Teacher Edition 2015(1) with cover

TMM A T HFOR ATHEMATICAL BILITIES & HINKING ABITSA UNIQUE SYSTEM THAT CHANGES THE FOCUSFROM ROTE PRACTICE TO REAL MATH WISDOMTEACHER’S EDITION Grade 1 • VVoOlLuUmMEeI1

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Spots for M.A.T.H. First Grade Mathbook Student’s Edition Volume 1Copyright © 2011 by Nechemia & Sarah G. Weiss, 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 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 StudioArt 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.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: 978-0-9851129-9-8 (Revised 2013 Edition) w 978-0-578-07398-9 (2012 Edition) w978-0-9851129-8-1 (Set of 2 Volumes) w Library of Congress Control Number: 20119116573 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 12�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Lesson Warm-Up Activities 14��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Suggested Activities for Practice and Review 16�����������������������������������������������������������������������������������������������������������������������������������Chapter 1 19���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Chapter 2 49���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Chapter 3 91���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������Chapter 4 131������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������This teacher’s edition includes lesson plans with step-by-step instruction, to develop core mathskills and advanced thinking abilities in the young student.Feel free to contact us directly for curriculum support. We are here to help you with professionaldevelopment and to provide extra support in meeting the educational needs of all learners. 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



































1 Introduction to Chapter One Goal: Concept Development: Students will be given an overview of chapter one: numbers one to ten. I. Introducing numbers 0-10 Materials needed: small bags Hand out a small bag containing ten pieces of O-shaped cereal or similar snack with ten pieces of O-shaped cereal; to each student. Together, count how many snacks each student has. Call out the enough for each student, real or number “two”and write the numeral 2 on the board. Say: You can eat this number paper leaves (optional) of snacks – two. [Give the students time to eat their snacks.] Now let’s count how many snacks you have left. [Continue in this way until all the snacks are finished.] Introductory Statement: This is our new math book. In this You can include zero as a number. Explain that “zero” means none. book we are going to learn about numbers and things we can do with II. Introducing “more” them. [Give time for the class to Pass out another bag containing ten pieces of popcorn. Ask each student to take look through their math books and some pieces out of the bag, put them on his/her desk, and put the rest of the bag share observations about what they on the side. Have the students count the pieces on their desks and remember see.] Look at pages I, 2, 3, and 4. These the number. Show the class a similar bag. Take one piece out and ask: Who has pages show the Table of Contents. more pieces out of the bag than I have? Raise your hand. [Ask a few students how The table of contents tells us about many they have. Compare amounts. For example:] Sarah has three. I have one. what is written in the book. Our math Three is more than one. book is divided into chapters. In each chapter we learn about a different On the board, draw a box and label it “new words.” Say: Here I will write some new topic in math. The Table of Contents words we will learn in math. [Write “more” in the box.] tells us what will be learned in each lesson in the chapters. Repeat this with other amounts of popcorn. ))You may want to read some of the III. Introducing “less” listings in the Table of Contents. Now we will do something different. [Remove eight pieces of popcorn.] Who has less pieces out of the bag than I have? Raise your hand. [Ask a few students how tHINKING tRIGGER: many they have. Compare amounts. For example:] Michael has five. I have eight. Today we will start the first chapter, Five is less than eight. Chapter One. Chapter One tells us about numbers 1-10. Who can think Write “less” in the “new words” box. of places we need to use numbers? How do we use them? Discuss the Repeat this with other amounts of popcorn. students’s answers. IV. Introducing “equal”22 Now we will do something else. [Show the class six pieces of popcorn.] I have six. Does anyone else have six? Does anyone else have the same amount? Raise your hand. [Ask a student how many he/she has. Compare amounts:] Liz has six. I have six. We have the same amount. Six and six are equal. Equal means the same amount. Write equal in the “new words” box. Repeat this with other amounts. Dear Parents, With great excitement, we are pleased to inform you that this year your first grader will be learning math using the Spots for M.A.T.H. approach. The Spots for M.A.T.H. approach is a conceptual, hands-on visually based program geared to maximize the mathematical abilities of every student. Since numbers are abstract, the children will be using special Dot Cards in the process of learning. These Dot Cards represent amounts and concepts in a way that is easily visualized, and are especially helpful for mastering addition and subtraction facts with automaticity. In this chapter Dot Cards 1-10 will be introduced. These cards will help your child develop an understanding of the amount each number ))Remember to send home the family letter. symbol is representing. Feel free to call me for any questions or concerns. Thanking you in advance for your cooperation, I remain, Family Letter • Chapter 1

Using Symbols to Add 1 + 3 = 4 is an Draw 1 more. Write the sum. addition sentence. more 1+1= 1.Now is the time 2. less 1equ+al 3 = 4 Of beginning for all, plus equals sum The beginning of school, The beginning of fall�Write the sum.1. 2. Down,2do+w1n=, down, 9+1= Yellow, red, and brown� 3+2= DrTahwe2lemaovree.sWarrieteftahlelinsgumd.own 3.All over the town� += 4. += 3 yellow leaves Falling to the ground, 1-2-3, 2+1= 3 leave1s+a2ll a=round�3. 4. 3 red leaves F5i.lF64l -ailn5ell-tai6nhv,egenstouamtlhbl eearrgosreuonnutdenn�dc,e. 6. Student Workbook page 4+2= 3+3= Student Workbook page 4 brown leaves 2+2= Falling to the ground,5. Chapter Opener 710-8l-e9a-1v0e,s+ all ar=ound� 6. 7.Now is the time 8. Of beginning for all, NumbersTThhee beginning of school,1+4= Chapter 1: begi+nning o=f fall! 35 36 6 6 55Using the Book: Pages 5-6Page 5: Say: Do you see the tree at the side of the page? What is falling off the tree? [leaves] What season is it? [fall/autumn] Justlike it is now (or almost will be)! In this chapter we will use things that are connected to fall to help us learn math.Draw students’attention to the group of numbers. Ask: Does anyone know what these are? [Wait for answers.] These are numbers.Find the yellow number. That is the number four. Does anyone know what number is in green? [Continue in this manner until youhave discussed all the numbers.]Display some sample Dot Cards. Say: These are Dot Cards. Can you find the Dot Cards on the page? These will be used to learn eachnumber. Let’s count the number of dots on each card.Point out the colorful “steps.” Explain that each step has a number. Draw a similar set of steps on the board, and have a small“doll” walk up the stairs while counting.Point out the new vocabulary. Say: These are words we will learn in this chapter. We have the same words on the board. [Read thelist and compare it to the words on the board.]Page 6: Read the poem and discuss it with the class. You may find it helpful to use real Closing Statement:or paper leaves to demonstrate as you read. Now we are ready to start learning first-grade math! 23

1.1 Chapter 1 Lesson 1: Numbers 1, 2, and 3CCSS 1. NBT.1 Read and write Concept Development:numerals and represent a numberof objects with a written numeral. I. Writing the numbers 1, 2, and 3 Place or draw a large pencil on the board. Ask: How many pencils did I put on theGoal: board? [one] I am going to write the number 1 under the pencil. [Draw writing lines andStudents will recognize and write write the numeral 1 under the pencil. As you form the number, show the class thethe numbers 1, 2, and 3. starting point (on top) and explain how to form the 1. Have the students trace a 1 inStudents will recognize Dot Cards 1, the air with their first fingers.]2, and 3.Materials needed: school Draw or place a large ruler on the board. In a similar way, ask how many, and writesupplies or schoo-supplies cutouts; 1 on the board.blank Dot Card; magnetic counters Do the same for the numbers 2 and 3: Draw or place two or three school supplies onIntroductory Statement: the board, ask how many, and write the numeral underneath. As you write, be sureNow we are ready to learn the first to stress the starting point and explain how to form the numeral. Have the studentslesson. We will learn about the trace a 2 and a 3 in the air with their first fingers.numbers one, two, and three. II. Dot Cards 1, 2, and 3 Display a blank Dot Board on the board. Say: This is a Dot Card. We will use Dot Cards this year to learn math. [Place a black counter on the card and ask:] How many black counters do you see on this card? [1] This is Dot Card 1. [Place Dot Card 1 on the board and write the numeral 1 underneath.] tHINKING tRIGGER: Add another counter to the blank Dot Card to form Dot Card 2. Ask: How many black counterss are on the card now? [2] [Place Dot Card 2 on the board and write the What were the first numbers we said numeral 2 underneath. Explain that this is Dot Card 2.] as we counted the snacks? [one, two, three] Let’s think together. What are Do the same for the number 3. things that come in ones? In twos? In III. Practice threes? [Accept all relevant answers.] Flash Dot Cards 1, 2, and 3, and have the class say the correct number for each one [Encourage the class to contribute together. Repeat this several times. Then flash the Dot Cards and have the students their own ideas.] show the corresponding number of fingers.)) Since this is the first time the class is doing Find the page of Dot Cards in the back of the student’s edition. Have the students an exercise like this, you may need to start punch out Dot Cards 1, 2, and 3, to start their collection. off with suggestions of your own. Student Teacher: Place Dot Cards 1, 2, and 3 on the board. Invite three students in turn to tell the numbershown by a Dot Card. Write the correct numeral under each Dot Card. Help the students explain how they are writing the numbers.Conclusion:Today we learned about the numbers one, two, and three. We learned to read and write the numbers, and we learned their Dot Cards.Using the Book: Pages 7-8 ))Remember: In the beginning it is important to check the students’ work in their math books to be sure each student understands the directions.Page 7:Help the students find page 7 in their books. Say: This is the first page that we will work on in our math book. This page has twoparts. The top part has writing lines, and the bottom part has Dot Cards. What do you think we will do in the top part of the page? [Allowstudents to answer.] I will read the directions. They are on the top of the page, above the writing lines.What number will we write on the first line? [1] The next two lines are for the number 2. What number will you write on the bottom lines? [3]24

Numbers 1, 2, and 3Write the number� 1� Color 2 pairs of scissors� 2� Color 1 apple� 3� Color 3 crayons� 4� Color 2 buses� Complete each pattern� 5� 6�Write how many dots there are on the Dot Card� Student Workbook page1. 2. 3. Student Workbook page 7� 77 38� 2 3 2 8Chapter 1 Lesson 1 CCSS 1� NBT�1 Read and write numerals and represent a number of objects with a written numeral� 8We will start with writing the number 1. [Review how to write the 1, demonstrating on the board. Remind the class to start at thestarting point.]Say: Use your pencil to write the one. Trace over the first ones in the book, and then continue on your own. Stop at the end of the line. [Pointout the dots on top that show the starting point for each number.]Direct students in the same way with writing the numbers 2 and 3.Say: Under the writing lines is a number line. Who can read the numbers that are in the squares? Use your pencils to trace over the numbers1, 2, and 3.What do you see on the bottom of the page? [Dot Cards 1, 2, and 3] I will read the directions. [Read and ask:] What do we need to do here?[write in the number of dots that are on the Dot Card] [Have the students write in the number of dots under each Dot Card.]Page 8: Help the class turn to page 8. Point out that this page also has two parts. Closing Statement:Help the class find the first line. Explain that there is a 1 next to the first line because this is What did we learn today in mathexample 1. Help them find examples 2, 3, and 4. class? [Accept relevant answers.] Today we learned the numbers one,Examples 1-4: Read the directions. Have the class color the pictures accordingly. two and three on our Dot Cards and how to read and write them.Examples 5-8: Remind the class of what they know about patterns. On the board, draw the Tomorrow we will learn the numbersfirst pattern. “Read” the pattern (yellow triangle, orange circle, yellow triangle, orange circle) that come next: four and five.and ask: What goes next? [yellow triangle] [In this way, fill in the next three shapes on theboard. Have the class do the same in their books.]Continue in this way until you complete the page. 25

1.2 Chapter 1 Lesson 2: Numbers 4 and 5 CCSS 1. NBT.1 Read and write Concept Development: numerals and represent a number of objects with a written numeral. I. Dot Cards 4 and 5 Place a blank Dot Card on the board and use black magnetic counters to create Goal: Dot Card-4. Say: Let’s count the dots together. Students will recognize and write the numbers four and five. Count the dots with the students and compare to the previous Dot Cards learned. Students will recognize Dot Cards 4 Write the numeral 4 underneath. and 5. Materials needed: blank Dot Place another blank Dot Card on the board. Write the numeral 5 underneath. Cards; black magnetic counters; Read the numbers and ask the class to “help” you form Dot Card-5. Slowly place sets of four and five school items each counter on the board as they count, until they tell you to stop. (e.g., pencils, rulers, crayons, books) Ask students to compare the cards. Help students conclude that Dot Card-5 has Lesson warm-up: all the green squares filled with dots. Flash Dot Cards 1, 2, and 3. Have the class identify each one in unison. II. Writing 4 and 5 Draw writing lines on the board, show the starting point, and explain how to )) Remember to show each card for only write the numbers 4 and 5. Have the students trace a 4 and a 5 in the air with one second! If necessary, or to provide their first fingers. additional practice, you may show Dot Cards more than once. III. Practice Have the students find Dot Cards 4 and 5 in their books, punch them out, and Introductory Statement: add them to their collection of Dot Cards. Yesterday, we learned to recognize the Dot Cards 1, 2, and 3. We also Display groups of four and five items on the board. Count the items with the students learned to recognize and write the and write the correct number underneath each group. Place the matching Dot Card numerals. Today, we will learn the next to each number, and ask the students to show their matching Dot Cards for next two numbers. each group. tHINKING tRIGGER: Student Teacher: Let’s count and see what numbers come next, after one, two, and three. Ask a student to draw a group of four or five items on the board. Invite another Let’s think: Who can find things student to count the number of items aloud and write the number and/or place around the room that come in four the correct Dot Card under each group. or five? [Accept all relevant answers. You may need to help the class by Conclusion: Today we learned about the numbers four and five. We learned directing their attention to such items.] to read and write the numbers, and we learned their Dot Cards.26 Using the Book: Pages 9-10 )) Remember: In the beginning, it is important to check the students’s work in their math books, to be sure each student is following correctly and understands what to do. Page 9: This page is divided into three parts. On top there are writing lines, and on the bottom there are steps and Dot Cards. We will start with the first section. [Read the directions to the class.] I see lines for us to write the numbers on. What number is on the first line? [4] Review how to write the 4 by demonstrating on the board. Use your pencil to write the 4. Trace over the first fours in the book, and then continue on your own. Stop when you get to the number 5. In the same way, direct the class to write the number 5 and trace over numbers

Numbers 4 and 5Write the number� Write how many in each group� 3� 1� 2� 13 2 4� 5� 6�Continue to count� Write how many dots there are on the Write how many dots there are on the Dot Card�Fill in the missing Dot Card� 7� 8� 9� 10� 11�numbers� 2. 3. Student Workbook page1. Student Workbook pageChapter 1 Lesson 2 CCSS 1� NBT�1 Read and write numerals and represent a number of objects with a written numeral� 99 10 101-5 on the number line.If necessary, review how to write in the book using the dots as starters (see lesson 1).Example 1: Find the steps in your books. I will read the directions. [Draw similar steps on the board and count the steps together.Fill in the numbers on each step while counting from one to five. Say:] You have the same steps in your books. Write the numberson the steps in your books.Examples 2-3: Now we will work with the Dot Cards. [Read the directions to the class. Place Dot Cards 4 and 5 on the board. As aclass, count the dots on each card.] Now you can write in the number of dots under the Dot Cards in your books.Page 10: This page has two sections! On the top of the page there are yellow boxes with school supplies. On the bottom there areDot Cards.Examples 1-6: Now look at the top section. I will read the directions. [Read, and then Closing Statement:draw four crayons on the board. As a group, count the crayons. Write the numeral 4underneath. Have the class find example 1 and point out that it is the same as the What did we learn today in mathexample on the board. Have them write in the number 4. Continue similarly for the next class? [Accept all relevant answers.]few examples. When appropriate for your class, you can work directly in the book, and Today we learned numbers four andcount the items drawn there.] five on our Dot Cards and how to read and write them. Tomorrow we willExamples 7-11: Read the directions to the class. For example 7, ask: What number does learn the numbers 6 and 7.this Dot Card show? [5] [Write 5 on the board. Have the students write the number in theirbooks. Have the class complete the section independently.] 27

1.3 Chapter 1 Lesson 3: Numbers 6 and 7 CCSS 1. NBT.1 Read and write Concept Development: numerals and represent a number of objects with a written numeral. I. Number 6 Place a blank Dot Card on the board and use black magnetic counters to create Dot Card- Goal: 6. Count the dots with the students and compare to the Dot Cards learned previously. Students will recognize and write Point out that in Dot Card-6, all the green squares and one red square are filled in with the numbers 6 and 7. dots. Students will recognize Dot Cards 6 and 7. Draw writing lines and a starting point. Write the numeral 6 on the line while explaining Students will identify and form how it is formed. Have the students trace a 6 in the air with their first fingers. groups that are more and less. Materials needed: a variety II. Number 7 of small snacks, such as pretzels or Repeat the activity for the number 7. Place a blank Dot Card on the board and use black chips; various school supplies magnetic counters to create Dot Card-7. Point out that in Dot Card-7, all the red squares and two green squares are filled in with dots. Lesson warm-up: Flash Dot Cards 1-5. Have the class Draw writing lines and a starting point. Write the numeral 7 on the lines while explaining identify each one in unison. how it is formed. Have the students trace a 7 in the air with their first fingers. )) Remember to show each card for only Have the students find Dot Cards 6 and 7 in their books, punch them out, and add them one second! If necessary, or to provide to their collection of Dot Cards. Flash number cards 1-7. Have the students raise their additional practice, you may show Dot matching Dot Cards. Cards more than once. III. More or less Introductory Statement: Display two groups of crayons: five red crayons and two blue crayons. Count the We’ve learned about the numbers number of crayons in each group and say: I have more red crayons than blue crayons. one, two, three, four, and five. Today [Write “more” on the board.] we will learn the numbers six and seven. Invite a student to show her pencils to the class. Ask her to count how many she has. Show a group of pencils that is considerably more than hers. Count your pencils, tHINKING tRIGGER: compare the groups, and say: I have more pencils than you. Have one student in each row count the number of students in her row. Show five crayons to the class. Count them and say: Who can show us less crayons than Write the number on a large piece I have? [Compare the amounts that the students are showing to yours (e.g., Kayla has of paper. Ask: Which row has the three crayons. Three is less than five.)] most students? Which row has the least? Let’s think: What can we do Student Teacher: so that both rows have the same number of students? [Encourage the Have students pair up. Distribute two sheets of papers, with a blank Dot Card printed on students to think of different ways each one, to each set of partners. Ask each pair to draw groups of six items on the page. this to accomplish this. Try out some Ask one partner to color in the Dot Card to make a six-formation, and ask the other to of their ideas.] write “6” on the page. Then have each pair repeat the activity with the number 7.28 Ask some volunteers to share their drawings with the class. Display the class’s work on your math bulletin board. Conclusion: Now we’ve learned about six and seven. We’ve also learned about more and less. Using the Book: Pages 11-12 )) Remember: In the beginning, it is important to check the students’ work as they work in their math books, to be sure each student is following correctly and understands what to do. Page 11: Ask the class: What do you think we need to do at the top of the page? [write the numbers 6 and 7] [Explain the correct way to write the numbers as you model writing the 6 and 7.] Be sure to find the starting point and fill two lines with the number 6. [Allow

Numbers 6 and 7Write the number� Write how many dots� Circle the number that is more� 1� 2� 3� 4� 5� 6�Write how many� orange purple Write how many dots� Circle the number that is less� 7� 8� 9� 10� 11� 12�61. Color 1 pair of scissors orange and the rest purple� scissors62. Color 2 pairs of scissors orange and the rest purple� scissors Student Workbook page- Student Workbook pageContinue to count� Write how many dots there are Draw a group with fewer leaves�Fill in the missing numbers� on the Dot Card�3. 4. 5. 13.Chapter 1 Lesson 3 CCSS 1� NBT�1 Read and write numerals and represent a number of objects with a written numeral� 11 11 12 12time to fill in the numbers.]What number will we write on the next line? [7] Let’s write one seven in the air. [Model as the class follows along.] Now write sevens on the line.Remember to look for the starting point. After you do that, you may trace over numbers one through seven on the number line.Examples 1-2: Read the directions. Ask: What number is written at the beginning of each row? [6] Count the pairs of scissors in each row. Howmany there are? [6] Each line has special directions. [Read the first set of directions.] How many will we color orange? [1] Color the rest purple.[Draw a table similar to the last two columns in this section. Label them “orange” and “purple,” as in the book.] Now we need to write howmany there are of each color. How many are orange? [1] Let’s write 1 in the column under the word orange. How many are purple? [5] Let’s write5 in the column under the word purple. [Model how to fill in the table.]Example 3: Read the directions. Draw similar stairs on the board. Ask: Who remembers how to fill these in? [Model on the board while theclass fills in the stairs in their books.]Examples 4-5: Read the directions. Count the dots together, and have the class fill in the number of dots.Page 12: Look at the page together and ask the class what they think they will do on this page.Examples 1-6: Help students find the first example at the top of the page. Read the directions.Ask: Which Dot Cards are shown in the first example? [5 and 6] [Place these Dot Cards on the Closing Statement:board.] What numbers do we need to write under the Dot Cards? [5, 6] [Write the numbers, andhave the class do the same in their books.] Which number shall we circle? [6] Why? [because six is What did we learn today in mathmore than five] [Model on the board as the students circle the number in their books.] class? [Accept relevant answers.] Today we learned the numbers sixExamples 7-12: Read the directions. Explain that for every example, the students are to write and seven on our Dot Cards andhow many dots are in each Dot Card and then circle the number that is less. how to read and write them. We also learned more and less. Tomorrow weExample 13: Read the directions. Ask: How many green leaves are there? [5] What do we need to will learn the numbers 0 and 8.do? [draw less than five leaves] [Instruct the class to draw. Ask some students how many leavesthey chose to draw and why.]Remember to check continually as the students work in their math books. They may need help 29finding the place, following along, or following the directions.

1.4 Chapter 1 Lesson 4: Numbers 0 and 8 CCSS 1. NBT.1 Read and write Concept Development: numerals and represent a number of objects with a written numeral. I. Number 8 Place a blank Dot Card on the board and use black magnetic counters to create Dot Card- Goal: 8. Count the dots with the students and compare to the Dot Cards learned previously. Students will recognize and write Point out that almost all the red squares of Dot Card-8 are filled in with dots. There are the numbers 0 and 8. only two empty squares. Students will recognize Dot Card 8. Students will identify and show Draw writing lines and a starting point. Write the numeral 8 on the lines while explaining equal groups. how it is formed. Have the students trace an 8 in the air with their first fingers. Materials needed: Drop-It form #1; blank Dot Card and magnetic Place four large rulers on the board. Count the rulers. Say: Today we are learning about counters; 8 crayons; 8 rulers or ruler eight. We need eight rulers. What should I do? [put up more rulers] How many more rulers cutouts; do I need to put up? [Wait for answers and then say:] I will put up rulers, and you count until we get to eight. [Draw a line after the four rulers, and add more rulers, one at a time.] Lesson warm-up: Now let’s count how many more rulers I put up. Repeat this activity using different starting Drop-It: Hand out Drop-It form #1. numbers to count up to eight. Have the students find Dot Card-8 in their books, punch Flash Dot Cards 1-7. Have each it out, and add it to their collection of Dot Cards. student write the correct number on his/her worksheet. Check students’ II. Introducing zero work. Show the class a container with eight crayons. Count the crayons together. Ask: How many crayons are in the box? [8] [Remove the crayons and ask:] How many are in the box )) Remember to show each card for only now? [none] In math there is a special way to show “none.” [Write a zero on the board.] This one second! If necessary, or to provide is the number “zero.” It means none. additional practice, you may show Dot Cards more than once. Draw writing lines and the numeral 0 on the lines while explaining how it is formed. Have the students trace a 0 in the air with their first fingers. Show an empty bag. Ask: Introductory Statement: How many apples are in this bag? [0] So far, we’ve learned to recognize the Dot Cards for numbers one, two, three, III. Showing equal four, five, six, and seven. We’ve also Ask two students to stand in front of the class. Give four crayons to each of them. Ask learned to recognize and write the them to count their crayons and write the amount on the board. Ask: Who has more numerals. Today we will learn the next crayons? Who has less? [Help them come to the conclusion that neither has more or less. number: eight, and we will also learn They have the same amount.] In math, we say that they have an equal amount of crayons. about zero. [Write “equal” on the board.] tHINKING tRIGGER: Student Teacher: We know what Dot Cards look like for the other numbers. What do you Draw circles on the board. Ask one student to draw a number of items inside the circle, think Dot Card 8 will look like? and have another student count them aloud and write the correct numeral underneath. Suggest to some of the students that they draw “zero” items.30 Conclusion: Today we learned to recognize and write the numbers zero and eight. We also learned when two groups are equal. Using the Book: Pages 13-14 )) Remember: In the beginning it is important to check the students’ work in their math books, to be sure each student is following correctly and understands what to do. Page 13: Ask the class: What do we need to do at the top of the page? [write the numbers 0 and 8] [Demonstrate on the board, and review the correct way to write each number.] Be sure to find the starting points. On the top line write the number zero, and on the second

Numbers 0 and 8Write the number� Look at the group of crayons in the blue box� Color the group that has an equal number of crayons� 1� 2�Draw more erasers to make a group of 8� Draw more dots to show the number� 56�81. 7 8 63� 4� 5� erasers82. erasersContinue to count� Write how many dots Student Workbook pageFill in the missing numbers� are on the Dot Card� Student Workbook page3. Circle the number that is more� 4. 7� 6 8 8� 5 4 9� 7 6 10� 2 3 Circle the number that is less� 11� 12� 13� 14� 45 87 01 13 13 43 14Chapter 1 Lesson 4 CCSS 1� NBT�1 Read and write numerals and represent a number of objects with a written numeral� 14and third lines write the number eight. For both numbers, we start at the top and turn to the left. When you finish writing the zeros and eights,you may trace over the numbers on the number line.Examples 1-2: Read the directions. Say: What number is written at the beginning of each row? [8] We need to make sure that there are eighterasers in each row. How many erasers are in the first row? [6] [Draw six erasers on the board.] We need to draw more so there will be eight.[Using a different color, draw more erasers until you have eight.] How many more did I draw? [2]. Now you draw two more in your books.Count to be sure you have eight altogether.Have the class work in pairs to complete the section.Example 3: Read the directions. Draw similar stairs on the board. Ask: Who remembers how to fill these in? [Have the class complete thisindependently.]Example 4: Read the next set of directions. Count the dots together, and have the class write in the number of dots.Page 14: Examples 1-2: Read the directions. Ask: How many crayons are there in example 1? [3] Look at the boxes. How many crayons are inthe first box? [3] How many are in the second box? [2] Which box has a number that is equal to the three colored crayons? [the first box] How doyou know? [the first box has the same number of crayons as the colored group] Color the crayons in the first box.Examples 3-6: Read the directions. Say: It looks like someone is all mixed up! These Dot Cards don’t match the numbers written. Use your blackcrayon to fill in the missing dots.Fill in the first Dot Card together. Place a blank Dot Card on the board, Write a 7 above the Dot Closing Statement:Card, and place six counters on the card. Guide the class to realize that you need to put onanother counter to make seven. Place the counter on the Dot Card, and have the class color an What did we learn today in mathadditional dot in their books. Have the class complete examples 4-6 independently. class? [Accept relevant answers.] Today we learned the numbers 0Examples 7-10: Read the directions. Ask: In example 7, which numbers are written in the and 8, and we learned about equalrectangle? [6, 8] We need to circle the one that is more. Which number should we circle? [8] [Have groups. Tomorrow we will learn thethe students complete the next three examples on their own.] numbers 9 and 10.Examples 11-14: Read the directions. Ask: Now which number do we need to circle? [the onethat is less] [Continue as above to complete the page.] 31

1.5 Chapter 1 Lesson 5: Numbers 9 and 10 CCSS 1. NBT.1 Read and write Concept Development: numerals and represent a number of objects with a written numeral. I. Numbers 9 and 10 Place a blank Dot Card on the board and use black magnetic counters to create Goal: Dot Card-9. Count the dots with the students and compare to the Dot Cards Students will recognize and write learned previously. Point out that all the green squares and almost all the red the numbers 9 and 10. squares are filled with dots. There is only one red square empty. Write the Students will recognize Dot Cards 9 numeral 9 underneath the Dot Card. and 10. Materials needed: blank Dot Place another blank Dot Card on the board. Write the numeral 10 underneath it. Card; magnetic counters; toy cars or Read the number, and ask the class to help you form Dot Card-10. Slowly place car cutouts each counter on the board as the class counts to ten. Note that this Dot Card is special because it is all full! Lesson warm-up: Flash Dot Cards 1-8. Have the class Draw writing lines on the board, and demonstrate and explain how to write each identify each one in unison. number. Have the students trace a nine and a ten in the air with their fingers.)) Remember to show each card for only Have the students find Dot Cards 9 and 10 in their books, punch them out, and one second! If necessary, or to provide add them to their collection of Dot Cards. additional practice, you may show Dot Cards more than once. II. Ordinal numbers Place ten large cars along the floor, side by side. If using toy cars, place a large Introductory Statement: colored sticker on each. If using drawn cars, color each a different color. Have Yesterday we learned about the the class sit where they can see the cars. Use tape to mark off about 20 spaces, numbers 0 and 8. Today we will learn in front of the cars. Say: These cars are going to have a race. The car that gets to the the next number: 9 and 10. end first wins the race. [Have students take turns choosing a Dot Card and moving a car ahead that many spaces. As the cars make each move, discuss the cars’ tHINKING tRIGGER: positions using ordinal numbers (e.g., the red car is first, the green car is now Who can think of different ways we third, etc.). Continue in this way until all the cars have been moved out and you can show the number ten? [Accept can talk about the tenth car. When a car wins, ask the class about the position of all relevant answers] each car. Encourage students to use ordinal numbers in their answers.] Have the students line up. Ask: Who is first? Who is second? [Continue until you ask: Who is tenth? Have the first ten students sit in their seats. Repeat until all the students are sitting.] Place blank Dot Boards on the board. Ask students to take turns placing magnetic counters on the cards to form a nine or a ten, and to write the correct numerals under the cards. Help them to explain what they are doing.Student Teacher:Place blank Dot Cards on the board. Ask students to take turns placing magnetic counters on the cards to form a nine or ten,and to write the correct numerals under the cards. Help them to explain what they are doing.Conclusion:Today we learned the numbers nine and ten and their Dot Cards. The ten is special, because its Dot Card is completely filled in. Wealso learned to use special words to explain where things are in line.32

Numbers 9 and 10Write the number� Circle the shape� 1�1. Write how many book bags� Fourth 2�2. Draw an X over one book bag� Ninth How many book bags are there now? 3� SeventhWrite how many dots there are on the Dot Card� 4� 3. 4. Fifth 5� Tenth 6� Eighth 7�Sixth 8�Third Write how many dots there are on the Dot Card� 9� 10� 11� 12� 13� Student Workbook page Student Workbook pageChapter 1 Lesson 5 CCSS 1� NBT�1 Read and write numerals and represent a number of objects with a written numeral� 15 15 16 16Using the Book: Pages 15-16))Remember: In the beginning, it is important to check the students’ work as they work in their math books, to be sure each student is following correctly and understands what to do.Page 15: What do we need to do at the top of the page? [write the numbers 9 and 10] [Demonstrate on the board and review thecorrect way to write each number.] Be sure to find the starting points. On the first two lines write the number 9. On third line writethe number 10. When you finish that, you may trace over numbers 1 through 10 on the number line.Examples 1-2: Read the directions. Count the book bags together and havethe class write the number in their books. Readthe next set of directions. Allow time for the students to complete the section. Discusstheir results. Closing Statement:Examples 3-4: Read the directions to the class. Together, count the dots on each card. What did we learn today in mathHave the students write in the number of dots under each Dot Card. class? [Accept relevant answers.]Page 16: Examples 1-8: Read the directions. Draw ten stars on the board. Say: Example 1 Today, we learned the numbers 9tells us to draw a circle around the fourth star. Let’s find it together. [Count to find the fourth and 10. We also learned to tell thestar on the board and circle it.] Now you do that in your books. order of things using special number- words. Tomorrow we will learn aboutRead aloud which shape is to be circled in each example. Model as necessary. number lines to find numbers that areExamples 9-13: Read the directions. Have students complete the section independently. before, after and in-between..Review the section together. 33

1.6 Chapter 1 Lesson 6: Before, Between, After CCSS 1. NBT.1 Counting to 120, Concept Development: starting at any number less than 120. I. Introducing the number line Divide the class into groups of ten. If you have extra students, appoint them as Goal: assistants. Distribute number cards one through ten to each group, so that each student has a number. Ask each group to stand in a line, in numerical order. Point Students will use a number line to out that they are making “number lines.” Explain that you will call out a number, and find the numbers that are before, whoever has that number should hold it above his/her head. after, and in-between. Materials needed: Drop-It form Call the number four. Ask: What number is (Sarah) holding? [4] Who is standing next #1; number cards 1-10 for a number in line after (Sarah)? What number is he/she holding? [5] We see that five is after four! line on the board; sets of number cards 1-10 for class groups Repeat the activity with several numbers, such as 2, 6, and 8. Lesson warm-up: Explain that students will try something different next. Call two numbers that are consecutive, skipping a number between them. Ask: What number is between these Drop-It: Hand out Drop-It form #1. two numbers? [Repeat this several times.] Flash Dot Cards 1-10. Have each student write the correct number on Continue the game, alternating requesting numbers that are before, after, and his/her worksheet. Check students’ between. work.)) Remember to show each card for only one Note: This game can be used similarly as a fun review for number order, and for numeral- and Dot Card recognition. second! II. Number lines on the board Introductory Statement: Draw a horizontal line on the board. Place number cards in order from one to ten We’ve already learned to recognize along the line. With a piece of paper, cover the numbers before and after a specific and write all the numbers from one to number. Ask: Which number comes before this number? Which number comes after ten! Today we will use a number line this number? [Remove the papers to show the correct numbers. Repeat several to find numbers that are before, after, times with different numbers.] and in-between. Place a number card on the board. Ask: What number comes before this number? What number comes after? [Write in the numbers. Remove the card and ask:] What number comes between these numbers? [Repeat this exercise several times, until the class is familiar with the concept.] tHINKING tRIGGER: Student Teacher:How can we know which number Draw a number line on the board. Fill in four of the numbers. Ask some students tocomes before or after another fill in the missing numbers and explain which numbers they are writing using thenumber? terms before, after, and between. Conclusion: Now we know how to find numbers that are before, after, and between! Using the Book: Pages 17-18 )) Remember: In the beginning, it is important to check the students’ work as they work in their math books, to be sure each student is following correctly and understands what to do.Page 17: Draw a blank number line with space for three numbers. Have students open their books to page 17. Write the numbers1-3 on your number line. Read the words under each crayon, and explain that the yellow crayon is putting in the number before;the green crayon is putting in the number between, and the red crayon is putting in the number after. As you explain, write the34

Before Between Before, Between, After Connect the dots from 1 to 10 to form a picture� 23 13 After 8 12 79Write the missing number�Before Between After1� 4� 7� 4356 2 4 67 6 5 2 1 10 Student Workbook page2� 5� 8� Student Workbook page Write the number before and the number after� 34 8 10 4 5 1� 2� 3�3� 6� 9� 69 7 3 89 4 6 89 4� 5� 6� 18 17 17 4 8 18Chapter 1 Lesson 6 CCSS 1� NBT�1 Counting to 120, starting at any number less than 120�appropriate word under each number on the board.Examples 1-9: Read the directions. Explain and show the class that the page is divided into columns, and each column has a heading.Draw similar columns on the board and write the headings. Explain that all the examples in the column belong to that heading.Find example 1. Ask: Which number is missing here? Which number comes before the five and six? [four] [You can suggest that the classrefer to the number line on the board as necessary. Write the numbers on the board in the appropriate column as the students fill inthe missing numbers in their books.In this way, complete the page with the class.Page 18: Top of page: In this section we have a hidden picture! To find it, we have to connect the dots. [Draw five dots to form the shapeof a square. Label them with numbers from 1 to 5.] There is a hidden shape on the board. To find it, we need to draw lines to connect thenumbers in order. [Start at 1 and ask the class where you should go next.] What shape didwe get? [square] What we did is called connecting the dots. You have a hidden picture in your Closing Statement:books. To find it, you need to connect the dots in order, just as we did on the board. Start with What did we do today in math class?one, draw a line to the two, and continue until you come to the end. [Accept all relevant answers.] TodayWhen the class is done, identify the picture (schoolhouse). we learned to find the numbers that come before, after, and in-between!Examples 1-6: Read the directions. Have students complete the page independently or in Tomorrow we will learn about onepairs, while you circulate to offer help as needed. more and one less. 35

1.7 Chapter 1 Lesson 7: One More, One Less CCSS 1. OA.5 Relate counting to Concept Development: addition and subtraction. I. One more Place a blank Dot Card on the board. Place three black counters on the Card and Goal: ask what number is shown. Say: Let’s show one more than three. [Add another Students will use Dot Cards to find counter to the card and ask what number it shows.] Four is one more than three. the number that is one more or one less than a given number. Continue similarly with other numbers. Materials needed: bag of small treats; blank Dot Cards; magnetic Place Dot Card-6 on the board. Ask: Who can think of the number that is one more? counters. [seven] To find the number that is one more, we can simply think of a Dot Card with one more dot. [Place Dot Card-7 on the board and compare Dot Cards 6 and 7.] Lesson warm-up: Repeat this activity with another number. Flash Dot Cards 1-10. Have the class identify each one in unison. II. One less)) Remember to show each card for only one Remove the cards. Place a blank Dot Card on the board. Fill in five counters. Say: I want to find the number that is one less than five. [Remove a counter.] What second! number do we have? [four] [Place Dot Card-5 on the board and Dot Card-4 next to it. Show that four is one less than five.] Introductory Statement: Yesterday we used a number line to Do the same for the numbers seven and six. tell which number comes before and after. Today we will use our Dot Cards Place Dot Card-3 on the board. Ask: What number is one less than three? Which to find numbers that are one more Dot Card has one dot less? [2] [Place Dot Card-2 on the board. Write 2 next to the and one less. card.] tHINKING tRIGGER: Do the same for numbers two, nine, and eight. Clear the board. Write the numeral 2 on the board. Have the class read the number )) Another option is to divide the board in two, label the sides “One More” and “One Less,” and together. Show your bag of treats organize the Dot Cards on the appropriate sides of the board. to the class. Say: You can choose how many treats you get. You can have Student Teacher: two treats or you can have one more than two treats. How many do you Place three Dot Cards on the board. Ask students to choose a Dot Card and tell want? [Allow class time to think. Ask what number is one more and/or one less than the given number. Ask them to a few students how many they want explain how they know and to show the appropriate Dot Card. and why. Ask:] Does anyone want less than two treats? [Pass out three Conclusion: treats to each student.] Now we know that to find one more than a number, we need to think of the Dot Card with one more dot. To find one less, we need to think of the Dot Card with one less dot.36

One More, One Less One less than 5 is 4� One more than 5 is 6� Write the number� 1� What is one less than 9? 2� What is one less than 7?Write the number�1� What is one more than 4? 2� What is one more than 3?3� What is one more than 8? 4� What is one more than 7? 3� What is one less than 10? 4� What is one less than 3? Student Workbook page Student Workbook page5� Nick has 6 crayons� ChallengeBen has one more crayon than Nick has� 5� Write two numbers that are more than 5�How many crayons does Ben have? crayons 6� Write two numbers that are less than 6�6� Ann has 9 crayons� 19 19 20 20 Bill has one more crayon than Ann has� How many crayons does Bill have?Chapter 1 Lesson 7 CCSS 1� OA�5 Relate counting to addition and subtraction�Using the Book: Pages 19-20)) Remember: In the beginning, it is important to check the students’ work as they work in their math books, to be sure each student is following correctly and understands what to do.Page 19: Top of page: What number does the first Dot Card show? [five] The second Dot Card shows one more. What number is onemore than five? [six] Now I will read what it says in the cloud: One more than 5 is 6.Examples 1-4: Read the directions. Then read the question in example 1. Write “One More” on the board. Ask: Which Dot Cardis shown here? [4] [Place Dot Card-4 on the board.] Who can think of the Dot Card that shows one more? [5] [Write 5 next to theDot Card; have the class fill in the answer in their books.]In this way, complete the section. Closing Statement:Examples 5-6: Read each story to the class. Discuss the story and its question. Encourage What did we learn to do today in mathstudents to suggest answers and to explain how they arrived at their answers. Show class? [Accept relevant answers.] Wehow to write answers in the book. learned to find a number that is one more and one less, by thinking ofPage 20: Examples 1-4: Read the top of the page, then read the directions, and read Dot Cards. Tomorrow we will learn toeach question together. Complete the page as a class. Demonstrate each example on count on from different numbers.the board.Examples 5-6: Read each question. Encourage the students to work in pairs on theChallenge examples. 37

1.8 Chapter 1 Lesson 8: Counting OnCCSS 1. OA.5 Relate counting to Concept Development:addition and subtraction. I. Introducing the conceptGoal: Make a large number line on the floor. You may use a long, wide piece of tape to form a long line, and smaller pieces of tape set evenly across it to mark off ten numbers. LabelStudents will count to ten beginning the number line with numbers 1 through 10. Explain that this is a number line.with any given number.Materials needed: Drop- II. Activities for the class number lineIt form #1; bag of small treats;blank Dot Cards; black magnetic Following is a list of activities. It is suggested that each activity be done by some of thecounters; large, child-sized number students, while the rest of the class watches. Be sure each student participates in at leastline formed with tape on the floor; one activity.stickers • Students take turns walking across the number line, counting their steps as they go. • Suggest that some students jump from number to number as they count. Lesson warm-up: • Start students in the middle of the line, at various numbers, and have the class count with them from that number on. Drop-It: Hand out Drop-It form #1. Flash Dot Cards 1-10. Have each • Ask students to start at a given number and jump on only two or three jumps. student write the correct number Challenge the class to figure out what number they will land on. on his/her worksheet.)) Remember to show each card for only one • Some students can jump between two given numbers (e.g., from 4 to 7). Ask the class how many numbers they jumped. second! III. Activities for a number line on the board Introductory Statement: Yesterday we found numbers that Draw a number line on the board. Fill it in with numbers 1 through 10. Have the class are one more than another number. read the numbers along the line, in order. Today we will do even more. We will continue counting from different • Circle a number on the line and count on from that number. Repeat with different numbers. numbers. tHINKING tRIGGER: • Draw three squares on the board and say: Now we will practice counting on two Show the class a closed (not see- numbers. I will write a number. We will all read it and count on two more numbers. through) box with five treats inside, [Write a number in the first square. Count on together two more numbers as and a clear bag with three treats. you fill in the next squares. Repeat this with different numbers. You can ask Tell the class what is inside each students to suggest the number to start from and then count on.] container. Challenge them to think of different ways they can count • Draw a set of three steps on the board. On the bottom step write 8. Ask a volunteer and show how many treats you to fill in the next two numbers. Repeat this beginning with the number 2. have. List and model the ways that are relevant. Distribute treats to the • Place three stickers in a folded paper. Write the number 3 on the paper. On class. a second paper place two more stickers. Show the class the two papers and explain: Inside this paper are three stickers, and here are two more stickers. Let’s count all the stickers. [Start with three stickers inside and count on: 4, 5.] • Repeat this with varied amounts of stickers, both hidden and shown. Student Teacher:Draw some pencil cases on the board. Next to each pencil case, draw two or three squares in which numbers will be written. Ask avolunteer to place some pencils in her pencil case and write how many on a pencil case on the board. Hand the volunteer two or threemore pencils, and ask him/her to count on aloud and write the numbers he/she counts on next to the pencil case on the board. The classmay help the volunteer count on. Help the volunteer explain what he/she is doing. Continue calling up volunteers until all the pencil casesare filled in.38

Counting OnCount on� Fill in the missing numbers� Start at 4�1� 2� 3� Continue to count� 5, 6, 7 4 46 3 4 5, 6, 74� 5� 6� Count on� Write the numbers� 1� 2� 1 47 2 5, 3 ,,7� 8� 9� 3� 4� 45 8 Student Workbook page jumps in all Student Workbook pageDraw the jumps� Write how many in all� 6 7,10� Red jumped from 3 to 5� 5� 6�1 2 3 4 5 6 7 8 9 1011� Blue jumped from 6 to 9� jumps in all 8 4 22 ,1 2 3 4 5 6 7 8 9 10 21 21Chapter 1 Lesson 8 CCSS 1� OA�5 Relate counting to addition and subtraction� 22Conclusion:Now we can continue to count on from any number!Using the Book: pages 21-22 )) Remember: In the beginning, it is important to check the students’ work as they work in their math books, to be sure each student is following correctly and understands what to do.Page 21: Examples 1-9: Read the directions. Look at the examples. Remind the class that the same thing was done on the board. Drawa set of steps on the board. Write the number 4 on the bottom step, and ask the class to tell you how to fill in the numbers for the nexttwo steps. Have the class trace over the answer in their books. Similarly, model the second and third example. You may ask the class tocomplete the section in pairs or independently.Examples 10-11: Remember how [names of students] jumped between numbers on the number line while we counted how many jumps theymade? These game pieces are also making jumps. We will count the jumps that the red game piece and the blue game piece are making. [Readeach direction, count the jumps as a class, and fill in the answers. It may be helpful to draw a number line on the board and model theseexamples.]Page 22: Read the directions. Say: Now we are counting crayons that are both in the box and out Closing Statement:of the box. [Draw the class’s attention to the top example, and ask:] How many crayons are in thebox? We need to count all the crayons. [Read what the orange crayon is “saying,” and count on as What did we learn to do today ina class.] math class? [Accept all relevant answers.] We learned to count onModel the first example on the board: Draw a box labeled 5, and two more crayons. Together, from different numbers, not just fromcount on from five while you write the numbers 6, 7 next to the box. Have the class fill in the one! Tomorrow we will learn to countnumbers in their books. back!Similarly, model the next two examples. Allow students to complete the page on their ownwhile you circulate to offer help as needed. 39

1.9 Chapter 1 Lesson 9: Counting BackCCSS 1. OA.5 Relate counting to Concept Development:addition and subtraction. I. Introducing the concept Invite ten students to come to the front of the classroom. Give each student aGoal: random number card from 1 through 10. Ask them to stand in numerical order.Students will count back from Together, read the numbers to check the order.a given number (working withnumbers to ten). Have the students standing in line move so that number ten is standing first. AsMaterials needed: Drop-It form a class, count the numbers from ten to one.#1; large number cards labeled from1 to 10; small doll II. Active games Play some or all of the following practice games:Lesson warm-up: • The Stairs Game: Label a flight of stairs with numbers 1 through 10 (or as high as they go), in ascending order. Have groups of students walk up and down the steps while counting forward and back. Drop-It: Hand out Drop-It form #1. • Rocket Ship: Have students sit on the floor with their hands raised above Flash Dot Cards 1-10. Have each their heads. Together, count down from ten to one and shout, “Blast off!” student write the correct number At “blast off,” everyone jumps up like a rocket ship. on his/her worksheet.)) Remember to show each card for only one • Jack-in-the-Box: Have students crouch down on the floor with their hands covering their heads. Turn out the lights and, together, count down from second! ten to one. At the number one, the lights are turned on and everyone jumps up and down, until the lights are turned off again. Introductory Statement: Yesterday we learned to count on • Back Crawl: Have students sit on the floor facing the front of the room. from numbers. Today we will do the As you count back from ten to one, each student crawls backward – ten opposite: We will count back! crawls in all. This can be done with varied movements: walking, jumping, creeping, etc. tHINKING tRIGGER: III. Games for the board • Draw a flight of stairs on the board. Label the steps from 1 through 10 inLet’s think: When would counting ascending order. With a small doll, model walking down the stairs. Countback help us? [Accept all relevant back as the doll walks down.answers. Encourage ideas that arerelated to daily living.] • Erase the numbers, leaving only the number 5. Have the doll walk down the stairs. While the class counts back, fill in the missing numbers. Continue in this way several times, beginning with different numbers. • Draw a number line on the board. Circle two numbers. Together, count back from the greater to the smaller number. Ask: How many numbers did we count back? [Draw the jumps between the numbers, and count them together.] Continue in this way until the class is familiar with the procedure.Student Teacher:Draw sets of three stairs. Write a number between three and ten on the top step. Invite students to fill in the numbers thatbelong on the other stairs while counting back.Draw some number lines. Circle two numbers on each. Ask students to jump back between the numbers and tell how manyjumps they make. Help the students explain how they arrived at their answer.40

Count back� Fill in the missing numbers� Counting Back 5 little ants crawling up the door�1� 2� 3� 3 1 fell down, now there are � 56 4 little ants crawling up the tree� 4 1 fell down, now there are �4� 5� 6� 3 little ants crawling on my shoe� 4 10 9 1 fell down, now there are � 4 2 little ants crawling on the bun�7� 8� 9� 1 fell down, now there is � 785 1 little ant all alone�4 He crawled away, now there are none� 24Draw the jumps� Write how many jumps back� Student Workbook page Student Workbook page10� Red jumped back from 8 to 5� jumps back1 2 3 4 5 6 7 8 9 1011� Blue jumped back from 5 to 3� jumps back1 2 3 4 5 6 7 8 9 10 23 23Chapter 1 Lesson 9 CCSS 1� OA�5 Relate counting to addition and subtraction� 24Conclusion:Today we learned to count back from different numbers!Using the Book: Pages 23-24)) Remember: In the beginning, it is important to check the students’ work as they work in their math books, to be sure each student is following correctly and understands what to do.Page 23: Examples 1-9: I see sets of stairs, just like the ones we went down [or: we drew on the board]. What do we need to do? [Readthe directions to the class. Find the first example. Explain that this one is filled in for us. Read the numbers together, and havethe students trace them in their math books.For example 2, ask: What number is written on the top step? [6] Let’s count back from six. [6, Closing Statement:5, 4] We need to fill in the steps with these numbers. [Draw a set of stairs on the board andmodel how to fill it in.] What did we learn to do today in math class? [Accept all relevant answers.]Continue in the same way until the end of the section. Today we learned to count back from different numbers. We learned to useExamples 10-11: Ask the class what they see on the number line. Read the description. a number line and stairs to help us.As a group, count the number of jumps the game pieces made and decide what to write Tomorrow we will learn about twoin the box. kinds of numbers: odd and even.Page 24: Read the rhymes to the class. Use toy ants or draw ants on the board to modelthe story as you go along. Challenge the class to tell you how many are left each time.Help the students write the correct number in the appropriate space in their books. 41

1.10 Chapter 1 Lesson 10: Odd and Even Numbers CCSS 2.OA.3 Determine whether Concept Development: a group of objects has an odd or even number of members. I. Introducing the concept Have the students who sit in two adjacent rows stand in a double line. Ask: In Goal: which rows does everyone have a partner? How many students are in your row? [On Students will identify numbers one the board, place Dot Cards with these numbers.] to ten as odd or even numbers. Materials needed: students’ Do the same for rows in which not everyone has a partner. Label the groups of pencils and crayons; handout #1 Dot Cards accordingly (all partners/one left over). (optional) Compare the Dot Cards. Show that on the Dot Cards that show that all the Lesson warm-up: students have partners, the dots also all have partners. Say: These cards show even Flash Dot Cards 1-10. Have the class numbers. [Do the same with the odd numbers, explaining that these numbers identify each one in unison. are called odd. Erase the previous label, and label the groups “even” and “odd.”])) Remember to show each card for only one II. Even and odd numbers of objects second! Ask the students to take out all the pencils they have and to pair them up. Ask: Who has an even number of pencils? Who has an odd number of pencils? How do Introductory Statement: you know? [even – each pencil has a partner; odd – one pencil does not have a You know all the Dot Cards so well! partner] [Ask students how many pencils they have, and add the appropriate Today we will use the Dot Cards to Dot Cards to the groups of Dot Cards on the board. For each number ask:] Is this help us learn something new about an even number or an odd number? Where should we put the Dot Card? numbers. Ask the students to take out their boxes of crayons. Write the number 3 on the tHINKING tRIGGER: board. Have each student take three crayons out of his/her box and pair them Place Dot Cards 1-10 on the board. to decide whether three is an odd or an even number. Continue in this way with Circle all the Dot Cards with even additional numbers until the class is comfortable with the process. numbers. Say: Who can think of what these numbers all have in common? Draw seven squares on the board. Ask: How can I tell if there is an even or an odd [Accept all relevant answers. ] number of squares on the board? [Elicit that we need to make pairs. Demonstrate how to draw lines to pair up the shapes.] Do all the squares have partners? [no] What kind of number do we have? [odd] Do the same with ten circles drawn on the board. Student Teacher: Draw two columns on the board. Label one “Even” and one “Odd.” Leave space underneath for the students’ drawings. Invite two students at a time to come up to the board. Have one draw between one and ten shapes. Have the other student explain how he/she will decide if the number is odd or even. After the second student draws lines to make pairs, have the two students choose the matching Dot Card and place it in the correct column. Conclusion: Now we know two new math words: even and odd. All the dots of an even number have partners. An odd number has one dot without a partner.42

All of these dots Odd and Even Numbers Draw socks� Pair them� Oddhave partners� Circle whether the number is odd or even� Even6 is an even One of these dotsnumber� does not have a 51� Odd partner� Even 5 is an odd 32� number� Odd 43� EvenWrite the number�Circle whether the number is odd or even� 64� Odd1� 2� 3� Even 75� Odd Odd Odd Odd Even Even Even 26 Even4� 5� 6� 26 Odd Odd Odd Student Workbook page Even Even Even Student Workbook page7� 8� 9� Odd Odd Odd Even Even EvenChapter 1 Lesson 10 CCSS 2�OA�3 Determine whether a group of objects has an odd or even number of members� 25 25Using the Book: Pages 25-26 )) Remember: In the beginning, it is important to check the students’ work as they work in their math books, to be sure each student is following correctly and understands what to do.Page 25: Have the class look at the top of the page. Ask: What Dot Cards do you see? [6 and 5] Let’s look at Dot Card-6. Do all thedots have partners? [yes] Then we know that six is an even number. [Read aloud the sentences next to the Dot Card.]Now look at Dot Card-5. Do all the dots have partners? [no] What kind of number is five? [odd] [Read the sentences next to thecard.]Read the directions on the page. Place Dot Card-10 on the board. Ask: What number is this? [10] Is ten an even or an odd number?[even] How do you know? [all the dots have partners] [Write“Odd”and“Even”on the board, and ask:] Which one should we circle?[Circle “even.” Have the students do the same in their books. Complete the page in a similar fashion.]If the class is ready, you can use the Dot Cards in the book rather than displaying them on the board.Some students may be able to complete the page independently. Closing Statement:Page 26: Read the directions and ask: How many socks do you need to draw in the first What did we learn to do today inexample? [5] [Have the students trace the five socks.] Now what do you need to do? [pair math class? [Accept all relevantthe socks] [Have the class trace the groups of two, and ask:] Is five an odd or an even answers.] Today we learned aboutnumber? [odd] Use your pencil to circle “Odd.” odd and even numbers. Tomorrow we will learn about the penny.Complete the page as a class, or students may work in pairs or independently while youoffer assistance as needed.Optional: Distribute handout #1. Read and discuss. 43