TMM A T HFOR ATHEMATICAL BILITIES & HINKING ABITSA UNIQUE SYSTEM THAT CHANGES THE FOCUSFROM ROTE PRACTICE TO REAL MATH WISDOM Teacher’s Edition Volume II

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TM M A T HFOR ATHEMATICAL BILITIES & HINKING ABITS A UNIQUE SYSTEM THAT CHANGES THE FOCUS FROM ROTE PRACTICE TO REAL MATH WISDOMSpots for M. A. T. H. - First Grade Mathbook - Teacher’s Edition - Volume ll Published by Spots Educational Resources, Brooklyn, N.Y.

Spots for M.A.T.H. First Grade Mathbook Teacher’s Edition Volume ll Copyright © 2013 by Spots Educational Resources. All Rights Reserved. Published in the United States by Spots Educational Resources, Brooklyn, N.Y. Program Authors: Nechemia Weiss, M.S. Ed., SpEd., Childhood Education Teacher, (Grades 1-6), Brooklyn, N.Y. Sarah G. Weiss, Math Curriculum Specialist, Brooklyn, N.Y. Senior Reviewer:Brenda Strassfeld, Ph.D. Chair of Mathematics Education Program, Graduate School of Education, Touro College, New York, N.Y. Consulting Reviewers:Mary F. Rinaldi, Ph.D. Assistant Principal & Math Chair, New York City Board of EducationJack Norman, M.A. Administrative Assistant Superintendent, New York City Board of Education, Brooklyn, N.Y. (retired); Adjunct Professor, Touro College, Brooklyn, N.Y.Matthew Shatzkes, M.S. Math Teacher & Mentor, New York City Board of Education, Brooklyn, N.Y. (retired)Louise Jarvis, M.S. Masters in Mathematics, University of Rhode Island, Kingston, R.I. Math Curriculum Writer & Editor, Seekonk, MA.Basi Blumberg, M.S., Ed. Math Curriculum Specialist, Queens ,N.Y.Hindy Fekete Math Curriculum Advisor, Brooklyn, N.Y.Breindi Rizel, M.S. Teacher Reviewers:Sara C. Mizrahi, B.A. Special-Education Teacher, Brooklyn, N.Y. Teacher’s Certification, Yavne Teachers’ College, Cleveland, OH. Art Design : w El Gee Design Inc. w Core Design LLC. w Gradient Design Inc. w Transfer Studio Art Credits: © Art Explosion® 800,000 Clip Art by Nova Development / Royalty-Free w ShutterstockCommon Core State Standards for Mathematics: corestandards.org © Copyright 2010 National GovernorsAssociation Center for Best Practices and Council of Chief State School Officers. All rights reserved.This product is not sponsored or endorsed by the Common Core State Standards for Mathematics initiativeof the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief StateSchool Officers (CCSSO).Special thanks to the many teachers, students, parents, principals, writers and work-study students whoparticipated in the Spots for MATH project development over the years.This publication, or parts thereof, may not be reproduced in any form by photographic, electrostatic,mechanical, or any other method, for any use, including information storage and retrieval, without writtenpermission from the publisher.Spots for Mathematical Abilities & Thinking Habits is a registered trademark of Spots Educational Resources.Dot Cards included herein are a Mathematical Educational Set protected with United States Patent Number:D621,878 S An additional Patent is Pending as a Educational Set of Cards for Addition and Subtraction.Special thanks to the many teachers, students, parents, principals, writers and work-study students who par-ticipated in the Spots for M.A.T.H. project development over the years.Publisher: Spots Educational Resources 5314 16th Avenue, Unit 101, Brooklyn, NY 11204Phone: (718) 306-9898 w Fax: (206) 888-4574 w Email: [email protected] w www.spotsmath.comISBN: 978-0-9893168-0-4 (Teacher’s Edition)ISBN: 978-0-9851129-8-1 (Student’s Textbook: Set of 2 Volumes)3 4 5 6 7 8 9 10 16 15 14 13Printed in the U.S.A

TABLE OF CONTENTSDeveloping Real Math Wisdom 2�����������������������������������������������������������������������������������������������������������������������������������������������������������������������Program Components 4����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Models and Strategies Overview 6�������������������������������������������������������������������������������������������������������������������������������������������������������������������The Lesson Format 10��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������The Daily Routine l 12����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Celebrating 100 14�����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������The Daily Routine ll 15�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Lesson Warm-Up Activities 16��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Suggested Activities for Practice and Review 18�����������������������������������������������������������������������������������������������������������������������������������Chapter 5 21�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Chapter 6 49���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Chapter 7 101������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Chapter 8 147������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Chapter 9 183������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Common Core Mathematics Standards Alignment 211������������������������������������������������������������������������������������������������������������������ 1

בס”ד TM M A T HFOR ATHEMATICAL BILITIES & HINKING ABITS A UNIQUE SYSTEM THAT CHANGES THE FOCUS FROM ROTE PRACTICE TO REAL MATH WISDOM Spots for M.A.T.H.: Developing Real Math Wisdom What is “Spots for M.A.T.H.”? Spots for M.A.T.H. is a revolutionary approach that fosters the development of real math wisdom. This includes: • Fluency with basic addition and subtraction facts and place-value concepts, which are the building blocks of all future work in mathematics • Modeling with mathematics through use of a variety of representations, such as the Dot Cards and Open Number Lines. At first, the models are used to scaffold learning. Then as students progress, the same models become tools to show and expand their thinking • Proficiency with computational skills and decomposition of numbers (e.g., 14 – 6 can be thought of as 14 – 4 - 2 ) • The ability to generalize and make connections as students become familiar with patterns and thinking strategies in mathematics (e.g., if 7 + 8 is 7 + 3+ 5, then 27 + 8 can be thought of as 27 + 3 + 5) • A methodical approach to problem solving that students can use and reuse as mathematics students Through the use of consistent visual models and strategies, Spots for M.A.T.H develops fluency with basic math facts while promoting students’ emerging number sense. The patented Dot Card system provides visual representations of numbers and operations, to break through their inherently abstract nature and make these constructs approachable for the younger student. The program’s predictability enables students to continually add layers of meaning to their knowledge base as they make connections from strand to strand in mathematics.2

Spots for M.A.T.H. expands on the Dot Card system to advance students’ operational skillsin a manner that fluidly builds confidence and automaticity while strengthening conceptualunderstanding. The Dot Cards used throughout provide constant visual reinforcement of conceptsand strategies, ensuring lasting internalization of skills learned. In addition to the Dot Card system,Spots for M.A.T.H. employs other innovative and research-based representational strategies, suchas use of the “Empty Number Line,” as well as “Puzzle Piece” models for real-world problem solving.Spots for M.A.T.H. places special emphasis on the development of critical thinking through theuse of “Thinking Triggers” and other discussion prompts in every lesson.The Spots for MATH Teacher’s Edition’s detailed lesson plans are carefully designed to introducemath facts and concepts, as well as practice strategies, in an incremental yet engaging manner,inspiring a “can do” attitude which is so foundational for students’ success as lifelong independentthinkers and learners. 3

PROGRAM COMPONENTSBooksSpots for M.A.T.H.™ Student Textbook SPOTS for Mathematical Abiliies & Thinking Habits - Student’s Edition - Volume ITM TM SPOTS for Mathematical Abiliies & Thinking Habits - Student’s Edition - Volume IThe program was created based on the Instructional Shifts and the Common Core M A T HFOR M A T HFOR ATHEMATICAL BILITIES & HINKING ABITS ATHEMATICAL BILITIES & HINKING ABITS A UNIQUE SYSTEM THAT CHANGES THE FOCUS A UNIQUE SYSTEM THAT CHANGES THE FOCUS FROM ROTE PRACTICE TO REAL MATH WISDOM FROM ROTE PRACTICE TO REAL MATH WISDOMState Standards (CCSS). The clearly laid-out student book provides intense practice TM TM M A T HFOR M A T HFOR ATHEMATICAL BILITIES & HINKING ABITS ATHEMATICAL BILITIES & HINKING ABITS A UNIQUE SYSTEM THAT CHANGES THE FOCUS A UNIQUE SYSTEM THAT CHANGES THE FOCUS FROM ROTE PRACTICE TO REAL MATH WISDOMof concepts and skills students have learned. Concept Representation Dot Cards FROMROTEPRACTICETOREALMATHWISDOMare included in each lesson for skill reinforcement. A specific number of sections is ISBN 978-0-9851129-8-1 (whole set) ISBN 978-0-9851129-9-8included in which these Dot Cards are intentionally omitted, so students learn to ISBN 978-0-9851129-8-1 (whole set) ISBN 978-0-9851129-9-8compute independently. VOLUME II VOLUME I Volume ll Volume lTeacher’s Edition TM TM TM TMThe Teacher’s Edition is an easy-to-use, comprehensive guide that provides step-by-step instructions for teaching each lesson. Its clear, innovative approach enables FOR FORteachers to develop core math concepts and cultivate thinking skills in their young MM AA TT HHATHEMATICAL& MM AA TT HHATHEMATICAL&students. The presentation style makes teaching easy and fun even for less experienced ATHEMATICAL& ATHEMATICAL&teachers. BIFLOITRIES HINKING ABITS BIFLOITRIES HINKING ABITS BILITIES HINKING ABITS BILITIES HINKING ABITS A UNIQUE SYSTEM THAT CHANGES THE FOCUS A UNIQUE SYSTEM THAT CHANGES THE FOCUS FARUONMIQRUOETESYPSRTAECMTITCHEATTOCRHEAANLGMEASTTHHWE FISODCOUMS FARUONMIQRUOETESYPSRTAECMTITCHEATTOCRHEAANLGMEASTTHHWE FISODCOUMS FROM ROTE PRACTICE TO REAL MATH WISDOM FROM ROTE PRACTICE TO REAL MATH WISDOM Teacher’s Edition Teacher’s Edition Grade 1 Volume 1Spots for M.A.T.H. ∙ First Grade Math Book ∙ Teacher’s Edition ∙ Volume I Grade 1 Volume 2Spots for M.A.T.H. ∙ First Grade Math Book ∙ Teacher’s Edition ∙ Volume II Published by Spots Educational Resources, Brooklyn, N.Y. Published by Spots Educational Resources, Brooklyn, N.Y. Volume l Volume llTeacher’s Resource Book TMThe Resource Book provides copy masters for teachers to use throughout the year. M a T hFor aTheMaTIcal BIlITIes & hInkInG aBITsIncludes: • Family Letters (to keep the families informed of and involved in all thatthe class is learning) • Drop-It Forms (used in the lesson warm-up section to develop a unIQue sYsTeM ThaT chanGes The Focusfluency and for ongoing assessment) • Cutouts and Lesson Handouts (which are used FroM roTe PracTIce To real MaTh WIsdoMoften to enhance the lessons) • Assessment Forms • Reproducible Game Cards andBoards • Number Writing Sheets (binder, 160 p.) Teacher’s resource Book Grade 1 Includes: • Family Letters • Drop-Its Forms • Cutouts • Lesson Handouts • Assessment Forms • Reproducible Game Cards and BoardsFocus Standards & Facts Fluency Practice Book FoFcaucst&sSFtalunednacrydsThis student work book provides additional practice to develop fluency of the core Practice Bookstandards. TM M A T HFOR ATHEMATICAL BILITIES & HINKING ABITS A UNIQUE SYSTEM THAT CHANGES THE FOCUS FROM ROTE PRACTICE TO REAL MATH WISDOMTeaching Materials Spots for M. A. T. H.™ Magnetic Dot-Boards These patented boards are used to model number concepts and operations. The magnetic strip makes them easy to place on classroom boards. Magnetic Two-Color Counters Teachers use these counters with the Dot Boards to demonstrate number- and math concepts. Two-Color Foam Counters Students use these to model addition with Dot Boards found in the back of the Student’s Edition. Double-Sided Number Sentence Wipe-Off Boards Students use these wipe-off boards to write number sentences on their own.4

Chapter Opener Count the mittens by tens. Write how many. 100 Colorful Mittens I see 10 little mittens all shiny and clean. I like them best — they are green. Colorful mittens for me and you! Colorful mittens big and small, Red ones, yellow ones, blue ones too! 10, 20, 30, 40, 50...60 in all! I see 10 little mittens sitting on my bed. I like them best — they are red! I see 10 little mittens that I just found. I like them best — they are brown. I see 10 little mittens waving hello! Colorful mittens big and small, I like them best — they are yellow. 10, 20, 30, 40, 50, 60...70 in all! Colorful mittens big and small, 10 red, 10 yellow — 20 in all! I see 10 little mittens all in a sack. I like them best — they are black. I see 10 little mittens — they’re prettiest, I think. Colorful mittens big and small, I like them best — they are pink. 10, 20, 30, 40, 50, 60, 70...80 in all! Colorful mittens big and small, 10 red, 10 yellow, 10 pink — 30 in all! I see 10 little mittens to put on my hand. I like them best — they are tan. I see 10 little mittens as I fly my kite. Colorful mittens big and small, I like them best — they are white. 10, 20, 30, 40, 50, 60, 70, 80...90 in all! Colorful mittens big and small, 10, 20, 30...40 in all! I see 10 little mittens — oh, what a great day! I like them best — they are grey. I see 10 little mittens, let me show them to you. Colorful mittens big and small, I like them best — they are blue. 10, 20, 30, 40, 50, 60, 70, 80, 90...100 in all! Colorful mittens big and small, Student Workbook page 10, 20, 30, 40...50 in all! Student Workbook page Student Workbook page 8 Copyright © by SPOTS Educational Resources. All rights reserved. Copyright © by SPOTS Educational Resources. All rights reserved. 8 99 10 10USING THE BOOK: Pages 8-10Pages 8-9: Read the title of the poem 100 Colorful Mittens. Ask: What is this poem about? [Mittens] We will read about 100mittens. That’s a lot of mittens to count! Luckily, they are of different colors, so it’s not so hard to count them.Read the poem together with the class. Ask: How many different colors are there? [Allow time for the students to count.] [10]CONCEPT DEVELOPMENT:I will read the poem again. This time I will put the mittens up on the board as we read about them. [Reread the poem. After you readthe first stanza, place the poster strip with ten red mittens on the board and write the number 10 next to it. Continue readingthe poem. After you read each stanza, place the poster strip with mittens of that color under the previous strip, and next to itwrite the number of mittens in total, up to that point.Page 10: Look at page 10 together. Say: The mittens on the board are the same as the mittens on the page! [Together, count themittens by tens. Have the students trace over the numbers at the end of each row of mittens.] CLOSING STATEMENT: We will learn about all this in Chapter 5! 25

5.1 Chapter 5 Lesson 1: Exploring Decade NumbersCCSS 1.NBT.2c The numbers 10, NOTE: This lesson is a continuation of the introduction to the chapter.20, 30, 40, 50, 60, 70, 80, 90, referto one, two, three, four, five, six, There are differences in its format.seven, eight, or nine tens (and 0ones). CONCEPT DEVELOPMENT:GOAL: I. Showing decade numbers with Dot CardsStudents will be introduced to the Refer to the mittens poster strips on the board. Ask how many mittens are onbase 10 number system as it applies each strip. [10] Say: There are ten mittens here. We wrote 10. We can also show 10to the decade numbers using a Dot Card-10. [At the end of the first strip, paste a copy of Dot Card-10 andMATERIALS NEEDED: 2-3 sheets say:] We have ten mittens here.of poster board; cutout #40 — tenof Dot Card-10 At the end of the second strip paste another copy of Dot Card-10 and say: We have another ten mittens here. We have 10…20 [pointing to the Dot Cards] altogether. Continue in this way for each line, counting the Dot Card-10 each time, until you’ve counted by tens to 100. CONCLUSION: Now we’ve counted, read, and written numbers that show groups of ten.26 Copyright © by SPOTS Educational Resources. All rights reserved.

Exploring Decade Numbers Thirty has 3 tens and 0 ones. Write how many. 3. The ty means many tens. 1. 2.Tens Ones Number 3. Tens Ones Number Tens Ones Number Tens Ones Number3 0 30 Eighty ThirtyWrite how many. 2. Sixty Seventy1. 4. 5.Tens Ones Number Tens Ones Number Tens Ones Number Tens Ones Number Tens Ones Number Ten Twenty Thirty Student Workbook page Student Workbook pageNinetyOne HundredCopyright © by SPOTS Educational Resources. All rights reserved.4. 5. Circle groups of ten. Write how many. 6. 7. Tens Ones Number Tens Ones Number Tens Ones Number Tens Ones Number Copyright © by SPOTS Educational Resources. All rights reserved. Forty Fifty 11 11 12Chapter 5 Lesson 1 CCSS 1.NBT.2c Understanding place value. 12USING THE BOOK: Pages 11-12Page 11: Read the demonstration at the top of the page. Read the directions. For each example, place a sample Dot Card-10 onthe board, and for each group of Dot Cards ask the class to tell how many tens, how many ones, and the total number. Explain:We have one ten and zero ones – that makes 10! ... We have two tens and zero ones. Do you see what number that makes? [20] Tracethe number 20. [Continue in this way until you have completed the page.]Page 12: Examples 1-5: Read the directions. Continue as on page 11 to complete the section.Examples 6-7: Read the directions. Have the students work on their own while you circulate and offer assistance as needed.Review the section together.NOTE: Give each student between two and CLOSING STATEMENT:ten small bags. Ask them to choose an object Who can tell us what we learned today? [Acceptand fill each bag with ten of that object. You will relevant answers.] Today we used groups ofbe using these bags for the next few lessons. mittens and groups of Dot Card-10 to show numbers to 100. We learned to see how many tens and how many ones there are for each number. Tomorrow we will count groups of ten in other ways, to help us understand these numbers better. 27

5.2 Chapter 5 Lesson 2: Representing Decade NumbersCCSS 1.NBT.2c The numbers 10, CONCEPT DEVELOPMENT: Ones Objects in All20, 30, 40, 50, 60, 70, 80, 90, referto one, two, three, four, five, six, I. Using objects to introduce tens and onesseven, eight, or nine tens (and 0 Display a large chart as shown:ones).NYS CCLS 1.MD.3 Recognize and Student’s Name Object Tens (Bags)identify coins, their names, andtheir values. Ask some students to show their bags to the class and help you fill in the chart accordingly. Discuss how many objects they put in each bag, and what thatGOAL: means (they have X groups of tens).Students will reinforce theirunderstanding of decade numbers. As you write the number of objects in all, discuss how to write the number: TheMATERIALS NEEDED: students’ first digit tells how many tens and the second digit tells how many ones.bags with ten objects; chart; 4 bagswith a dime in each bag If possible, photograph the objects the students brought in, and add the pictures to the chart at a later date.LESSON WARM-UP:Flash 8-10 Teen Addition Dot Cards. [Note: We will be using these groups of ten in later lessons as well. If time isHave the class identify each one in short, you need not use everyone’s collection in this lesson.]unison. II. Dimes and pennies as a form of tens and onesINTRODUCTORY STATEMENT: Tell the class: I filled some bags too. I put ten cents in each of my bags. Can you thinkToday we will work with “tens”; tens of some ways I could have put 10 cents into a bag? [Wait for answers. Then showare two-digit numbers that have only the four bags with a dime in each.] I put in dimes. What makes the dime similar totens and no ones. the bags you made? [it is worth ten cents, which is the same as ten pennies] How many groups of ten did I bring in? [4] THINKING TRIGGER:Did you enjoy your homework Fill in the chart to show what you brought in.activity? How did you decide whatobject to use? Was it hard to put The final chart could look like this:exactly ten in each bag? Were youable to do it yourself, or did someone Student’s Name Object Tens (Bags) Ones Objects In Allhelp you? Ezra 6 0 60 Clips Michel 3 0 30 Crayons Teacher 4 0 40¢ Review the chart with the class. Discuss what each child brought in, the number Copyright © by SPOTS Educational Resources. All rights reserved. of tens, the number of ones, and how many in all. III. Tens and ones in decade numbers Point to a number in the last column. Ask: What number is this? How many tens are in this number? How many ones? Repeat this for three or more numbers. IV. Counting by tens Place ten of Dot Card-10 on the board. As a class, count the cards by tens to 100, and write each number as you count. Repeat this with ten model dimes.28

Write how many. Representing Decade Numbers Read each number.1. 2. 3. Write how many. 1. 2. 3. 70 50 30Tens Ones Number Tens Ones Number Tens Ones Number Tens Ones Tens Ones Tens Ones4. 5. 6. 4. 5. 6. 80 60 40Tens Ones Number Tens Ones Number Tens Ones Number Tens Ones Tens Ones Tens Ones7. 8. 9. 7. 8. 9. 90¢ 50¢ 20¢ Student Workbook pageDimes Pennies Dimes PenniesDimes Pennies Student Workbook pageDimes Pennies Amount Dimes Pennies Amount Dimes Pennies Amount Count by tens. Write how many.Copyright © by SPOTS Educational Resources. All rights reserved. 10. ¢ ¢ ¢ Copyright © by SPOTS Educational Resources. All rights reserved. LET’S THINK 13 13 ,,,,,,,,, 14 14 Why does the number 40 have a 0?Chapter 5 Lesson 2 CCSS 1.NBT.2c Understanding place value. NYS CCLS 1.MD.3STUDENT TEACHER:Choose three students. Have each one choose a number from the last column on the chart and show it using Dot Cards.CONCLUSION:Today we practiced with two-digit numbers that have only tens and no ones.USING THE BOOK: Pages 13-14Page 13: Read the directions. Model the first example on the board. Have the class complete the page independently whileyou offer help as needed. Review the page together.Let’s Think: Read the question and discuss it together. CLOSING STATEMENT:Page 14: Examples 1-9: Read the directions to the class. Discuss how example 1 is Who can tell us what we learned today?filled out. Have the class complete the section together. [Accept relevant answers.] Today we practiced with tens. We counted groupsExample 10: You may choose to do this example together or have the class complete of tens, and we read and wrote numbersit independently. that have only tens. Tomorrow we will learn to see the difference between teen numbers and numbers that have only tens. 29

5.3 Chapter 5 Lesson 3: Decade and Teen Numbers CCSS 1.NBT.2c The numbers 10, CONCEPT DEVELOPMENT: Copyright © by SPOTS Educational Resources. All rights reserved. 20, 30, 40, 50, 60, 70, 80, 90, refer to one, two, three, four, five, six, I. Representing decade and teen numbers with manipulatives seven, eight, or nine tens (and 0 Choose a student who has three bags of objects (see lesson 2), and ask the ones). student to present his/her bags. Ask: How many (objects) do you have in all? [30] CCSS 1.NBT.2b The numbers 11 to How do you think we write 30? Why? [it has three tens and zero ones] [Write the 19 are composed of a ten and one, number.] two,... or nine ones. NYS CCLS 1.MD.3 Recognize and Display similar objects: a group of ten and three loose objects. Say: I brought identify coins, their names, and similar things to school, but I don’t have so many. I have one bag with ten, and three their values. more. How many do I have? [13] How do we write the number 13? [Accept answers CCSS 1.OA.6 Add and subtract and write the number.] Why do we write it this way? [we have one ten and three within 20. ones] GOAL: II. Representing decade and teens numbers with Dot Cards Students will differentiate between How can we show the numbers 30 and 13 with Dot Cards? [Have the students direct similar decade and teen numbers. you to place three of Dot Card-10 and a Teen Dot Card with a ten and three ones.] MATERIALS NEEDED: Drop-It form #2; students’ bags of ten objects Continue in the same way with two additional sets of objects. Each time, write (see lesson 2); objects similar to the the number of objects the student brought in and the number you brought in (a students’ objects, in groups of ten group of ten and ones) and show the numbers with Dot Cards. and ones (see lesson) III. Identifying and differentiating between teen and tens numbers LESSON WARM-UP: Read each number on the board. Ask the class to wiggle their fingers if it is a Drop-It: Hand out Drop-It form teen number. Then read the numbers on the board again and ask them to clap #2. Flash ten Teen Addition Dot for each tens number. Cards. Have the students write each equation on their papers. Check the Place a group of eight dimes on the board. Ask: How much money do we have? students’ work. [80¢] [Write the amount on the board.] Do the same with a dime and four pennies. [14¢] INTRODUCTORY STATEMENT: Today we will learn to see the Clear the board. difference between teen numbers and numbers that have only tens. IV. Reading number words Show 13 and 30 using Dot Cards. Ask students to tell you how many are in each THINKING TRIGGER: group, and write the numbers. Say: Now we will read the numbers when they are Write 14 and 40 on the board. Ask: written out in words. [Write “thirteen” and “thirty” next to their numbers, and read Each of these numbers has a four. the words. Stress the word endings, and use another color to highlight the word What is the difference between the endings as you read the words. fours? Do the same with additional number pairs 14 and 40, 15 and 50, 16 and 60, 1730 and 70.] Write the number-word “eighteen” on the board. Ask the class to read it and tell you how to write the number. Do the same with the number-word “eighty.” Write “ninety” and “nineteen” on the board, and underneath write the numbers 19 and 90. Ask the class to help you match the number words to the numbers. STUDENT TEACHER: Have the students work in pairs. Have each pair choose one or two number pairs (a teen number and a decade number), write their numerals and their number-

Decade and Teen Numbers 16 60 Circle the correct number word and fill in the number. We have 1 ten and 6 ones. We have 6 tens. 1. 2. 3. We say sixty. We say sixteen. Fourteen Forty Twelve Twenty Thirteen Thirty 3.Write how many. Make a simple math drawing to show the number. 301. 2. 4. 12 5. 20 6. 13 7.Circle the correct number. 6. Write the number. Eighteen 10. Twenty4. 5. 8. Thirty 9.30 13 Student Workbook page70 1750 1511. Nineteen 12. Fifty 13. Fourteen Student Workbook page7. 8. 9. Add.Copyright © by SPOTS Educational Resources. All rights reserved. 60¢ 16¢ 20¢ 12¢ 40¢ 14¢ 14. 9 15. 7 16. 6 17. 4 18. 6 19. 7 Copyright © by SPOTS Educational Resources. All rights reserved. 16 15 15 +8 +7 +8 +7 +9 +5Chapter 5 Lesson 3 CCSS 1.NBT.2c Understanding place value. CCSS 1.NBT.2b, NYS CCLS 1.MD.3, CCSS 1.OA.6 16words, and draw groups of objects to show each number. Have each pair show their work to the class.CONCLUSION:Today we compared teen numbers with numbers that have only tens.USING THE BOOK: Pages 15-16 CLOSING STATEMENT:Page 15: Read and discuss the demonstration at the top of the page. Who can tell us what we learnedFor each section, read the directions and model the first example on the board. Have today? [Accept relevant answers.]the class complete each section independently while you offer help as needed. Review Today we practiced with teenthe page together. numbers and numbers that havePage 16: For each section, read the directions and model the first example on the board. only tens. We learned the differenceHave the class complete each section independently while you offer help as needed. between them, and we learned toReview the page together. read their number words. Tomorrow we will learn how to compare Display the 7 + 6 Dot Card and its number numbers to figure out which is greater sentence on the Math Poster. and which is less. 31

5.4 Chapter 5 Lesson 4: Comparing Numbers CCSS 1.NBT.3: Compare two-digit CONCEPT DEVELOPMENT: numbers based on meanings of the tens and ones digits I. Reviewing representing decade and teen numbers NYS CCLS 1.MD.3 Recognize and On the board write 30 and 15. Read the numbers and ask a student to tell you how identify coins, their names, and their values. to show these numbers with Dot Cards. GOAL: Repeat with 18 and 20. Students will compare the values of two-digit numbers. Write 70¢ on the board, and draw two spaces underneath for the dimes and pennies. MATERIALS NEEDED: model Ask: How many dimes do we need for this amount? [7] How many pennies? [0] coins; “number grab bag” with teen- and decade number cards Repeat with 16¢ and 50¢. LESSON WARM-UP: II. Identifying which number is greater Flash 8-10 Teen Addition Dot Cards. On the board write 30 and 19. Read the numbers and ask a student to tell you how Have the class identify each one in unison. to show these numbers with Dot Cards. INTRODUCTORY STATEMENT: Repeat with 14 and 60. Now that we’ve learned about tens and ones, we will practice comparing On the board write 40 and 17. Do not show the numbers with Dot Cards. Read the which number is greater or less. numbers and ask: How many tens are there in 40? How many tens are there in 17? Which number has more tens? [40] Which number is greater? [40] Why? [it has more THINKING TRIGGER: tens] When we compare two-digit numbers, we look at the number of tens to know Do you remember my little brother which number is greater. Let’s circle the greater number. who wanted lots of coins? If I were to offer him a choice of a dime and Repeat this with the number pairs 16 and 50, and 20 and 19. For each pair circle the seven pennies [place samples on number that is greater. the board] or three dimes [place samples on the board], what do you III. Identifying which number is less think he would choose? What would On the board write 50 and 18. Read the numbers and ask: How many tens are there in you choose? Why? 50? How many tens are there in 18? Which number has more tens? [50] Which number has fewer tens? [18] This time, let’s circle the number that is less. When we compare two-32 digit numbers, we look at the number of tens to know which number is greater or less. Repeat this with the number pairs 19 and 60, and 40 and 17. For each pair circle the number that is less. IV. Comparing the value of decade numbers and teen numbers greater On the board write 30 is less than 18. Read the sentence and say: Now we will circle the correct word. Which number do we need to look at to decide whether the number is greater or less? [the number of tens] Does 30 have more tens or less tens than 18? [more] So 30 is greater than 18. [Circle the word “greater,” and read the sentence.] Write 16 is greater than 40. Ask: Does 16 have more tens or less tens than 40? [less] So less 16 is less than 40. [Circle the word “less,” and read the sentence.] Repeat with the number pairs 19 and 80, and 60 and 16. V. Applying the concept to dimes and pennies Copyright © by SPOTS Educational Resources. All rights reserved. In a similar way, demonstrate the concept with coins: On the board, display a group of a dime and six pennies, and a group of 4 dimes. Between the groups, write greater is less than. Together, count the value of the coins and decide which group is greater and which is less. Circle “less,” and read the sentence. Repeat this activity with additional groups of coins. STUDENT TEACHER: Draw two columns on the board. Label one “greater” and the other “less.” Have two students at a time each choose a number out of the “number grab bag.” Have them tell which number is greater and which is less, and place them next to each other in

Comparing Numbers Write how much. Circle the correct word. 1.The number of tens tells us which number is greater. 2 tens is greater than ¢ is greater than ¢. 1 ten and 9 ones. less20 is greater than 19.Circle the number that is greater. 2.1. 2. 3. ¢ is greater than ¢. less 60 40 15 50 18 40Circle the number that is less. 3.4. 5. 19 6. ¢ is greater than ¢. less 90 30 60 70 80 6.Circle the correct word. Practice. Write how many of each coin you need.7. Student Workbook page8. Student Workbook pagegreaterthan70.greaterthan15.4. 90¢ 5. 17¢ 40¢ 17 is less 40 is lessCopyright © by SPOTS Educational Resources. All rights reserved.9. 10. greater greater less60 is less than 16. 13 is than 20. Dimes Pennies Dimes Pennies Dimes Pennies 7. 80¢ 8. 19¢ 9. 16¢ Copyright © by SPOTS Educational Resources. All rights reserved.11. greater than 30. 12. greater than 19. less less 20 is 80 is 17 17 Dimes Pennies Dimes Pennies Dimes Pennies 18Chapter 5 Lesson 4 CCSS 1.NBT.3: Compare two-digit numbers based on meanings of the tens and ones digits NYS CCLS 1.MD.3 18the correct column. Repeat this until all the cards are used.CONCLUSION:Now we’ve learned how to find numbers that are greater and numbers that are less.USING THE BOOK: Pages 17-18Page 17: Read and discuss the demonstration at the top of the page. Ask a student to explain why the statement “20 is greater than19” is true.Examples 1-6: Read the directions and have the students complete the section on their own.Examples 7-12: Read the directions. Model the first example on the board, and solve it CLOSING STATEMENT:together. Have the class complete the section on their own. Who can tell us what we learnedReview the page together. today? [Accept relevant answers.] Today we practiced comparingPage 18: Examples 1-3: Read the directions. Model example 1 on the board with model numbers. We saw that we need to look greater at the number of tens to see whichcoins. Write is less than on the board, and circle the correct answer. Have the students number is greater or less. Tomorrow we will learn to find numbers that arecomplete the section on their own. ten more and ten less.Examples 4-9: Read the directions. Explain that this section is a practice of skills they’vealready learned. Have the students complete the section on their own.Review the page together. 33

5.5 Chapter 5 Lesson 5: Ten More, Ten Less CCSS 1.NBT.5 Given a two-digit CONCEPT DEVELOPMENT: Copyright © by SPOTS Educational Resources. All rights reserved. number mentally find 10 more or 10 less than the number. I. Ten more with Dot Cards Use Dot Cards to show the number 40. Write 40 on the left side of the board. Add GOAL: another Dot Card-10. Ask the class to explain what you did. Say: Ten more than Students will find the numbers that 40 is 50. [Under the 40 write 50.] I want to show ten more than 50. How can I show are ten more and ten less than a that? [add another Dot Card-10, and add 60 to the list] given number. MATERIALS NEEDED: Drop-It form Continue in this way until you’ve shown and written 90. #6; hundred-chart, bag marked “50” containing 50 paper clips; group Read the list of numbers and ask: What changed in each number? [the number of of 10 paper clips; bag marked “40” tens] To count ten more than a number, we can think of adding another ten. [Display containing 40 rubber bands the hundred chart. Highlight the number ten and ask:] How much is ten more? [20] [Highlight the 20 and ask:] How much is ten more? [30] [Continue in this way LESSON WARM-UP: until you’ve highlighted the entire column.] Did you notice something interesting Drop-It: Hand out Drop-It form #6. here? [the number that is ten more is underneath] Why is it this way? [because Flash 8-10 addition flash cards with there are ten numbers in each row] [Read the numbers in the column together.] teen totals. Have the students write the sums on their papers. Check the II. Ten less with Dot Cards students’ work. Until now we’ve talked about finding ten more. Now let’s find the number that is ten less. [Point to the group of cards on the board. Ask:] How many are here? INTRODUCTORY STATEMENT: [90] [Write “90” on the right side of the board.] How can I show ten less? [Accept Yesterday we learned to find which answers and remove a Dot Card-10.] How many are there now? [80] [Write “80” number is greater than or less than. under the “90.”] 80 is ten less than 90. Today we will learn something new about tens. We will find numbers that In this way, continue to ask how much ten less than each number is, remove a are ten more and ten less. Dot Card-10, and write the new number on the list. THINKING TRIGGER: Read the list together and ask: What changes in the number when we take away Write pairs of numbers on the ten? [the number of tens decreases by 1 (becomes one less)] board: 80, 90; 10, 20; 40, 50. Ask: Who can think of why I wrote these Clear the board. Write the number 30 on the board, and show it with Dot Cards. numbers as pairs? What is similar in Say: How can we show ten less than this number? [take away a Dot Card-10] How all these pairs? [Accept all relevant much is ten less than 30? [20] suggestions.] Write the number 60 on the board, and show it with Dot Cards. Ask: How much is34 ten less than 60? How can we show it? [take away a Dot Card-10] Ten less than 60 is 50. III. Applying the concept to other objects Display a bag with 50 paper clips, marked “50.” Add a group of ten paper clips to the bag. Explain what you are doing and ask: How many paper clips do you think are in the bag now? [60] If I add another ten paper clips, how many will there be? [70] Show a bag containing 40 rubber bands. Remove a group of ten and ask: How many are in the bag now? [30] If I take out another ten, how many will be left? [20] IV. Practicing the skill Write the number 20 on the board. Say: Now let’s try it with just numbers. Let’s think: How much is 10 more than 20? [30] Repeat this with 50 and 80. Write the number 20 on the board. Say: Now let’s try ten less. Let’s think: How much is 10 less than 20? [10] Repeat this with 60 and 90. Use Dot Cards to demonstrate, as necessary.

Ten More, Ten Less Cross off to show ten less. Write the number. 1. 2. 20 30 40Ten less than Ten more than Ten less than 40 is ____. Ten less than 60 is ____. 30 is 20. 30 is 40. 3. 4.Draw to show ten more. Write the number. Ten less than 30 is ____. Ten less than 50 is ____. 1. 2. 5. 6.Ten more than 40 is ____. Ten more than 50 is ____. Ten less than 20 is ____. Ten less than 70 is ____.3. 4. Student Workbook pageTen more than 30 is ____. Ten more than 60 is ____.Write the number that is ten more.10. Student Workbook pageSolve the story problem. 7. 8. 9. 70, 5. Bill has 70¢.Copyright © by SPOTS Educational Resources. All rights reserved. Dan has 10¢ more than Bill has. 30, 80, 50, How much money does Dan have? Write the number that is ten less. 14. , 80 Copyright © by SPOTS Educational Resources. All rights reserved.Chapter 5 Lesson 5 CCSS 1.NBT.5 Given a two-digit number mentally find 10 more or 10-less than the number. 11. 12. 13. , 70 19 19 , 90 , 50 20 20STUDENT TEACHER:Write a list of numbers on the board: 20, 40, 80, 50. Draw a blank space before and after each number. Have students come upto the board and fill in the number that is ten less and the number that is ten more than each number listed.CONCLUSION:Now we’ve learned to find the number that is ten more and the number that is ten less.USING THE BOOK: Pages 19-20Page 19: Read and discuss the demonstration at the top of the page.Examples 1-4: Read the directions. Model example 1 on the board, and have the students complete the section on their own.Review the section together. CLOSING STATEMENT:Example 5: Read, discuss, and solve the story problem together. Who can tell us what we learned today? [Accept relevant answers.]Page 20: Examples 1-6: Model example 1 on the board, and have the students complete Today we learned to find numbersthe section on their own. that are ten more and ten less. We added or took away one ten eachExamples 7-14: For each section, read the directions and have the students complete time. Tomorrow we will add tens.it on their own.Review the page together. 35

5.6 Chapter 5 Lesson 6: Adding Decade Numbers CCSS 1.NBT.4 Add within 100 CONCEPT DEVELOPMENT: Copyright © by SPOTS Educational Resources. All rights reserved. using concrete models and drawings. I. Introducing adding tens with manipulatives CCSS 1.NBT.2c The numbers 10, Distribute the bags with ten objects in each (see materials needed). Name a 20, 30, 40, 50, 60, 70, 80, 90, refer specific object and ask that the students who have that object come up to the to one, two, three, four, five, six, front of the classroom with their bags. Divide their bags into two groups. Ask seven, eight, or nine tens (and 0 the class to tell you how many objects are in each group, and write the number ones). sentence. Count the bags to see how many objects there are in all. Write the sum. CCSS 1.OA.6 Add and subtract within 20. Continue in this way for several more rounds. CCSS 1.OA.1 Use addition and subtraction to solve word Note: Be sure to limit the sums to 90. problems. II. Adding tens with Dot Cards GOAL: Place three of Dot Card-10 on the board and ask: How much do we have? [30] [Place another two of Dot Card-10 under them.] How many more did I put up? [20] Students will use Dot Cards and How many are there altogether? [50] We just added! Now, can you help me write the manipulatives to add decade number sentence? [Write 30 + 20 = 50 vertically, next to the Dot Cards.] numbers. Students will use what they know Place a group of five of Dot Card-10 on the board and ask: How many tens do we about adding ones in order to add have? [We have 5 tens] [Write 5 tens next to the Dot Cards. Place a group of three decade numbers. of Dot Card-10 under the five cards and ask:] How many more tens do we have? [3 MATERIALS NEEDED: bags with 10 tens] [Write + 3 tens next to the Dot Cards.] How many tens in all? [8 tens] [Write objects in each bag (use those that 8 tens as the sum.] 5 tens and 3 tens are 8 tens altogether. 50 + 30 = 80. [Write the the students brought in); poster equation 50 + 30 = 80 vertically, next to the other number sentence.] board; strings; beads, O-shaped cereal or other, similar items Repeat this with 4 tens + 3 tens. LESSON WARM-UP: III. Using a number sentence to help Now let’s add tens without Dot Cards. [Write 60 + 20 = ___ on the board and draw Flash 10-12 addition flash cards a blank (helping) number sentence format underneath (see p. 22 in the Student with sums to 10. Have the class read Edition).] and solve the number sentences in unison. How many tens are in the first group? [6] [Write 6 tens.] How many tens are in the second group? [2] [Write 2 tens.] How many tens are there altogether? [8] [Write 8 INTRODUCTORY STATEMENT: tens.] We have 8 tens in all. 6 tens plus 2 tens equals 8 tens. How many are there in 8 We know so much about tens. Now tens? [80] Then 60 + 20 equals 80. [Write the sum.] we are ready to learn to add these numbers. Repeat this with 50 + 40 and 40 + 30. THINKING TRIGGER: IV. Practicing the skill Write 40 + 20 = ___ on the board. Write 50 + 20 = ___ on the board. Say: Now we will just think of (not write) the tens Ask: How can we solve this? What can that we are adding. [Model the thinking process by “thinking” aloud:] 50 + 20. we use to find the sum? [Allow the There are 5 tens and 2 tens. 5 + 2 = 7; 7 tens in all. 7 tens are 70. 50 + 20 = 70. [Fill in students to discuss this and make the sum.] suggestions. Demonstrate a few of these suggestions to the class.] Write 70 + 20 and 40 + 40 on the board. Have students tell you how to solve each equation in the same way, while describing their thinking.36 STUDENT TEACHER: Divide the class by rows. Give each row a poster board. Hand out a bag with beads (or other, similarly shaped items) and strings to each group. Have the students

Adding Decade NumbersDraw tens to add. Write the sum. Add.1. 2. 1. + 63 2. + 6300 3. + 32 4. + 3200 5. + 25 6. + 2500 30 + 20 = 40 + 30 = 7. 1 8. 10 9. 3 10. 30 11. 5 12. 50 7 70 4 40 3 303. 4. + + + + + +20 + 10 = 30 + 30 = Write the number sentence that will help add the tens. Solve. 13. 60 + 20 = 14. 50 + 40 =Match the number sentence to the Dot Cards. += +=Write the sum.5. 6. 15. 10 + 80 = 16. 40 + 40 =6 + 2 = 60 + 20 = 50 + 40 = 5+4= += += Student Workbook page7.8.40 + 20 =Make a simple math drawing to show the story problem.Copyright © by SPOTS Educational Resources. All rights reserved. Student Workbook page Write the number sentence and solve. 7 + 2 = 70 + 20 = 4+2=Copyright © by SPOTS Educational Resources. All rights reserved. 17. Amy has 30 peanuts,Chapter 5 Lesson 6 CCSS 1.NBT.4 Add within 100. CCSS 1.NBT.2c, CCSS 1.OA.6, CCSS 1.OA.1 21 21 and 20 almonds in a bag. 22 How many nuts does she have? nuts += 22group ten beads on each string, decide on a number sentence, write it on the poster board, and attach the appropriate numberof beaded strings to show the equation. Have the groups show and explain their work to the class.CONCLUSION:Today we added groups of tens and learned to think of a number sentence to help us add the tens.USING THE BOOK: Pages 21-22Page 21: Examples 1-4: Read the directions. Review example 1 together. Have the students complete the section on their ownwhile you offer help as needed.Examples 5-8: Read the directions. Model examples 5 and 6 on the board while the students fill in the answers in their books.Have the students complete the section on their own while you offer help as needed.Review the page together.Page 22: Examples 1-12: Read the directions. Model examples 1 and 2 on the board. Discuss how solving example 1 helpssolve example 2.Have the class complete the section independently, and review it together. CLOSING STATEMENT:Examples 13-16: Review example 13 together. Have the students complete the section Who can tell us what we learnedon their own. Circulate to offer help as needed. Review the section together. today? [Accept relevant answers.] Today we learned to add tens.Example 17: Read the story problem to the class. Have the students draw it using simple Tomorrow we will add tens on amath drawings, write a number sentence and solve the problem. number line.Review the page together. 37

5.7 Chapter 5 Lesson 7: Using the Number Line to Add CCSS 1.NBT.4 Add within 100 CONCEPT DEVELOPMENT: Copyright © by SPOTS Educational Resources. All rights reserved. using concrete models and drawings. I. Jumping on the number line CCSS 1.OA.6 Add and subtract Remember our jumping frog? [Show the toy frog.] It jumps spaces on the number line within 20. to help us add and subtract. GOAL: Draw an open number line on the board. Write 3 + 2 = 5. Ask a student to tell you Students will add decade numbers how to show it on the number line. using a number line. MATERIALS NEEDED: Drop-It form Display a toy kangaroo. Explain: A kangaroo’s jumps are larger than a frog’s jumps. #4; small toy frog or frog cutout; Kangaroos jump higher and farther than frogs. This kangaroo jumps in “tens.” Each small toy kangaroo or kangaroo jump it makes is a jump of ten spaces. cutout; adding tens equation cards Draw a number line on the upper section of the board. Have the kangaroo start at LESSON WARM-UP: the beginning and make a jump. Say: The kangaroo just jumped ten. [Write 10 under Drop-It: Hand out Drop-It form #4. the kangaroo. Then have the kangaroo make another jump.] Now the kangaroo Flash ten addition flash cards with jumped another ten. Which number should I write now? [20] [Continue making jumps sums to ten. Have the students write with the kangaroo and filling in the number line until you’ve written 100.] the sums on their papers. Check the students’ work. II. Adding tens on the number line Write 30 + 20 = ___ on the board. Say: Now, let’s add tens using the number line. INTRODUCTORY STATEMENT: [Use the kangaroo and the number line you just made.] At which number should the Yesterday we learned to add tens. kangaroo start? [30] [Place the kangaroo at the 30.] How many jumps of ten do we Today we will add tens on a number need to make to add 20? [2 jumps of ten] [Model the kangaroo’s jumps as you count line. on.] Let’s count as the kangaroo jumps in tens, to see where it will land. We begin at 30, and we jump to 40 and 50. Which number did the kangaroo reach? [50] The kangaroo THINKING TRIGGER: started at 30 and jumped two more tens. It got to 50. [Point to the numbers on the Draw an open number line on the number line as you explain:] The kangaroo showed us that 30 + 20 = 50. [Fill in the board, and write 50 + 40. Ask: How sum.] In the same way, use the kangaroo to solve the addition problems 40 + 30 do you think we can show this on the and 70 + 20. number line? III. Adding tens on an open number line38 Write 60 + 30 = ___. Say: Let’s solve this problem using an open number line. [Draw an open number line.] We will begin the number line with 60. Then we will count on by tens and draw the jumps as we count. We will write only the last number we get to. [Begin the number line with 60. Together with the class, count on 70, 80, and 90, as you draw the jumps. Write 90 under the last space where you finished jumping.] Now we see that 60 + 30 = 90. [Fill in the sum.] Repeat this process with 60 + 20 and 50 + 30. IV. Practice Write 40 + 20 = ___ vertically on the board. Say: Let’s solve this problem mentally, by thinking about it. We can think of jumping tens on the number line, or we can think of a “helping number sentence” (___ tens + ___ tens). Think of how you would solve it and what the sum is. Ask some students to share how they solved the equation. Do the same with other, similar equations. STUDENT TEACHER: Have the students work in pairs. Give each pair an equation card and a paper. Ask them to show how to solve their equation using a number line and again by writing a number sentence that will help. Ask them to share their work with other students. You may hang some of this work on your math bulletin board.

Using the Number Line to Add Complete the number line. Fill in the sum. We can jump tens 1. 60 + 30 = on the number line.50 + 40 = 90 10 20 30 40 50 60 70 80 90 100 2. 70 + 20 =Complete the number line. Fill in the sum. 3. 40 + 30 =1. 30 + 30 =2. Add. 5. 20 6. 60 7. 30 8. 70 + 50 + 30 + 30 + 10 40 + 40 = 4. 40 + 40 Student Workbook page3.9. + 1800 10. + 2300 11. + 2600 12. + 5400 13. + 2200 Student Workbook page 50 + 30 = Add.Copyright © by SPOTS Educational Resources. All rights reserved.4. 23 23 14. 8 15. 6 16. 9 17. 7 18. 4 19. 8 Copyright © by SPOTS Educational Resources. All rights reserved. 24 +8 +7 +5 +5 +9 +6 40 + 20 = 24Chapter 5 Lesson 7 CCSS 1.NBT.4 Add within 100 using concrete models and drawings. CCSS 1.OA.6,CONCLUSION:Now we’ve learned another way to add tens: We can think of jumping tens on a number line.USING THE BOOK: Pages 23-24Page 23: Read and discuss the demonstration at the top of the page.Examples 1-4: Read the directions. Model example 1 on the board, and have the class complete the section independently. Reviewit together.Page 24: Examples 1-3: Read the directions, and have the students complete the section on their own. Explain that examples 2 and3 are more challenging because the students need to fill in the starting number and the jumps on their own.Examples 4-13: Read the directions. Direct students to solve the problems by thinking of either the number line or the “helpingnumber sentence.” Have the students complete the section on their own. Review it together.Examples 14-19: Read the directions. This is a review of what was covered in Chapter 4. Students can refer to the first-addendbanner posted in front of the classroom or to the banner found at the back of the Student CLOSING STATEMENT:Edition. Review.Display the 8 + 5 Dot Card and its number Who can tell us what we learnedsentence on the Math Poster. today? [Accept relevant answers.] Today we added tens on a number line. Tomorrow we will subtract tens. 39

5.8 Chapter 5 Lesson 8: Subtracting TensCCSS 1.NBT.6 Subtract multiples CONCEPT DEVELOPMENT: Copyright © by SPOTS Educational Resources. All rights reserved.of ten.CCSS 1.OA.6 Add and subtract I. Introducing the concept with manipulativeswithin 20. Present 7 bags with 10 objects in each bag (the bags should all contain the sameCCSS 1.NBT.2c The numbers 10, objects). Remind the students that each bag contains 10 objects. Set aside a20, 30, 40, 50, 60, 70, 80, 90, refer group of 4 bags. Say: Here is a subtraction sentence that we can write: How manyto one, two, three, four, five, six, objects are in all the bags together? [70] [Write 70.] How many objects are in theseven, eight, or nine tens (and 0 bags that we took away? [40] [Write – 40.] How many objects are left? [30] [Writeones). = 30.]CCSS 1.OA.1 Use additionand subtraction to solve word Repeat this with 60 – 40. (Present 6 bags and remove 4 bags.)problems. II. Using Dot Cards to subtract tensGOAL: Place five of Dot Card-10 on the board and ask: How many tens do we have? [5Students will use what they know tens] [Write 5 tens next to the Dot Cards. Draw an X over two of the Dot Cardsabout subtracting ones in order to and ask:] How many tens did we cross off? [2 tens] [Write – 2 tens next to the Dotsubtract decade numbers. Cards.] What is the difference? [3 tens] [Write 3 tens as the difference.] 5 tens minusMATERIALS NEEDED: Drop-It form 2 tens equals 3 tens. 50 – 20 = 30. [Write the equation 50 – 20 = 30 vertically on#2; bags with 10 objects in each bag the board.](that students brought in) Repeat this with 7 tens – 3 tens.LESSON WARM-UP:Drop-It: Hand out Drop-It form #2. III. Using a “helping number sentence”Flash ten Subtraction Dot Cards. Now let’s subtract tens without Dot Cards. [Write 60 – 20 = ___ on the board andHave the students write each draw a blank (helping) sentence format underneath (see p. 26 in the Student’sequation on their papers. Check the Edition).]students’ work. How many tens are there in all? [6] [Write 6 tens.] How many tens are we subtracting?INTRODUCTORY STATEMENT: [2] [Write 2 tens.] How many tens are left? [4] [Write 4 tens.] We have 4 tens left. 6We’ve already learned to add tens. tens minus 2 tens equals 4 tens How many are there in 4 tens? [40] Then 60 minus 20Today we will subtract tens. equals 40. [Write the difference.] THINKING TRIGGER: Repeat this with 80 – 60 and 70 – 40.Write 8 – 4 = ___ and 80 – 40 = ___on the board. Ask a student to tell IV. Practicing the skillyou how much 8 – 4 is. Ask: Can you Write 70 – 20 = ___ on the board. Say: Now we will only think of (and not write)think of how knowing that 8 – 4 = 4 the tens that we are subtracting. [Model the thought process by “thinking” aloud:]helps to solve 80 – 40? 70 – 20. There are 7 tens, and we need to take away 2 tens. 7 – 2 = 5. This number sentence helps me solve 70 – 20. Now I know that there are 5 tens left. 5 tens is 50. 70 – 20 = 50. [Write in the difference.] Write 80 – 40 and 60 – 40 on the board. Have students tell you how to solve each equation in the same way, while describing their thinking. STUDENT TEACHER: Call two students up to the board. Have one student write a subtraction equation using decade numbers, and have the other write a number sentence to help solve it. Then have them solve both equations. Repeat this with additional pairs of students.40

Subtracting Tens Subtract.Cross off the dots to subtract. Write the difference. 1. 7 2. 70 3. 6 4. 60 5. 9 6. 90 – 6 – 60 – 4 – 40 – 6 – 601. 2. 60 – 20 = 50 – 20 = 7. 8 8. 80 9. 9 10. 90 11. 4 12. 40 – 4 – 40 – 5 – 50 – 3 – 303. 4.70 – 30 = 70 – 50 = Write the number sentence that will help you subtract the tens. Solve. 13. 50 – 30 = 14. 60 – 50 =Match the number sentence to the Dot Cards. –= –=Write the difference.5. 6. 15. 80 – 50 = 16. 70 – 40 = –= –=5 – 4 = 50 – 40 = Student Workbook page6 – 3 = 60 – 30 = Student Workbook page7. 8. Fill in the math puzzle. Write the number sentence and solve.Copyright © by SPOTS Educational Resources. All rights reserved. 4 – 3 = 40 – 30 = 3–1= 30 – 10 = 17.Gabby has 10 buttons. He uses Whole Copyright © by SPOTS Educational Resources. All rights reserved. some buttons for a snowman. 25 25 Now he has 6 buttons left. How Part Part 26 many buttons did he use to make his snowman? ___ buttons =Chapter 5 Lesson 8 CCSS 1.NBT.6 Subtract multiples of ten. CCSS 1.OA.6, CCSS 1.NBT.2c, CCSS 1.OA.1 26CONCLUSION:Today we learned to subtract tens.USING THE BOOK: Pages 25-26Page 25: Examples 1-4: Read the directions. Have the class complete the section independently.Examples 5-8: Read the directions. Model example 1 on the board, and have the students complete the section on their own,while you offer help as needed.Review the page together.Page 26: Examples 1-12: Read the directions. Model examples 1 and 2 on the board. Discuss how solving example 1 helpssolve example 2.Have the class complete the section independently, and review it together. CLOSING STATEMENT:Examples 13-16: Review example 13 together. Have the students complete the section Who can tell us what we learnedon their own. Circulate to offer help as needed. Review the section together. today? [Accept relevant answers.] Today we learned to subtract tens.Example 17: Read the story problem and solve together with the class. Tomorrow we will subtract tens on a number line. 41

5.9 Chapter 5 Lesson 9: Using the Number Line to SubtractCCSS 1.NBT.6 Subtract multiples CONCEPT DEVELOPMENT:of ten. II. Reviewing subtracting tensCCSS 1.OA.6 Add and subtract Write 80 – 20 on the board. Ask a student to tell you the number sentence that will helpwithin 20. solve this (8 tens – 2 tens = 6 tens), and write the difference. If needed, repeat this with other equations.GOAL: II. Reviewing adding tens on a number line Draw an open number line. Say: A few days ago we added tens on a number line. Let’sStudents will subtract decade review that before we learn to subtract.numbers on a number line. Write 50 + 40 on the board. Ask the class to tell you how to solve it on the number line.MATERIALS NEEDED: Drop-It form Fill in the start number on the number line. Draw the jumps as you count on by tens,#4; small toy frog or frog cutout; and write in the number at which you land. Fill in the sum.small toy kangaroo or kangaroocutout; subtracting tens equation III. Counting back by tenscards Display the kangaroo. Remind the students: A kangaroo’s jumps are bigger than a frog’s jumps. Kangaroos jump higher and farther than frogs do. The kangaroo jumps in “tens.” Each jump it makes is a jump of ten spaces.LESSON WARM-UP: Draw a number line at the top of the board. Have the class help you fill it in by counting by tens from 10 to 100. Say: Today the kangaroo will subtract tens. Do you remember whichDrop-It: Hand out Drop-It form direction we jump for subtraction? [back] Why? [because we start with a bigger number,#4. Flash ten subtraction flash we take away, and we get to a smaller number]cards. Have the students write thedifferences on their papers. Check Let’s count as the kangaroo jumps back from 100. [Jump the kangaroo as the studentsthe students’ work. count back from 100 to 10.] Note: Leave this number line on the board for the student to refer to, until the end of the lesson.INTRODUCTORY STATEMENT: IV. Subtracting tens on a number line Say: Now we are ready to subtract on the number line. Think about the suggestions weYesterday we learned to subtract made before (in the Thinking Trigger). Which ones do you think will work? Which ones won’ttens. Today we will subtract tens on a work? [Write and solve 60 – 30 using one or more of the suggestions.]number line. Write on the board: 70 – 30= ___. Read the equation together and say: This means that we have 70 and we need to take away 30. [Place the kangaroo on the 70 on the number line.] How many jumps of ten do we need to make to subtract 30? [3 jumps of ten] In which direction do we need to jump? [back] [Jump the kangaroo back three jumps of ten while counting along: We begin with 70. We jump back ten, and we get to 60. We jump back another ten, and we get to 50, and then THINKING TRIGGER: we make one more jump back, and we get to 40. The kangaroo got to 40. 70 – 30 = 40. [Fill in the difference.]Draw an open number line andwrite 60 – 30 on the board. Say: Repeat this with the equation 90 – 20 = ___.Think about how we added tens on V. Subtracting tens on an open number line Copyright © by SPOTS Educational Resources. All rights reserved.the number line. How do you think Write 80 – 20 = ___. Say: Let’s solve this problem using an open number line. [Draw an openwe can show the subtraction problem number line.]60 – 30 on the number line? With which number should we start? [80] Let’s think: Where should I write the eighty – at the beginning or the end of the line? [at the end] Why? [because we need to jump back] [Write 80 on the right side of the number line.] How many jumps of ten do we need tomake? [two] [Let’s count as I jump: We begin with 80. We jump back ten and get to 70, and then we jump back another ten and get to 60. [Drawthe jumps as you count. Write 60 under the last space where you finished jumping.] We got to 60. So 80 – 20 = 60. [Fill in the difference.]Repeat with 90 – 30, 60 – 30, and 90 – 40. Solve each equation on a number line: Fill in the starting number, draw the jumps as you countback, and write the number at which you land. Then fill in the difference.42

70 – 30 = 40 Using the Number Line to Subtract Complete the number line. Fill in the difference. We can jump back tens 1. 90 – 40 = on the number line. 10 20 30 40 50 60 70 80 90 100 2. 60 – 20 =Complete the number line. Fill in the difference. 3. 70 – 30 =1. 90 – 30 =2. Subtract. 5. 80 6. 50 7. 80 8. 90 – 20 – 50 – 10 – 40 70 – 20 = 4. 80 – 303. Student Workbook page9. 90 10 70 11. 50 12. 60 13. 90 Student Workbook page– 20 – 30 – 20 – 20 – 30 80 – 30 =Copyright © by SPOTS Educational Resources. All rights reserved.4. 27 27 Add. Copyright © by SPOTS Educational Resources. All rights reserved. 28 50 – 20 = 14. 6 15. 6 16. 8 17. 10 18. 4 19. 9 +6 +5 +7 +6 +7 +8Chapter 5 Lesson 9 CCSS 1. NBT.6 Subtract multiples of ten using concrete models and drawings. CCSS 1.OA.6 28VI. PracticeWrite 40 – 20 = ___ vertically on the board. Say: Let’s solve this mentally, by thinking about it. We can think of jumping tens on the number line,or we can think of a “helping number sentence” (___ tens – ___ tens). Think of how you would solve it and what the difference is.Ask some students to share how they solved the equation. Do the same with other, similar equations.STUDENT TEACHER:Draw some open number lines on the board. For each, have a student choose a tens subtraction equation card and solve it on the numberline. Help the students explain their thought processes.CONCLUSION:Now we’ve learned another way to subtract tens: We can think of jumping back tens on a number line.USING THE BOOK: Pages 27-28Page 27: Read and discuss the demonstration at the top of the page.Examples 1-4: Read the directions. Model example 1 on the board, and have the students complete the page on their own. Review ittogether.Page 28: Examples 1-3: Read the directions, and have the students complete the section on CLOSING STATEMENT:their own. Point out that in examples 2 and 3 they need to fill in the starting number and thejumps on their own. Who can tell us what we learned today? [Accept relevant answers.]Examples 4-13: Read the directions. Direct students to solve the equations by thinking of either Today we subtracted tens on athe number line or the “helping number sentence”. Have the students complete the section on number line. Tomorrow we will learntheir own. Review it together. about a new kind of story problem with our math puzzles.Examples 14-19: Read the directions. This is a review of what was covered in Chapter 4. Studentscan refer to the first-addend banner posted at the front of the classroom or to the banner foundat the back of the Student Edition. Review. 43

5.10 Chapter 5 Lesson 10: Story Problems with Start UnknownCCSS 1.OA.1 Use addition CONCEPT DEVELOPMENT:and subtraction to solve wordproblems. I. Reviewing drawing to solve story problems Distribute blank sheets of paper to each student. Tell a story: Kevin and his neighbors made 5GOAL: big snow men and 4 little snow men. How many snow men did they make? Draw to show this storyStudents will subtract to solve problem, and write a number sentence to solve it. Choose a few students to share their answer andstory problems in which the start is drawings. Be sure to include one or two students who drew simple drawings to help them solve it.unknown.MATERIALS NEEDED: Magnetic Do the same for the following story: Laura has a box of 11 crayons. 6 crayons are sharpened and themath puzzle; blank sheets of paper; rest have broken tips, how many crayons have broken tips?small dolls; toy train cars; counters II. Using manipulatives and math puzzles to solve story problems with an unknown start Now let’s tell some more story problems. These are a little different from the other ones we’ve discussed, so listen carefully:LESSON WARM-UP: My baby has lots of dolls! Her grandma gave her 2 new dolls for her birthday. Now she has 8 dolls. How many dolls did my baby have before?Flash 10-12 subtraction flash cards.Have the class read and solve the What information do we want to find out? [how many dolls the baby had in the beginning] [Shownumber sentences in unison. a group of 8 small dolls.] Let’s think of how we can solve this problem. [Listen to the students’ suggestions, and model some using the dolls. Then say:] Here is my way to show this. How manyINTRODUCTORY STATEMENT: dolls does the baby have now? [8] How many are new? [2] [Move two to the side to show they areWe’ve learned so much about two- the new ones. Point to the two dolls.] These are the dolls Grandma just gave her. [Now point todigit numbers. Today we will do the group of six dolls.] What is this group? [the dolls the baby had before] How many did she havesomething different; we will tell story before? [6]problems. Review the story while pointing at the dolls: Grandma gave my baby two dolls. Now she has eight THINKING TRIGGER: dolls. Before, my baby had six dolls.Write a plus sign on the boardand ask: What are some stories that Now I will tell you another story. This is about my son Todd. Todd has an electric train in his room.we can solve by adding? [Accept Today he added on 2 more cars. Now he has 7 cars on the train. He asked me: “Mommy, how manyanswers and discuss. Then write train cars did I have before?” He had some cars on the train, he added on two more, and now he hasa minus sign on the board and 7. How many did he have before?ask:] What are some stories that wecan solve by subtracting? [Accept Let’s help Todd figure this out. What information do we want to find out? [how many train cars heanswers and discuss.] had in the beginning] How many train cars does he have now? [7] [Display seven cars.] How many of these cars did he just add on? [2] [Move two to the side.] These are the cars he added on. [Point to the other cars.] What are these cars? [the cars he had before] How many did he have before? [5] Let’s think. How did we solve this problem? Did we put groups together, or did we take a group away? [took away] What did we take away? [the two train cars he added on] When we take that group away, what do we have in the other group? [the cars he had in the beginning] [Draw an equation format and fill it in accordingly. Point out that we know how many were added on and how many he has now. We subtracted to find how many he had before.]Place the magnetic math puzzle on the board. Say: Let’s fill this in together to show our story. Copyright © by SPOTS Educational Resources. All rights reserved.We know many cars Todd added on…? [2] Is 2 a part or the whole? [part] [Write 2 in the puzzle.] We also know how many cars he has now…? [7] Is 7 a part orthe whole? [whole, it’s the total number of cars that he has] [Write in 7.] Now we need to fill in the other part. What is it? [5] Five what…? [5 cars Todd hadbefore] How did we find the missing part? [subtracted]Summarize: When we know the whole and one part, we subtract to find the part we had in the beginning.Tell the following story: My niece Cheryl is saving money. She has some coins in a jar. Today I gave her 4 more coins to put in. Then we counted 10 coins in thejar. How many coins did she have before I gave her 4 more?Distribute counters, and have the students use them to show and solve the story problem, as above. Place a math puzzle on the board and fill it in asyou go along. Say: We need to use the numbers from the story to fill in the math puzzle. We know she got 4 more coins, and she has 10 coins in all. What is 4? [apart, the coins she got today] What is 10? [the whole, all the coins she has] What information is missing? [the other part, the coins she had before] [Drawa blank number sentence format.] How can we find how many coins Cheryl had before? [We need to subtract the coins she got.] [Write the equation and44

Story Problems with Start Unknown When we know the whole and one part, Make a simple math drawing to show the story problem. we subtract to find out how much we had at first. Fill in the math puzzle. Write the number sentence and solve. Make a simple math drawing to show the story problem. 1. A line of toy train cars stands Whole Fill in the math puzzle. Write the number sentence and solve. on the shelf. Danny connects 3 more train cars. Now there are Part Part 1. There are some pennies in a Whole 9. How many train cars were mug. Franco drops in 4 more there to begin with?___ train = pennies. Now there are 10. How Part Part cars many pennies were there to begin with? ___ pennies = added began with 2. There are some candies in a 2. Ella has a sticker collection. Whole dish. Grandma adds 4 more Her friend gives her 2 more candies to the dish. Now there are stickers. Part Part 7. How many candies were in Now she has 10 stickers. the dish before?___ candies How many stickers did Ella have = at first? ___ stickers Whole Student Workbook page Student Workbook page Part Part = 29 29 30 Copyright © by SPOTS Educational Resources. All rights reserved. 30 Chapter 5 Lesson 10 CCSS 1.OA.1 Use addition and subtraction to solve word problems. solve.] How many coins did she have before? What is the other part? [6] Cheryl had 6 coins before I gave her 4 more today. III. Making simple drawings Linda has a box of crayons. Her friend returned three crayons that she borrowed. Now Linda has ten crayons in her box. How many crayons were there before her friend returned the crayons? Draw a math puzzle on the board. Repeat the story in short, and fill in the puzzle, as above. Then restate the rule: When we know the whole and one part, we subtract to find the other part. [Write an equation for this story and solve it. Complete the puzzle.] Hand out blank sheets of paper, and have the students work in pairs to draw the story with simple math drawings. When the students are done, have some partners show their work and explain what they did. Then model on the board: I will use lines to show the crayons. I will draw 10 crayons. That is the number of crayons Linda has in all. She got back three of the crayons. I will draw a circle around three of the lines and write from friend. These [point to the group of three] are the crayons that her friend returned to her. [Point to the rest of the drawings.] What are these? [The crayons Linda had before.][Circle and label them had before.] Let’s count how many she had. [Count the seven “crayons”/lines together.] Linda had 7 crayons before. Tell the following story: Sammy has a paper airplane collection. His brother made him 5 airplanes, and now he has 8 airplanes in all. How many did he have before? [Draw a math puzzle and fill it in with the known numbers. Have the students work with their partners to draw the story with simple math drawings and write a number sentence to show what they did. Ask some students to show and explain their work. Then model the drawing on the board. Write the equation and complete the math puzzle.] STUDENT TEACHER: Tell another story: 5 children came into the classroom. Now there are 9 children. How many were there before? Hand out blank sheets of paper to each student. Have the students work in pairs to fill in a math puzzle, write an equation and draw the storyCopyright © by SPOTS Educational Resources. All rights reserved. using simple math drawings. Have each pair share their work with another pair of students. Hang the CLOSING STATEMENT: work on your math bulletin board. CONCLUSION: Who can tell us what we learned today? [Accept relevant answers.] Today we told story problems in which we know the whole amount and one part. We subtracted to find the Today we learned about another kind how much we had at first. of story problem. We learned that when we know the whole amount USING THE BOOK: Pages 29-30 Pages 28-29: Read and discuss the text at the top of the page. Read the directions. Read each story. and one part, we subtract to find how Complete the pages together. much we had at first. Tomorrow we will review this chapter. Display the 8 + 6 Dot Card and its number sentence on the Math Poster. 45

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