurement in Estimate the area of a Find the perimeter and square centimeters to square triangle, a parallelogram, a area of a figure made up of squares, rectangles, meters, and vice versa. rhombus and a trapezoid. triangles, parallelograms, rhombuses, circles, Find one side of a rectangle Find the area of a figure semicircles and quadrants. given the other side and its made up of triangles, area or perimeter. parallelograms, rhombuses Solve word problems and trapezoids. involving circumference and area of a circle, semicircle Find the length of one side and quadrant. of a square given its area or perimeter. Describe the total surface area of solids and name the Find the area and perimeter unit of measure. of a figure made up of squares and/or rectangles. Find the total surface area of prisms, pyramids, cylinders, Solve word problems cones and spheres using involving area and perimeter formulae. of figures made up of squares and/or rectangles. Solve word problems involving total surface area of solids. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6959-4 T29

Year/Grade 4 Year/Grade 5 Year/Grade 6 MEASUREMENT (continued) Volume Convert a measurement Convert a measurement of Visualize the volume of solids of volume of liquid from volume of liquid from a larger using non-standard units. a larger unit of measure unit of measure involving a involving a fraction or a decimal to a smaller unit, mixed number to a smaller and vice versa. unit. Convert a measurement Convert a measurement of Find the relationship of volume of liquid from volume of liquid from a larger between the volume of a a larger unit of measure unit of measure involving a prism and a pyramid. involving a mixed number to decimal to compound units, compound units. and vice versa. Express a measurement Differentiate solid figures from Find the relationship of volume of liquid in the plane shapes and recognize between the volume of a smaller unit as a fraction of that solid figures have cylinder and a cone. a measurement in the larger volume. unit. Multiply or divide a Visualize a solid that is made Find the relationship measurement of volume of up of unit cubes and state its between the volume of a liquid in compound units. volume in cubic units. cylinder and a sphere. Solve up to 2-step word Visualize the sizes of 1 cubic Find the volume of prisms, problems involving volume centimeter and 1 cubic pyramids, cylinders, cones of liquid in compound units. meter. and spheres using formulae. Find the volume of a solid Solve word problems made up of 1-centimeter or involving volume of solids. 1-meter cubes. Scholastic Compare the volumes of solids Solve challenging word made up of 1-centimeter or problems involving volume. 1-meter cubes. Use appropriate units of measure for volume. Find the volume of a cuboid given its length, breadth and height. Recognize the equivalence of 1 liter, 1000 milliliters and 1000 cubic centimeters. Convert from one unit of measure of volume to another. Find the volume of liquid in cubic or rectangular containers. 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. Mass Convert a measurement of Convert a measurement of mass from a larger unit of mass from a larger unit of measure involving a fraction measure involving a decimal or a mixed number to a to a smaller unit, and vice smaller unit. versa. Convert a measurement of Convert a measurement of mass from a larger unit of mass from a larger unit of measure involving a mixed measure involving a decimal to number to compound units. compound units, and vice versa. T30 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

Year/Grade 4 Year/Grade 5 Year/Grade 6 MEASUREMENT (continued) Interpret a speed as the distance traveled per unit of Mass (continued) Express a measurement of time. mass in the smaller unit as a Read and write units of fraction of a measurement speed such as km/h, m/min, in the larger unit. m/s and cm/s. Understand the relationship Multiply or divide a between distance, time and measurement of mass in speed. compound units. Calculate speed, distance or time taken given two of the Solve up to 2-step word quantities. problems involving mass in Calculate average speed. compound units. Solve word problems involving speed. Time: Clock Convert a measurement of Solve challenging word time from a larger unit of problems involving speed. measure involving a fraction or a mixed number to a T31 smaller unit. Convert a measurement of time from a larger unit of measure involving a mixed number to compound units. Express a measurement of time in the smaller unit as a fraction of a measurement in the larger unit. Scholastic Tell time to the second. Estimate and find the 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. 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. Speed © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6959-4

Year/Grade 4 Year/Grade 5 Year/Grade 6 MEASUREMENT (continued) Temperature Read and measure Meter reading temperature using a thermometer. Estimate temperature. Convert a unit of temperature from degrees Celsius to degrees Fahrenheit, and vice versa. Solve problems involving temperature in real-life situations. Read and interpret electric and water meter readings. Solve a word problem involving electric and water consumption. GEOMETRY Plane Shapes Understand the properties of Recognize that the sum of Solve challenging problems involving triangles and four- squares and rectangles. the angle measures in a sided figures. Scholastic triangle is 180°. Use properties of squares Find an unknown angle and rectangles to find measure in a triangle given unknown angle measures. the other two angle measures. Use properties of squares Identify a right triangle. and rectangles to find unknown lengths. Identify a symmetric figure. Recognize that when one angle of a triangle is a right angle, the sum of the measures of the other two angles is 90°. Cut out a symmetric figure Recognize that the measure from a piece of folded of the exterior angle of a paper. triangle is equal to the sum of the measures of its interior opposite angles. Determine whether a line Find an unknown angle is a line of symmetry of a measure in a triangle figure. involving an exterior angle. Draw a line of Symmetry. Identify an isosceles triangle and an equilateral triangle. Complete a symmetric Recognize that the angles figure with respect to a opposite the equal sides given horizontal or vertical of a triangle have equal line of symmetry. measures. Make a symmetric pattern. 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. T32 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

Year/Grade 4 Year/Grade 5 Year/Grade 6 GEOMETRY (continued) Identify the unit shape in a tessellation. Plane Shapes (continued) Identify if a given shape can tessellate. Solid Shapes 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. Build a solid with unit cubes. Identify different types of prisms and pyramids. Visualize a solid drawn on dot Understand the properties of paper and state the number prisms and pyramids. of unit cubes used to build the solid. Scholastic Identify the front, top and Understand that cross side views of a solid. sections of a prism are of the same shape and size as the parallel faces of the prism. Visualize and identify the new Understand that cross solid formed by changing sections of a pyramid are of the number of unit cubes of the same shape as the base a given solid drawn on dot but of different sizes. paper. Identify cylinders, cones and spheres. Understand the properties of cylinders, cones and spheres. Make a model of a prism, a pyramid, a cone, a cylinder and a sphere. Identify solids of revolution. Understand that solids can be formed by nets. Identify the nets of a cube, cuboid, prism, pyramid, cylinder and cone. Identify the solid which can be formed by a net. Line Segments Draw perpendicular line Angles segments with a protractor or a set square. Draw parallel line segments with a set square and a ruler. Use notations such as ∠ABC Recognize that the sum of and ∠x. the angle measures on a line is 180°. Recognize that the measure Recognize that the sum of of a right angle is 90°. the angle measures at a point is 360°. Estimate and measure the Recognize that vertically size of an angle in degrees. opposite angles have equal measures. © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6959-4 T33

Year/Grade 4 Year/Grade 5 Year/Grade 6 GEOMETRY (continued) Angles (continued) Recognize an acute and an Find the unknown measure of obtuse angle. an angle involving angles on a line, angles at a point and vertically opposite angles. Draw an angle. Recognize that the sum of the angle measures in a triangle is 180°. Relate turns to right angles. Find an unknown angle measure in a triangle given the other two angle measures. Relate a 41-turn with 90°, a Recognize that when one 1-turn with 180°, a 2-turn angle of a triangle is a 24 right angle, the sum of the with 270° and a complete measures of the other two angles is 90°. turn with 360°. Tell direction in relation to Recognize that the measure the 8-point compass. of the exterior angle of a triangle is equal to the sum of the measures of the interior opposite angles. Read a simple map. Find an unknown angle measure in a triangle involving an exterior angle. Scholastic Understand the properties of Recognize that the angles squares and rectangles. opposite the equal sides of a triangle have equal measures. Use properties of squares Find an unknown angle and rectangles to find measure involving isosceles unknown 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 Present data in a bar graph. Present data in a pie chart. Solve problems using data Read and interpret a pie presented in a bar graph. chart. Make a line graph. Solve problems using data presented in a pie chart. Tables Read, interpret and present 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. Read and interpret a table. Solve problems using data presented in a table. T34 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

Year/Grade 4 Year/Grade 5 Year/Grade 6 STATISTICS AND PROBABILITY (continued) Averages 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 Record outcomes in a Describe experimental Describe probability of simple experiment. probability. chance events. Quantify probability using Express the outcomes in Perform an experimental proportion and percentage. an experiment in words, probability and record its symbols, tables or graphs. results. Perform experiments and record the outcomes. Record favorable outcomes Analyze data obtained from of an event. chance using experiments Make lists and draw involving letter and number diagrams of outcomes cards. to show the number of favorable outcomes. Find the probability of an Solve and create problems Make simple predictions of event. involving experimental events based on the results probability. of experiments. Scholastic Solve problems involving Solve and create problems probability. involving a simple experiment. PATTERNS AND ALGEBRA Patterns Determine the missing term(s) Write a rule in finding the Write a rule in finding the in a sequence of numbers. next term in a sequence of nth term in a sequence of numbers. numbers. Understand what an Expressions Use letters to represent equation is. unknown numbers. Identify an algebraic equation. Write a simple algebraic Differentiate an algebraic expression in one variable. expression from an algebraic equation. Find the value of a simple Identify the variable(s) in an algebraic expression using algebraic expression and substitution. equation. Solve an algebraic equation. Simplify an algebraic Solve word problems by expression in one variable. forming an algebraic equation. Solve word problems by forming an algebraic expression. Equations © 2017 Scholastic Education Inte rnational (S) Pte Ltd ISBN 978-981-47-6959-4 T35

Scholastic

Chapter 1: Exponents Strand: Numbers and Number Sense Total Duration: 4 h 30 min Scheme of Work Let’s Remember Blended Learning Program Print-based Program Sc(30 min)Lesson Learning Outcomes Vocabulary Materials Resources Materials Resources •• Carry out the prime factorization of •• 1 copy of Let's numbers using continuous division Remember Worksheet (WS1.1) •• Do mixed operations involving per student addition, subtraction, multiplication and division with and without parentheses hLesson 1: Exponential Notation oExpressing a 2h •• CWB pp. 1–3 number in lexponential asnotation •• Express a number in exponential •• base notation •• cubed •• exponent •• exponential notation •• power •• root •• squared ticFinding the value •• Find the value of a number given in of a number exponential notation •• CWB p. 3 given in 2h •• CWB pp. 4–5 exponential notation Lesson 2: Mixed Operations Carrying out •• Understand and apply the GEMDAS mixed operations rule to do mixed operations with and without exponents © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

Chapter 1 Scholastic –– Guide students to write 4 and 8 as a product of Exponents repeated factors. Chapter Overview –– Write ‘4 = 2 × 2’ and ‘8 = 2 × 2 × 2’ on the board. Let’s Remember –– Highlight to students that these numbers can Lesson 1: Exponential Notation Lesson 2: Mixed Operations be expressed as a product of repeated factors. The repeated factor of both multiplication Note for Teachers sentences is 2. In this chapter, students will learn to express a number –– Lead students to see that in ‘4 = 2 × 2’, the in exponential notation and find the value of a number factor 2 is multiplied by itself two times, while in given in exponential notation. They have learned the ‘8 = 2 × 2 × 2’, the factor 2 is multiplied by itself function of parentheses in number sentences, and three times. to do mixed operations involving the four operations –– Point out to students that we can write with parentheses. Students will be introduced to the a number that has a repeated factor in order of operations to carry out mixed operations exponential notation. with exponents. They will learn to do mixed operations –– Write ‘4 = 2 × 2 = 22’ on the board. involving the four operations with parentheses and –– Explain to students that 22 is a number expressed exponents. in exponential notation, and 22 is read as 2 raised to the power of 2, or 2 squared. Recall Prior Knowledge –– Write ‘8 = 2 × 2 × 2 = 23’ on the board. –– Explain to students that 23 is also a number Distribute a copy of Let's Remember Worksheet (WS1.1) expressed in exponential notation, and 23 is to each student. Have students attempt the worksheet read as 2 raised to the power of 3, or 3 cubed. to help them recall these previously acquired related knowledge: (b) Stage: Abstract Representation •• Carry out the prime factorization of numbers In this example, students see different exponential using continuous division (CWB 4A Chapter 1) notations of the same number. Students will also learn to identify the base or root, and the exponent or power •• Do mixed operations involving addition, of a number expressed in exponential notation. subtraction, multiplication and division with and without parentheses (CWB 5A Chapter 2) –– Guide students to write 16 as a product of repeated factor 2. For answers. go to CW Manual p. 113. –– Write ‘16 = 2 × 2 × 2 × 2 = 24’ on the board. Lesson 1: Exponential Notation –– Explain to students that 24 is an exponential Duration: 2 h notation of 16, and 24 is read as 2 raised to the power of 4. Learn –– Point out to students that 16 can also be written Expressing a number in exponential notation as a product of repeated factor 4 and guide (CWB pp. 1–2) them to do so. –– Write ‘16 = 4 × 4 = 42’ on the board. Learning Outcome: –– Explain to students that 42 is also an exponential •• Express a number in exponential notation notation of 16, and 42 is read as 4 raised to the power of 2, or 4 squared. Vocabulary: –– Guide students to identify the base or root, and •• base the exponent or power in a number expressed •• cubed in exponential notation. Have them see that the •• exponent base or root is the factor that is being multiplied, •• exponential notation and the exponent or power is the number of •• power times we multiply the base or root by itself. •• root –– Have students conclude that in 24, the base or •• squared root is 2 and the exponent or power is 4, and in 42, the base or root is 4 and the exponent or (a) power is 2. Stage: Abstract Representation In this example, students will be introduced to the (c) concept of exponential notation. Students have been Stage: Abstract Representation introduced to prime factorization in earlier grades. They In this example, students reinforce their knowledge of will now build upon the knowledge of prime numbers expressing a number in exponential notation, then and factors to express a number in exponential notation. identifying the base or root, and the exponent or power in an exponential notation. 2 Chapter 1 –– Guide students to express 243 in exponential notation. –– Have students see that 3 is the smallest prime factor of 243, and that the factor 3 can be multiplied by itself 5 times to get the product of 243. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

–– Write ‘243 = 3 × 3 × 3 × 3 × 3 = 35’ on the board. Scholastic Independent practice (For Print-based Program): –– Point out and explain to students that in the Task 3 requires students to identify the base and exponential notation 35, the base is 3 and the exponent of an exponential notation. exponent is 5. Task 4 requires students to express a number in (d) exponential notation. Stage: Abstract Representation In this example, students learn to express a number Task 5 requires students to write the prime factorization that cannot be expressed as a product of one of a number, then express the number in exponential repeated factor only in exponential notation. They will notation. see that they have to write the prime factorization of the number first in order to do so. For answers, go to CW Manual p. 113. –– Guide students to express 180 in exponential Learn notation by carrying out prime factorization of Finding the value of a number given in the number. exponential notation (CWB p. 3) –– Have students recall that when using Learning Outcome: continuous division, we need to first divide the •• Find the value of a number given in number by its smallest prime factor. exponential notation –– Have students look at the continuous division (a) on CWB p. 2 and point out that the prime Stage: Abstract Representation factors of 180 are 2, 3 and 5. Students will now learn to find the value of a number given in exponential notation. In this example, students –– Write ‘180 = 2 × 2 × 3 × 3 × 5 = 22 × 32 × 5’ on will first learn to write the multiplication sentence of an the board. exponential notation with only one repeated factor, then find its value. –– Have students see that in ‘180 = 22 × 32 × 5’, the factor 2 is multiplied by itself two times, the –– On the board, write ‘53’. Guide students to factor 3 is also multiplied by itself two times and identify the base and the exponent. the factor 5 is multiplied once. –– Have students see that the base is 5 and –– Explain to students that writing a number in the exponent is 3. So, we multiply 5 by itself exponential notation is a shortened way of three times. writing a number as a product of its repeated factors. Some numbers are a product of the –– Write ‘53 = 5 × 5 × 5’ on the board and have same repeated factor, while others are a students find the value. product of several repeated factors. –– Have students conclude that the value of Practice 1 (CWB pp. 2–3) 53 is 125. Class practice (For Print-based Program): (b) Stage: Abstract Representation Task 1 requires students to express a product of In this example, students will first learn to write the repeated factors in exponential notation. multiplication sentence of an exponential notation with more than one repeated factor, then find its value. Task 2 requires students to express a number in exponential notation by finding its repeated factors first. –– On the board, write ‘72 × 23’. Guide students to identify the base and the exponent. Remediation Task 1: Reteach expressing a number as a product –– Have students see that in 72, the base is 7 and of repeated f­actors. Then, go through Task 1. Have the exponent is 2. So, we multiply 7 by itself two ­students see that in each multiplication sentence, there times. Have them also see that in 23, the base is one ­repeated factor only. Guide students to write is 2 and the exponent is 3. So, we multiply 2 by each ­multiplication sentence in exponential notation. itself three times. Task 2: Reteach expressing a number in exponential –– Write ‘72 × 23 = 7 × 7 × 2 × 2 × 2’ on the board notation. Then, go through Task 2. Guide students to and have students find the value. see that 5 is the smallest prime factor of 125 and that the factor 5 is multiplied by itself three times to get the –– Have students conclude that the value of product of 125. 72 × 23 is 392. Teaching tips Tasks 1 and 2 ¾¾ Remind students that in an exponential notation, the base is the factor that is being multiplied and the exponent indicates how many times the base is multiplied by itself. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4 Chapter 1 3

Practice 2 (CWB p. 3) Scholastic –– Have a student show the working on the board. Guide him/her to see that we should multiply Class practice (For Print-based Program): 6 and 8 first to get 48, and divide 4 by 2 first to get 2. Next, lead him/her to subtract 2 from 48, Task 1 requires students to find the value of a number then add 7 to get 53. given in exponential notation. –– Conclude that 6 × 8 − 4 ÷ 2 + 7 equals to 53. Remediation Task 1: Reteach finding the value of a number given in (b) exponential notation. Then, go through Task 1. Stage: Abstract Representation Have students identify the base and the exponent. In this example, students will recall how to do Guide students to write the multiplication sentence mixed operations involving the four operations with of the exponential notation and then find its value. parentheses. Teaching tips –– Write ‘82 + 12 × (16 ÷ 2)’ on the board. Task 1 –– Have students see that the expression has ¾¾ Remind students that the exponent indicates parentheses or brackets and involves addition, how many times the base is multiplied by itself. multiplication and division. –– Remind students that when there are Independent practice (For Print-based Program): parentheses, we carry out the operations in the parentheses first. Then we work from left to right, Task 2 requires students to find the value of a number and carry out multiplication and division first given in exponential notation. before addition and subtraction. –– Have a student show the working on the board. Task 3 requires students to find the value of the square Guide him/her to see that the operation in the of a number. parentheses is division. Hence, he/she should divide 16 by 2 first to get 8. Task 4 requires students to find the value of the cube of –– Next, lead him/her to multiply 12 by 8 to get 96, a number. then add 82 to get 178. –– Conclude that 82 + 12 × (16 ÷ 2) equals to 178. For answers, go to CW Manual p. 113. –– Have students see that in (a) and (b), the expressions did not have exponents. Lesson 2: Mixed Operations –– Explain to students that when there are exponents in a mathematical expression, Duration: 2 hL we can follow the GEMDAS rule, where GEMDAS is an abbreviation of Grouping, Learn Exponent, Multiplication, Division, Addition and Carrying out mixed operations (CWB p. 4) Subtraction. Learning Outcome: (c) •• Understand and apply the GEMDAS rule to do Stage: Abstract Representation mixed operations with and without exponents Having previously learned to do mixed operations with and without parentheses, students will now learn to do (a) mixed operations with exponents. They will see that the Stage: Abstract Representation exponents change the order in which the operations Students learned to do mixed operations involving are carried out. addition, subtraction, multiplication and division with and without parentheses in the previous grade. –– Write ‘30 − (6 − 2) × (3 + 4) + 52’ on the board. In this example, students will recall how to do mixed –– Have students see that the expression has operations involving the four operations without parentheses. exponents, parentheses or brackets and involves subtraction, multiplication and addition. –– Write ‘6 × 8 − 4 ÷ 2 + 7’ on the board. –– Explain to students that when there are –– Have students see that the expression involves parentheses and exponents, we carry out the operations in the parentheses first. Then we four different operations—multiplication, work from left to right, and evaluate exponents subtraction, addition and division. first, and carry out multiplication and/or division, –– Remind students that when there are mixed before addition and/or subtraction. operations like these, we work from left to right, –– Guide them to see that the operation in the first and carry out multiplication and division first parentheses is subtraction, and the operation before addition and subtraction. in the next parentheses is addition. Hence, we should subtract 2 from 6 first to get 4, and add 3 and 4 first to get 7. –– Draw a brace below the numbers in the parentheses and write ‘= 30 − 4 × 7 + 52’ below the expression, as shown on the page. 4 Chapter 1 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4

–– Then, have students evaluate the exponent 52 ChapterWrap-up to get 25. Reiterate the following points: –– Draw a brace below the exponent and write –– In an exponential notation, the base or root is ‘= 30 − 4 × 7 + 25’ below the expression, as the factor being multiplied, and the exponent shown on the page. or power is the number of times we multiply the base or root by itself. –– Then, have students multiply 4 and 7 to get 28. –– When doing mixed operations, involving –– Draw a brace below ‘4 × 7’ and write addition, subtraction, multiplication and division with parentheses and exponents, we apply the ‘= 30 − 28 + 25’ below the expression, as shown GEMDAS rule: on the page. Step 1: S implify expressions within groupings –– Then, have students subtract 28 from 30 to (or parentheses) get 2, then add 25 to get 27. Step 2: Evaluate exponents –– To conclude, complete the expression by Step 3: M ultiply or divide in order from left writing ‘= 27’ on the next line on the board. to right –– Reiterate that 30 − (6 − 2) × (3 + 4) + 52 equals Step 4: Add or subtract in order from left to right to 27. Practice 3 (CWB p. 5) Class practice (For Print-based Program): Task 1 requires students to do mixed operations with exponents. ScholasticTask 1(a) requires students to carry out operations involving addition and subtraction. Task 1(b) requires students to carry out operations involving multiplication, division and addition. Remediation Task 1: Reteach doing mixed operations involving addition, subtraction, multiplication and division with parentheses and exponents. Then, go through Task 1. Guide students to do the operations in the parentheses first, then evaluate the exponents and do multiplication and/or division before addition and/or subtraction. Teaching tips Task 1 ¾¾ Reiterate to students the importance of following the rules when doing mixed operations with parentheses and exponents. ¾¾ Students may get an incorrect answer by not following the rules of operations. ¾¾ Point out to students that they can use the acronym GEMDAS to help them remember the rules of doing mixed operations: Grouping (Parentheses)  Exponents  Multiplication and Division (work from left to right)  Addition and Subtraction (work from left to right) Independent practice (For Print-based Program): Task 2 requires students to do mixed operations with parentheses and exponents, including addition, subtraction, multiplication and division. For answers, go to CW Manual p. 113. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6959-4 Chapter 1 5