Algebra Readiness Made Easy: Grade 1: An Essential Part of Every Math Curriculum (Best Practices in Action)

91 Pages·2008·2.02 MB·English

by  Mary Cavanagh

Grade 1
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Algebra Readiness Made Easy: Grade 1 © 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
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York, NY 10012.
Editor: Maria L. Chang
Cover design by Jason Robinson
Interior design by Melinda Belter
Illustrations by Teresa Anderko
ISBN-13: 978-0-439-83924-2
ISBN-10: 0-439-83924-6
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 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
B R A READI
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Table of Contents A S
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
PROBLEM SETS
Fishy Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Guess the Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Count the Spots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Find the Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Face the Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
How Much Is This Bag? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
PROBLEM-SOLVING TRANSPARENCY MASTER . . . . . . . . . . . . . 77
SOLVE IT TRANSPARENCY MASTERS . . . . . . . . . . . . . . . . . . . . 78
ANSWER KEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
COLOR TRANSPARENCIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
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
• reasoning about proportional relationships
• identifying and continuing patterns
• interpreting mathematical relationships
• writing and solving equations
• solving for the values of one or 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 1 © 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 Name _____________________________________________ Date __________________
SOLVE FISHY PRICES
problems/tasks in the set, the algebra and problem- PROTBHLEEM How much does each fish cost?
solving focus, the number concepts or skills needed to
I cost $1 less I cost $2 more
than Bronco. than Flash.
solve the problems, the math language that is Bronco
Arty
emphasized in the problems, and guiding questions to be $1 $2 $3 I cost the least.
used with the first two problems of the set to help Match each price tag with its fish. Flash
children grasp the key concepts and strategies. I’ll start with
Flash. His price tag
The first two problems in each set are designed to be has the least
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Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources 5
B R A READI
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with the problem and come up with some strategies they might use to solve it. Then gather
children together and use the guiding questions provided to help them discover 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—Shorty
Trunks, Carl Cargo, or Levi Sam—has the correct answer. Name _____________________________________________ Date __________________
MAKE FISHY PRICES
Before they can identify the correct solution, children CTAHSEE How much do PB and J cost together?
have to solve the problem themselves and analyze each of We cost $3 more I cost $5 less
than Dolly. than Ringo.
the responses. Invite them to speculate about why the PB and J Dolly
other two characters got the wrong answers. (Note: $2 $7 $5 I cost the most.
Match each price tag with its fish. Ringo
Although we offer a rationale for each wrong answer,
No, PB and J
other explanations are possible.) As children justify their cost $7.
Clearly, PB and J
choices in the “Make the Case” problems, they gain are $3. I see that
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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 1 © 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 discussion of each problem.
The remaining four transparencies are designed to
SOLVE IT : FISHY PRICES PROBLEM-SOLVING TRANSPARENCY
SOLVE
be used together. Three of these transparencies feature IT How much does each fish cost?
six problems, one from each of the problem sets. Cut
Shaggy Barb Glow
these three transparencies in half and overlay each prob-
Use the clues to figure out the price of each fish.
lem on the Problem-Solving Transparency. Then invite CLUES:A) Shaggy costs $4 less than Barb.
BC)) GBalorwb ccoossttss t$h7e mleoarset .than Glow. $5 $2 $9
children to apply our three-step problem-solving process:
1.Look What is the problem?
1) Look: What is the problem? What information do
SOLVE IT : GUESS THE NUMBER
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These problem-solving transparencies encourage writ-
ing 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 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources 7
B R A READI
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References
Findell, Carol, Mary Cavanagh, Linda Dacey, Carole Greenes, Linda Sheffield, & Marian Small.
(2004). Navigating through problem solving and reasoning in grade 1. Reston, VA: National
Council of Teachers of Mathematics.
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.
Usiskin, Zalman. (1997). Doing algebra in grades K–4. Teaching Children Mathematics. 3 (6),
346–356.
8 Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources
B R A READI
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Fishy Prices A S
Overview
Children use clues to interpret mathematical relationships 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 dollar amounts • Add basic facts • Subtract basic facts
Math Language
Cost, cost more, cost less • $ (dollar sign) • Greatest • How much? •
Least, less than • Most, more than • Price tag
Introducing the Problem Set
Make photocopies of “Solve the Problem: Fishy Prices” (page 11) and distribute to chil-
dren. 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 dis-
cussion on how to solve the problem:
•
What did Ima do first to figure out how much each fish costs? (She matched the tag
with the least price to the fish that cost the least.)
•
Which fish costs the least? (Flash)
•
How much does Flash cost? ($1)
•
Which fish’s price tag can you figure out next? (Bronco)
Algebra Readiness Made Easy: Grade 1 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources 9