engaging mathematics: teks-based activities algebra … · teks-based activities algebra i teacher...

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TEKS-BasedTEKS-BasedActivitiesActivities

Algebra IAlgebra I

ISBN: 978-1-934950-04-3

www.theansweris4.net

Engaging Mathematics:TEKS-Based Activities

Algebra I

Teacher Edition

Product ID: 407-1469

Creating solutions that are the worldwide standard for

educational excellence®

Revolutionizing education to inspire and advance future

generations®

SAMPLE

Table of Contents

Introduction ......................................................................................................... i–vii Overview of Materials ............................................................................................ i Texas Essential Knowledge and Skills (TEKS) Alignment Chart .......................... iv

Functional Relationships .................................................................................. 1–29 Functional Relationships, Activity 1 ...................................................................... 2 Functional Relationships, Activity 2 ...................................................................... 4 Functional Relationships, Activity 3 ...................................................................... 6 Generating Patterns, Activity 1 ............................................................................. 8 Generating Patterns, Activity 2 ........................................................................... 10 Generating Patterns, Activity 3 ........................................................................... 12 Generating Patterns, Activity 4 ........................................................................... 14 Modeling Functions, Activity 1 ............................................................................ 16 Modeling Functions, Activity 2 ............................................................................ 18 Proportional Relationships, Activity 1 ................................................................. 20 Proportional Relationships, Activity 2 ................................................................. 22 Proportional Relationships, Activity 3 ................................................................. 24 Proportional Relationships, Activity 4 ................................................................. 28

Properties and Attributes of Functions ......................................................... 30–87 Interpreting Graphs, Activity 1 ............................................................................ 30 Interpreting Graphs, Activity 2 ............................................................................ 32 Continuous and Discrete, Activity 1 .................................................................... 34 Continuous and Discrete, Activity 2 .................................................................... 38 Domain and Range, Activity 1 ............................................................................ 42 Domain and Range, Activity 2 ............................................................................ 44 Scatterplots, Activity 1 ........................................................................................ 46 Scatterplots, Activity 2 ........................................................................................ 48 Scatterplots, Activity 3 ........................................................................................ 50 Scatterplots, Activity 4 ........................................................................................ 52 Evaluating Expressions, Activity 1 ...................................................................... 54 Evaluating Expressions, Activity 2 ...................................................................... 56 Evaluating Expressions, Activity 3 ...................................................................... 58 Simplifying Expressions, Activity 1 ..................................................................... 60 Simplifying Expressions, Activity 2 ..................................................................... 62 Writing Expressions, Activity 1 ............................................................................ 66 Writing Expressions, Activity 2 ............................................................................ 68 Polynomial Multiplication, Activity 1 .................................................................... 70 Polynomial Multiplication, Activity 2 .................................................................... 72 Polynomial Multiplication, Activity 3 .................................................................... 74 Polynomial Multiplication, Activity 4 .................................................................... 76 Polynomial Multiplication, Activity 5 .................................................................... 78 Factoring, Activity 1 ............................................................................................ 80 Factoring, Activity 2 ............................................................................................ 82 Factoring, Activity 3 ............................................................................................ 86

SAMPLE

Linear Functions ............................................................................................ 88–147 Slope & Rate of Change, Activity 1 ..................................................................... 88 Slope & Rate of Change, Activity 2 ..................................................................... 90 Slope & Rate of Change, Activity 3 ..................................................................... 92 Slope & Rate of Change, Activity 4 ..................................................................... 94 Slope & Rate of Change, Activity 5 ..................................................................... 96 Slope & Rate of Change, Activity 6 ..................................................................... 98 Interpreting Intercepts, Activity 1 ....................................................................... 102 Interpreting Intercepts, Activity 2 ....................................................................... 104 Interpreting Intercepts, Activity 3 ....................................................................... 106 Graphing Lines, Activity 1 ................................................................................. 108 Graphing Lines, Activity 2 ................................................................................. 110 Graphing Lines, Activity 3 ................................................................................. 112 Equations of Lines, Activity 1 ............................................................................ 114 Equations of Lines, Activity 2 ............................................................................ 118 Attributes of Linear Functions, Activity 1 ........................................................... 120 Attributes of Linear Functions, Activity 2 ........................................................... 122 Attributes of Linear Functions, Activity 3 ........................................................... 124 Proportional Thinking, Activity 1 ........................................................................ 126 Proportional Thinking, Activity 2 ........................................................................ 128 Solving for y, Activity 1 ...................................................................................... 132 Solving for y, Activity 2 ...................................................................................... 136 Solving for y, Activity 3 ...................................................................................... 138 Direct Variation, Activity 1 ................................................................................. 140 Direct Variation, Activity 2 ................................................................................. 142 Direct Variation, Activity 3 ................................................................................. 144 Direct Variation, Activity 4 ................................................................................. 146

Linear Equations and Inequalities .............................................................. 148–223 Solving Equations, Activity 1 ............................................................................. 148 Solving Equations, Activity 2 ............................................................................. 150 Solving Equations, Activity 3 ............................................................................. 152 Solving Equations, Activity 4 ............................................................................. 156 Solving Equations, Activity 5 ............................................................................. 160 Systems of Linear Equations, Activity 1 ............................................................ 162 Systems of Linear Equations, Activity 2 ............................................................ 164 Systems of Linear Equations, Activity 3 ............................................................ 166 Systems of Linear Equations—Graphing, Activity 1 .......................................... 170 Systems of Linear Equations—Graphing, Activity 2 .......................................... 174 Systems of Linear Equations—Graphing, Activity 3 .......................................... 176 Systems of Linear Equations—Substitution, Activity 1 ...................................... 180 Systems of Linear Equations—Substitution, Activity 2 ...................................... 182 Systems of Linear Equations—Substitution, Activity 3 ...................................... 186 Systems of Linear Equations—Elimination, Activity 1 ....................................... 188 Systems of Linear Equations—Elimination, Activity 2 ....................................... 190 Systems of Linear Equations—Elimination, Activity 3 ....................................... 194 Systems of Linear Equations—Best Method, Activity 1 .................................... 196

SAMPLE

Systems of Linear Equations—Best Method, Activity 2 .................................... 200 Systems of Linear Equations—Best Method, Activity 3 .................................... 204 Inequalities, Activity 1 ....................................................................................... 208 Inequalities, Activity 2 ....................................................................................... 210 Inequalities, Activity 3 ....................................................................................... 212 Inequalities, Activity 4 ....................................................................................... 214 Inequalities, Activity 5 ....................................................................................... 216 Linear Inequalities, Activity 1 ............................................................................ 220 Linear Inequalities, Activity 2 ............................................................................ 222

Quadratic and Other Nonlinear Functions ................................................. 224–281 Graphing Quadratics, Activity 1 ........................................................................ 224 Graphing Quadratics, Activity 2 ........................................................................ 226 Graphing Quadratics, Activity 3 ........................................................................ 228 Graphing Quadratics, Activity 4 ........................................................................ 230 Graphing Quadratics, Activity 5 ........................................................................ 232 Solving Quadratic Equations, Activity 1 ............................................................ 234 Solving Quadratic Equations, Activity 2 ............................................................ 236 Solving Quadratic Equations, Activity 3 ............................................................ 240 Solving Quadratic Equations, Activity 4 ............................................................ 242 Quadratic Applications, Activity 1 ..................................................................... 244 Quadratic Applications, Activity 2 ..................................................................... 246 Quadratic Applications, Activity 3 ..................................................................... 248 Quadratic Applications, Activity 4 ..................................................................... 250 Quadratic Applications, Activity 5 ..................................................................... 252 Quadratic Applications, Activity 6 ..................................................................... 254 Exponents, Activity 1 ........................................................................................ 256 Exponents, Activity 2 ........................................................................................ 258 Exponents, Activity 3 ........................................................................................ 260 Exponents, Activity 4 ........................................................................................ 262 Exponents, Activity 5 ........................................................................................ 264 Exponents, Activity 6 ........................................................................................ 268 Exponential Equations, Activity 1 ...................................................................... 270 Exponential Equations, Activity 2 ...................................................................... 272 Exponential Equations, Activity 3 ...................................................................... 274 Inverse Variation, Activity 1 .............................................................................. 276 Inverse Variation, Activity 2 .............................................................................. 278 Inverse Variation, Activity 3 .............................................................................. 280

SAMPLE

Engaging Mathematics: Algebra I TEKS-Based Activities

© Region 4 Education Service Center All rights reserved.

Activity Objective The student will find rate of change using measurement.

Materials How Long Will This Be? Ruler Graphing calculator (optional)

Facilitation Questions

What does it mean to measure to the 1

4 inch?

It means I need to identify the 1

4 inch marks on my ruler and determine which one the

measurement is nearest.

Answers

Step Length (in.)

1 3

4 inches

3 1

24

inches

6 1

42

inches

7 1

54

inches

1. 3 inches

2. 3

34

inches

3. 3

4 inches

Generating Patterns, Activity 4

14

SAMPLE



Student Name: ________________________________________ Date: ________________

How Long Will This Be?

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Step 7

Measure the length of each line segment to the nearest 1

4 inch and record your answers in the

table.

Step Length (in.)

1

3

6

7

1. If the line lengths are increasing at a constant rate, how long would you expect the line

segment in Step 4 to be? 2. Draw the line segment for Step 5 and record its length. 3. What is the rate of change for this situation? Communicating About Mathematics Describe the strategy you used to find the rate of change. _______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

15

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Activity Objective The student will determine rates of change using a graph, table, and contextual clues.

Materials Get Me Outta Here! Highlighter or colored pencil Graphing calculator

Facilitation Questions What do you need to know before you can determine which runner is fastest?

how long it takes each runner to run the same distance

What strategy could you use to find the rate of change of the graph? I could find a point that intersects the grid at an exact value and then count up and over to the next point that intersects the grid at an exact value.

What differences do you need to consider when determining the rate of change in the table? the difference in the y-values compared to the difference in the x-values

Answers

1.

2.

3. 4. H

Slope and Rate of Change, Activity 2

Michael →

15 ↓

2.5 →

90

SAMPLE



Student Name: ________________________________________ Date________________

Get Me Outta Here! Shade the box with the correct answer for each question.

1. Michael runs 5 miles in 36 minutes. Andrea runs 2 miles in 15 minutes. Which runner is the fastest?

2. What is the rate of change of the graph to the right?

3. What is the rate of change of data in the table below?

4. Start at 1 and use the direction arrow from each shaded answer choice to find your way to a lettered exit. Circle the letter for your exit.

1 2 3 G

A

J

3 2 3

H 3

B C D F

Communicating About Mathematics Explain in your own words what a rate of change represents.

x y

4 10

6 15

8 20

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

Andrea ↓Michael →

2 → 15 ↓ 30 ←

2.5 → 5 ↓ 10.5 ←

91

SAMPLE



Activity Objective The student will match the table, graph, and/or context for systems of linear equations.

Materials Match ‘Em Up Match ‘Em Up Cards—one set per pair of students Scissors Tape or glue

Facilitation Questions What would finding the rate of change help you determine?

the slope of each line

What do the y values tell you when x is equal to zero? the y-intercept

Answers

Systems of Linear Equations—Graphing, Activity 3

At T-Shirts R Us, the cost to make new shirts is

$1.50 per shirt plus a $50 set-up fee. At T-Shirt

Planet, the set-up fee is $75 and printing is $1 per

shirt.

176

SAMPLE




Match ‘Em Up Cut apart the Match ‘Em Up Cards. Determine which cards match together to represent the same system of linear equations. Each card will only be used once. Attach the cards below when you have found the correct solution.

Communicating About Mathematics How could you use a table to determine the point of intersection? _______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

177

SAMPLE



Match ‘Em Up Cards Cut along the bold dotted line. Two sets of cards are provided.




shirt.




shirt.

178

SAMPLE



Activity Objective The student will explore a quadratic equation using a table and a graph.

Materials Pitcher Up! Graphing Calculator

Facilitation Questions How could you enter the given equation into your graphing calculator?

I would need to open the ! Editor and then type the equation using the x key to represent the independent variable and the q key to enter the exponent.

Why do you think the same heights appear twice in the table? The ball reaches that height on its way up and again on its way back down.

Answers

1. Baseball Pitch

X Y

0 0

1 30

2 50

3 60

4 60

5 50

6 30

7 0

Dis

tanc

e (m

eter

s)

Baseball Pitch

Time (seconds)

2. The ball reaches a height of 50 meters at t2 seconds on its way up and again at 5 seconds, on its way back down.

3. The maximum height reached by the ball is approximately 61, meters which can be seen from the graph between 3 and 4 seconds. The table also shows that the maximum height must be above 60 meters and occurs between 3 and 4 seconds.

4. The ball returns to its original height at 7 seconds. Both the graph and the table reflect a height of zero meters above the starting point at this time.

Quadratic Applications, Activity 2

246

SAMPLE




Pitcher Up! A baseball is thrown straight up into the air, traveling at an initial rate of 35 meters per second. The equation below describes the approximate distance in meters, d, above the starting point at t seconds after the ball was thrown.

235 5d t t 1. Use your graphing calculator to complete the table and graph below.

Baseball Pitch

X Y

0

1

2

3

4

5

6

7

Dis

tanc

e (m

eter

s)

Baseball Pitch

Time (seconds)

2. When is the ball at a height of 50 meters above the starting point? Explain your answer. 3. What is the approximate maximum height reached by the ball above its starting point? How

do you know? 4. When does the ball return to its starting height? How do you know? Communicating About Mathematics Write an equation that could be used to determine exactly how long it will take for the ball to reach a height of 55 meters above its starting point. Estimate the solution using your graph.

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

247

SAMPLE

engaging mathematics: teks-based activities algebra … · teks-based activities algebra i teacher...

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