Teaching Algebra with Manipulatives
Teaching Algebra with Manipulatives
For use with Glencoe Algebra 1 Glencoe Algebra 2
Manipulatives
Glencoe offers three types of kits to enhance the use of manipulatives in your Pre-Algebra classroom.
? The Glencoe Mathematics Overhead Manipulative Resources contains translucent manipulatives designed for use with an overhead projector.
? The Glencoe Mathematics Classroom Manipulative Kit contains classroom sets of frequently used manipulatives in algebra, geometry, measurement, probability, and statistics.
? The Glencoe Mathematics Student Manipulative Kit contains an individual set of manipulatives often used in Student Edition activities.
The manipulatives contained in each of these kits are listed on page viii of this booklet.
Each of these kits can be ordered from Glencoe by calling (800) 334-7344.
Glencoe Mathematics Overhead Manipulative Resources Glencoe Mathematics Classroom Manipulative Kit Glencoe Mathematics Student Manipulative Kit
0-07-830593-4 0-02-833116-8 0-02-833654-2
Glencoe/McGraw-Hill
Copyright ? by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe Algebra 1 or Glencoe Algebra 2. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240
ISBN: 0-07-827755-8
Teaching Algebra with Manipulatives
1 2 3 4 5 6 7 8 9 10 079 11 10 09 08 07 06 05 04 03 02
Contents
Easy-to-Make Manipulatives
Page
Grid Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Centimeter Grid Paper . . . . . . . . . . . . . . . . . . . . .2
10 10 Centimeter Grids . . . . . . . . . . . . . . . . . . .3
Coordinate Planes . . . . . . . . . . . . . . . . . . . . . . . .4
Coordinate Planes in Space . . . . . . . . . . . . . . . . .5
Coordinate Planes for Trigonometric Functions
(degrees) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Coordinate Planes for Trigonometric Functions
(radians) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Conic Graph Paper -- circles and lines . . . . . . . .8
Conic Graph Paper -- overlapping circles . . . . . .9
Algebra Tiles -- units . . . . . . . . . . . . . . . . . . . . .10
Algebra Tiles -- variables . . . . . . . . . . . . . . . . .11
Integer Models Summary . . . . . . . . . . . . . . . . . .12
Polynomial Models Summary . . . . . . . . . . . . . . .13
Equation Models Summary . . . . . . . . . . . . . . . .14
Integer Mat . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Equation Mat . . . . . . . . . . . . . . . . . . . . . . . . . . .16
Product Mat . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
Rectangular Dot Paper . . . . . . . . . . . . . . . . . . . .18
Isometric Dot Paper . . . . . . . . . . . . . . . . . . . . . .19
Problem Solving Guide . . . . . . . . . . . . . . . . . . .20
Spinners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
Die Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
Protractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Rulers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
Normal Distribution Curve . . . . . . . . . . . . . . . . .25
Algebra 1
Activities
Page
CHAPTER 1
Teaching Notes and Overview . . . . . . 27
1-2 Mini-Project: Evaluating Expressions .30
1-5 Using Overhead Manipulatives:
Distributive Property . . . . . . . . . . .31
1-5 Algebra Activity Recording Sheet . . . .33
1-7 Algebra Activity: Make a Model . . . . .34
1-8 Algebra Activity Recording Sheet . . . .35
CHAPTER 2 Teaching Notes and Overview . . . . . . 36
2-2 Mini-Project: Adding and Subtracting Integers . . . . . . . . . . . . . . . . . . . . .39
2-2 Using Overhead Manipulatives: Adding and Subtracting Integers . . .40
2-3 Using Overhead Manipulatives: Multiplying Integers . . . . . . . . . . . .42
2-4 Algebra Activity: Multiplying and Dividing Rational Numbers . . . . . .43
2-5 Using Overhead Manipulatives: Measures of Central Tendency . . . .45
2-5 Using Overhead Manipulatives: Statistics and Line Plots . . . . . . . . .46
2-6 Using Overhead Manipulatives: Experimental Probability . . . . . . . .48
2-6 Algebra Activity Recording Sheet . . . . . . . . . . . . . . . . . . . . . . .49
CHAPTER 3 Teaching Notes and Overview . . . . . . 50
3-1 Algebra Activity Recording Sheet . . . .56 3-1 Algebra Activity: Formulas . . . . . . . . .57 3-2 Algebra Activity Recording Sheet . . . .59 3-2 Using Overhead Manipulatives:
Solving Equations by Using Addition and Subtraction . . . . . . . .60 3-2 Mini-Project: Using Logic . . . . . . . . . .65 3-3 Using Overhead Manipulatives: Solving Equations by Using Multiplication and Division . . . . . 66 3-4 Algebra Activity Recording Sheet . . . .68 3-4 Using Overhead Manipulatives: Solving Equations Using More Than One Operation . . . . . . . . . . . .69 3-4 Algebra Activity: Solving Equations . . .1 3-5 Using Overhead Manipulatives: Solving Equations with the Variable on Both Sides . . . . . . . . . . . . . . . . .73 3-6 Using Overhead Manipulatives: Proportions . . . . . . . . . . . . . . . . . . .75 3-6 Using Overhead Manipulatives: Solving Percent Problems . . . . . . . .76 3-7 Using Overhead Manipulatives: Percent of Change . . . . . . . . . . . . .77 3-7 Mini-Project: The Music Business . . . .79 3-8 Algebra Activity: Mixture Problems . .80
CHAPTER 4 Teaching Notes and Overview . . . . . . 82
4-3 Using Overhead Manipulatives: Relations . . . . . . . . . . . . . . . . . . . .85
4-3 Algebra Activity Recording Sheet . . . .86 4-5 Using Overhead Manipulatives:
Graphing Linear Relations . . . . . . .87 4-6 Using Overhead Manipulatives:
Functions . . . . . . . . . . . . . . . . . . . .88 4-6 Mini-Project: Functions or Not? . . . . .89 4-8 Algebra Activity Recording Sheet . . . .90 4-8 Algebra Activity: Functions . . . . . . . .91
CHAPTER 5 Teaching Notes and Overview . . . . . . 93
5-1 Using Overhead Manipulatives: Find the Slope of a Line . . . . . . . . .96
5-3 Algebra Activity Recording Sheet . . . .98 5-3 Using Overhead Manipulatives: Slope-
Intercept Form of Linear Equations 99 5-5 Using Overhead Manipulatives:
Linear Equations in Point-Slope and Standard Form . . . . . . . . . . .100
iii
Algebra 1
Activities
Page
5-6 Algebra Activity: Perpendicular
Lines . . . . . . . . . . . . . . . . . . . . . .102
5-6 Algebra Activity Recording Sheet . . .104
5-7 Algebra Activity Recording Sheet . . .105
5-7 Using Overhead Manipulatives:
Scatter Plots . . . . . . . . . . . . . . . . .106
5-7 Mini-Project: Scatter Plots . . . . . . . .107
CHAPTER 6 Teaching Notes and Overview . . . . . 108
6-1 Using Overhead Manipulatives: Solving Inequalities Using Addition and Subtraction . . . . . . .111
6-1 Mini-Project: Multiplying Inequalities by 1 . . . . . . . . . . . .114
6-2 Algebra Activity Recording Sheet . . .115 6-4 Algebra Activity: Compound
Inequalities . . . . . . . . . . . . . . . . . .116 6-5 Algebra Activity Recording Sheet . . .119 6-6 Using Overhead Manipulatives:
Graphing Inequalities . . . . . . . . . .120
CHAPTER 7 Teaching Notes and Overview . . . . . 122
7-1 Mini-Project: Comparing Options . . .124 7-2 Algebra Activity Recording Sheet . . .125 7-3 Using Overhead Manipulatives:
Elimination Using Addition and Subtraction . . . . . . . . . . . . . . . . . .126 7-5 Algebra Activity: Graphing Systems of Inequalities . . . . . . . . . . . . . . . .127
CHAPTER 8 Teaching Notes and Overview . . . . . 129
8-1 Using Overhead Manipulatives: Multiplying Monomials . . . . . . . .134
8-1 Algebra Activity Recording Sheet . . .135 8-4 Algebra Activity Recording Sheet . . .136 8-5 Algebra Activity Recording Sheet . . .137 8-5 Using Overhead Manipulatives: Adding
and Subtracting Polynomials . . . . .138 8-5 Mini-Project: Multiplying Binomials .141 8-6 Using Overhead Manipulatives:
Multiplying a Polynomial by a Monomial . . . . . . . . . . . . . . . . . . .142 8-7 Algebra Activity Recording Sheet . . .144 8-7 Using Overhead Manipulatives: Multiplying Polynomials . . . . . . . .145 8-7 Algebra Activity: Multiplying Polynomials . . . . . . . . . . . . . . . . .147 8-8 Using Overhead Manipulatives: Three Special Products . . . . . . . . .149 CHAPTER 9 Teaching Notes and Overview . . . . . 152 9-2 Algebra Activity Recording Sheet . . .156 9-3 Algebra Activity Recording Sheet . . .159 9-3 Using Overhead Manipulatives: Factoring Trinomials . . . . . . . . . . .160
9-4 Using Overhead Manipulatives: Factoring Trinomials . . . . . . . . . . .162
9-4 Algebra Activity: Factoring Trinomials . . . . . . . . . . . . . . . . . .163
9-5 Using Overhead Manipulatives: Factoring Differences of Squares .165
9-5 Algebra Activity Recording Sheet . . .167 9-6 Using Overhead Manipulatives:
Factoring Perfect Square Trinomials . . . . . . . . . . . . . . . . . .168 9-6 Mini-Project: Factoring Trinomial Squares . . . . . . . . . . . . . . . . . . . . .170 9-6 Algebra Activity: Factoring Trinomial Squares . . . . . . . . . . . .171
CHAPTER 10 Teaching Notes and Overview . . . . . 173
10-1 Algebra Activity Recording Sheet . . .176 10-1 Mini-Project: Graphing Quadratic
Functions . . . . . . . . . . . . . . . . . . .177 10-3 Using Overhead Manipulatives:
Solving Quadratic Equations by Completing the Square . . . . . . .178 10-5 Algebra Activity: A Fascinating Fold .180 10-7 Algebra Activity Recording Sheet . . .181 10-7 Algebra Activity Recording Sheet . . .182
CHAPTER 11 Teaching Notes and Overview . . . . . 183
11-2 Mini-Project: Matching Radicals . . . .185 11-4 Using Overhead Manipulatives: The
Pythagorean Theorem . . . . . . . . . .186 11-4 Algebra Activity: The Pythagorean
Theorem . . . . . . . . . . . . . . . . . . . .187 11-4 Using Overhead Manipulatives:
Graphing Irrational Numbers . . . .189 11-6 Using Overhead Manipulatives:
Similar Triangles . . . . . . . . . . . . .190 11-7 Algebra Activity Recording Sheet . . .191 11-7 Algebra Activity Recording Sheet . . .192
CHAPTER 12 Teaching Notes and Overview . . . . . 193
12-5 Using Overhead Manipulatives: Dividing Polynomials by Monomials and by Binomials . . . .195
12-5 Algebra Activity Recording Sheet . . .197 12-9 Mini-Project: Rational Roundup . . . .198
CHAPTER 13 Teaching Notes and Overview . . . . . 199
13-3 Algebra Activity: Modeling Data . . . .200 13-5 Algebra Activity Recording Sheet . . .203
CHAPTER 14 Teaching Notes and Overview . . . . . 204
14-1 Algebra Activity Recording Sheet . . .206 14-3 Algebra Activity: Probability and
Compound Events . . . . . . . . . . . .207
iv
Algebra 1
Activities
Page
14-5 Algebra Activity: Theoretical and
Experimental Probability . . . . . . .208
14-5 Algebra Activity Recording Sheet . . .209
Algebra 2
Activities
Page
CHAPTER 1
Teaching Notes and Overview . . . . . 210
1-2 Algebra Activity Recording Sheet . . .212
1-2 Algebra Activity Recording Sheet . . .213
1-3 Algebra Activity: Solving Equations .214
1-6 Mini-Project: Solving Absolute Value
Inequalities . . . . . . . . . . . . . . . . . .216
CHAPTER 2 Teaching Notes and Overview . . . . . 217
2-5 Algebra Activity Recording Sheet . . .218 2-6 Mini-Project: Graphing Absolute
Value Functions . . . . . . . . . . . . . .219
CHAPTER 3 Teaching Notes and Overview . . . . . 220
3-2 Mini-Project: Solving Systems of Equations by Elimination . . . . . . .222
3-3 Algebra Activity: Graphing Systems of Inequalities . . . . . . . . . . . . . . . .223
3-5 Algebra Activity Recording Sheet . . .225 3-5 Algebra Activity: Equations of Planes 226
CHAPTER 4 Teaching Notes and Overview . . . . . .228
4-1 Algebra Activity: Matrices . . . . . . . .229 4-3 Mini-Project: Determinants . . . . . . . .231
CHAPTER 5 Teaching Notes and Overview . . . . . .232
5-2 Algebra Activity Recording Sheet . . .234 5-4 Algebra Activity Recording Sheet . . .235 5-5 Algebra Activity: Radical Roots of
Polynomials . . . . . . . . . . . . . . . . .236 5-6 Algebra Activity Recording Sheet . . .238 5-9 Mini-Project: nth Roots of Negative
Numbers . . . . . . . . . . . . . . . . . . . .239 5-9 Algebra Activity Recording Sheet . . .240
CHAPTER 6 Teaching Notes and Overview . . . . . .241
6-1 Mini-Project: Parabolas . . . . . . . . . . .243 6-4 Algebra Activity Recording Sheet . . .244 6-4 Algebra Activity: Completing the
Square . . . . . . . . . . . . . . . . . . . . .245 6-6 Algebra Activity: Quadratic
Functions . . . . . . . . . . . . . . . . . . .247
CHAPTER 7 Teaching Notes and Overview . . . . . .249
7-4 Mini-Project: Synthetic Substitution and Zeros . . . . . . . . . . . . . . . . . . .252
7-7 Algebra Activity: Exploring Iteration . . . . . . . . . . . . . . . . . . . .253
7-8 Algebra Activity: Inverse Relations . .256 7-8 Algebra Activity Recording Sheet . . .258
CHAPTER 8 Teaching Notes and Overview . . . . . .259
8-1 Algebra Activity Recording Sheet . . .263 8-2 Algebra Activity Recording Sheet . . .264 8-2 Mini-Project: Conics . . . . . . . . . . . . .265 8-4 Algebra Activity Recording Sheet . . .266 8-4 Algebra Activity Recording Sheet . . .267 8-6 Algebra Activity: Conic Sections . . . .268 8-6 Algebra Activity Recording Sheet . . .270
CHAPTER 9 Teaching Notes and Overview . . . . . .271
9-1 Mini-Project: Interpreting Powers of a Binomial Geometrically . . . . . . . . . . . . . . . .272
9-3 Algebra Activity Recording Sheet . . .273
CHAPTER 10 Teaching Notes and Overview . . . . . .274
10-1 Algebra Activity Recording Sheet . . .275 10-1 Algebra Activity: Exponential
Functions . . . . . . . . . . . . . . . . . . .276 10-6 Mini-Project: Graceful Numbering
of Graphs . . . . . . . . . . . . . . . . . . .278
CHAPTER 11 Teaching Notes and Overview . . . . . .279
11-1 Mini-Project: Sequences . . . . . . . . . .282 11-1 Algebra Activity Recording Sheet . . .283 11-6 Algebra Activity Recording Sheet . . .284 11-6 Algebra Activity Recording Sheet . . .285 11-6 Algebra Activity: Investigating
Fractal Cut Outs . . . . . . . . . . . . . .286
CHAPTER 12 Teaching Notes and Overview . . . . . .288
12-4 Algebra Activity Recording Sheet . . .291 12-4 Algebra Activity: Probability . . . . . . .292 12-8 Mini-Project: Probability . . . . . . . . . .294 12-8 Algebra Activity Recording
Sheet . . . . . . . . . . . . . . . . . . . . . .295 12-9 Algebra Activity Recording
Sheet . . . . . . . . . . . . . . . . . . . . . .296
CHAPTER 13 Teaching Notes and Overview . . . . . .297
13-1 Algebra Activity: Indirect Measurement . . . . . . . . . . . . . . . .299
13-2 Algebra Activity Recording Sheet . . .301 13-6 Mini-Project: Linear Interpolation
by Graphing . . . . . . . . . . . . . . . . .302
CHAPTER 14 Teaching Notes and Overview . . . . . .303
14-7 Mini-Project: Trigonomessage . . . . . .304
v
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