Algebra Readiness Made Easy: Grade 2: An Essential Part of Every Math Curriculum (Best Practices in Action)

91 Pages·2008·1.88 MB·English

by  Mary Cavanagh

Grade 2
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Algebra Readiness Made Easy: Grade 2 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
Scholastic Inc. grants teachers permission to photocopy the activity sheets from this book for classroom
use. No other part of this publication may be reproduced in whole or in part, or stored in a retrieval
system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording,
or otherwise, without written permission of the publisher. For information regarding permission, write to
Scholastic Inc., 557 Broadway, New York, NY 10012.
Editor: Maria L. Chang
Cover design by Jason Robinson
Interior design by Melinda Belter
Illustrations by Teresa Anderko
ISBN-13: 978-0-439-83927-3
ISBN-10: 0-439-83927-0
Copyright © 2008 by Carole Greenes, Carol Findell, and Mary Cavanagh
All rights reserved.
Printed in China.
1 2 3 4 5 6 7 8 9 10 15 14 13 12 11 10 09 08
Algebra Readiness Made Easy: Grade 2 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
B R A READI
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Table of Contents A S
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
PROBLEM SETS
How Old Am I? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Number on a Hat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Polka Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Weird Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Face Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Snack Bags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
PROBLEM-SOLVING TRANSPARENCY MASTER . . . . . . . . . . . . . 75
SOLVE IT TRANSPARENCY MASTERS . . . . . . . . . . . . . . . . . . . . 76
ANSWER KEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
COLOR TRANSPARENCIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Algebra Readiness Made Easy: Grade 2 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources 3
B R A READI
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A S Introduction
Welcome to Algebra Readiness Made Easy! This book is designed to help you introduce young
children to problem-solving strategies and algebraic-reasoning techniques, to give them
practice with major number concepts and skills, and to motivate them to write and talk about
big ideas in mathematics. It also sets the stage for the formal study of algebra in the upper
grades.
Algebra Standards
The National Council of Teachers of Mathematics identifies algebra as one of the five major
content areas of the mathematics curriculum to be studied by children in all grades (NCTM,
2000). The council emphasizes that early and regular experience with the key ideas of algebra
helps students make the transition into the more formal study of algebra in late middle school
or high school. This view is consistent with the general theory of learning—that understanding
is enhanced when connections are made between what is new and what was previously studied.
The key algebraic concepts developed in this book are:
• representing quantitative relationships
• representing unknowns with letters
• interpreting mathematical relationships
• reasoning about proportional relationships
• identifying and continuing patterns
• writing and solving equations
• solving for the values of two unknowns
• replacing unknowns with their values
Building Key Math Skills
NCTM also identifies problem solving as a key process skill and the teaching of strategies and
methods of reasoning to solve problems as a major part of the mathematics curriculum for
children of all ages. The problem-solving model first described in 1957 by renowned
mathematician George Polya has been adopted by teachers and instructional developers
nationwide and provides the framework for the problem-solving focus of this book. All the
problems contained here require children to interpret data displays—such as text, charts,
4 Algebra Readiness Made Easy: Grade 2 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
INTRODUCTION
diagrams, graphs, pictures, and tables—and answer questions about them. As they work on the
problems, children learn and practice the following problem-solving strategies:
• making lists or cases of possible solutions and testing those solutions
• identifying, describing, and generalizing patterns
• working backward
• reasoning logically
• reasoning proportionally
The development of problem-solving strategies and algebraic concepts is linked to the
development of number concepts and skills. As children solve the problems in this book,
they’ll practice counting, computing, applying concepts of place value and number theory, and
reasoning about the magnitudes of numbers.
Throughout this book, we emphasize the language of mathematics. This language includes
terminology (e.g., odd number, variable) as well as symbols (e.g., >, <). Children will see the
language in the problems and illustrations and use the language in their discussions and
written descriptions of their solution processes.
How to Use This Book
Inside this book you’ll find six problem sets—each composed of nine problems featuring the
same type of data display (e.g., diagrams, scales, and arrays of numbers)—that focus on one or
more problem-solving strategies and algebraic concepts. Each set opens with an overview of the
type of problems/tasks in the set, the algebra and
problem-solving focus, the number concepts or skills Name _____________________________________________ Date __________________
SOLVE HOW OLD AM I?
needed to solve the problems, the math language that is PROTBHLEEM How old are the cats?
emphasized in the problems, and guiding questions to be Iam 1 year younger Iam 1 year older
than Rocky. than Mouser.
used with the first two problems of the set to help Screech Fancy
Iam 4 years older Iam the
than Fancy. youngest.
children grasp the key concepts and strategies.
CATS’ AGES Mouser
The first two problems in each set are designed to be Rocky 4 7 8 3
discussed and solved in a whole-class setting. The first,
“Solve the Problem,” introduces children to the type of I’ll start with
dtfiwmnhiirisi etsgapht nh sl peatythryt u.of e aoWsb neprlme dert omo sapbu l sr ligoioennglmbdvseletis erva tmuii ndttc.hd u ttTai haocthle onlyeyym.o n owEu ergin l hualic ntapoehv n upeewcra ricao itcrhghushei n lsib doltcdeerhmferrio enleidrnn eswr t tetyorohnoarge tkutee or tgoeeh inwnseet grsr te oa htasgfhitnseleedy ©2008byGreenes,Findell&Cavanagh,ScholasticTeachingResourcesAlgebraReadinessMadeEasy:Gr.2 12345.....MFRSRaooconccruckkesyyyee criiishss i s___is ____ M_____t____h_o__e__u_ _s _lyyyee_ eeeray aaa.yse rrreHtasss are n rsoooru lll omodddall..egbddree.. rti.shan Mouser.Ima Thinker 11
use the guiding questions provided to help them discover
Algebra Readiness Made Easy: Grade 2 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources 5
B R A READI
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key mathematical relationships and understand the special vocabulary used in the problem.
This whole-class discussion will enhance student understanding and success with the problem-
solving strategies and algebraic concepts in each problem set.
The second problem, “Make the Case,” comes as an overhead transparency and uses a
multiple-choice format. Three different characters offer possible solutions to the problem.
Children have to determine which character—Señorita
Name _____________________________________________ Date __________________
Rita, Granny Knot, or Ms. Yogi—has the correct answer.
MAKE HOW OLD AM I?
Before they can identify the correct solution, children CTAHSEE How old is Chase?
Iam 3 years Iam 4 years
have to solve the problem themselves and analyze each of older than Spike. older than Dash.
Chase Lucky
the responses. Invite them to speculate about why the Iam 1 year Iam the
younger than Lucky. youngest.
other two characters got the wrong answers. (Note:
Spike RABBITs’ AGES Dash
Although we offer a rationale for each wrong answer, 6 5 2 8
other explanations are possible.) As children justify their
I’m certain that Chase is
cgioiomnhrbnteosp oa“eiWo Sctrwereovhthrasla iv atelniieetnoxt c tpnwtthhheosoe ir eral eidk Penn“rinrMdnceoc onghabeu kl yodeurepnoams ogt i tnhat”ehh nge aeec d nCsmhs eeddia als fsod.“tie h MrrTn”se thloanp akittr nsw teo uogto bnatu htllpdaaekegrelm k operC ssbr.ata,ol basetvneohmi”ddue se.yts h siWtgt hoa aoieu siwrnilkrdini ntdagokwe 12 8SCyeheñaaoWsrresi tohiasld oR.istae nose NkGorn5 awnoyaneywya. r CKssh no?aolsdte. is 3dMyeesf.ai nrYisot egolilyd . AlgebraReadinessMadeEasy:Gr.2©2008byGreenes,Findell&Cavanagh,ScholasticTeachingResources
approximately one math period.
The rest of the problems in each set are sequenced by difficulty. All problems feature a
series of questions that involve analyses of the data display. In the first three or four problems
of each set, problem-solving “guru” Ima Thinker provides hints about how to begin solving the
problems. No hints are provided for the rest of the problems. If children have difficulty solving
these latter problems, you might want to write “Ima” hints for each of them or ask children to
develop hints before beginning to solve the problems. An answer key is provided at the back of
the book.
The problem sets are independent of one another and may be used in any order and
incorporated into the regular mathematics curriculum at whatever point makes sense. We
recommend that you work with each problem set in its entirety before moving on to the next
one. Once you and your students work through the first two problems, you can assign
problems 1 through 7 for children to do on their own or in pairs. You may wish to have them
complete the problems during class or for homework.
6 Algebra Readiness Made Easy: Grade 2 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
INTRODUCTION
Using the Transparencies
In addition to the reproducible problem sets, you’ll find ten overhead transparencies at the
back of this book. (Black-line masters of all transparencies also appear in the book.) The first
six transparencies are reproductions of the “Make the
Case” problems, to help you in leading a whole-class dis- SOLVE IT: HOW OLD AM I?
PROBLEM-SOLVING TRANSPARENCY
SOLVE
cussion of each problem. IT How old are the mice?
Iam3months Iam 10
The remaining four transparencies are designed to older than months younger
Lindy. than Squeaky.
Scooter
be used together. Three of these transparencies feature IyoamuBnog6oeBmro otonh.tahns Ioaldme stth.e BooBoo
six problems, one from each of the problem sets. Cut MICE’S AGES
Lindy 7 4 20 10 Squeaky
these three transparencies in half and overlay each prob-
1.Look What is the problem?
lem on the Problem-Solving Transparency. Then invite
children to apply our three-step problem-solving process: SOLVE IT: NUMBER ON A HAT
What is Z?
1) Look: What is the problem? What information do 2.ZPslatann adnsd f oDro a nWumhabte wr.ill you do first? How will you solve the problem?
Use the clues.
you have? What information do you need? CLUES:
Z
1) Zis a number you say
when you count by 10s.
2) Plan and Do: How will you solve the problem? 2) Zis between 20 and 60.
3.3)A Benvosetwnh enoruf ma Znbde’sr Csd.higeictks arHe ow can you be sure your answer is correct?
What strategies will you use? What will you do first?
What’s the next step? What comes after that?
76
3) Answer and Check: What is the answer? How can
you be sure that your answer is correct?
These problem-solving transparencies encourage writing about mathematics and may be
used at any time. They are particularly effective when used as culminating activities for the set
of problems.
Algebra Readiness Made Easy: Grade 2 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources 7
B R A READI INTRODUCTION
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References
Greenes, Carole, Mary Cavanagh, Linda Dacey, Carol Findell, & Marian Small. (2001).
Navigating through algebra in grades pre-kindergarten–grade 2. Reston, VA: National Council of
Teachers of Mathematics.
Greenes, Carole, & Carol Findell. (Eds.). (2005). Developing students’ algebraic reasoning abilities.
(Vol. 3 in the NCSM Monograph Series). Boston, MA: Houghton Mifflin.
Greenes, Carole, & Carol Findell. (2005). Groundworks: Algebraic thinking. Chicago: Wright
Group/McGraw Hill.
Moses, Barbara. (Ed.). (1999). Algebraic thinking, grades K–12: Readings from NCTM’s school-based
journals and other publications. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathe-
matics. Reston, VA: National Council of Teachers of Mathematics.
Polya, George. (1957). How to solve it. Princeton, NJ: Princeton University Press.
Small, Marian, Linda Sheffield, Mary Cavanagh, Linda Dacey, Carol Findell, & Carole Greenes.
(2004). Navigating through problem solving and reasoning in grade 2. Reston, VA: National
Council of Teachers of Mathematics.
Usiskin, Zalman. (1997). Doing algebra in grades K–4. Teaching Children Mathematics. 3(6),
346–356.
8 Algebra Readiness Made Easy: Grade 2 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
B R A READI
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How Old Am I? A S
Overview
Children use clues to interpret age relationships among animals and work backward
through the clues to answer the questions.
Algebra
Represent quantitative relationships • Write and solve equations
Problem-Solving Strategies
Work backward • Use logical reasoning
Related Math Skills
Compare ages and numbers • Add • Subtract
Math Language
Greatest number • How old? • Least number • Months • Older than, oldest •
Years • Younger than, youngest
Introducing the Problem Set
Make photocopies of “Solve the Problem: How Old Am I?” (page 11) distribute to
children. Have children work in pairs, encouraging them to discuss strategies they
might use to solve the problem. You may want to walk around and listen in on some
of their discussions. After a few minutes, display the problem on the board (or on the
overhead if you made a transparency) and use the following questions to guide a
whole-class discussion on how to solve the problem:
•
What did Ima do first to figure out the ages? (She matched the least number to the
youngest cat.)
•
Which cat is the youngest? (Mouser)
•
How old is Mouser? (3 years old)
•
Which cat’s age can you figure out next? (Fancy)
Algebra Readiness Made Easy: Grade 2 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources 9