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From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools www.hisparks.com August 9, 2010

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Page 1: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

From Concrete to Abstract:Helping ALL Students Develop

Algebraic Thinking Skills

Heather Sparks, NBCTTaft Middle SchoolOklahoma City Schoolswww.hisparks.com

August 9, 2010

Page 2: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

*Adapted from Van de Walle and Lovin

Page 3: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

Turtle and Snail

On summer day, Little Green Turtle challenged Teeny Tiny Turtle to a race from the oak tree to the elm tree.Turtle travels at a rate of 3 feet per minute and Snail travels at a rate of 2 feet per minute. The trees are 12 feet apart.

STORY:

Page 4: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

Turtle and Snail

12 feet

PICTURE

Page 5: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

time distance time distance

TABLE

0

1

2

3

4

Turtle Snail

0

1

2

3

4

Page 6: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

RULE OREQUATION

Turtle: multiply by 3 d= 3t

Snail: multiply by 2 d = 2t

Page 7: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

GRAPH

distance in feet

time

0 1 2 3 4 5 6 7 8

12

11

10

9

8

7

6

5

4

3

2

1

0

Page 8: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools
Page 9: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

x y2 53 64 75 86 9

x y-2 7 0 3 1 14 -56 -9

What’s My Rule?

Page 10: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

Every graph tells a story…

Page 11: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools
Page 12: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools
Page 13: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools
Page 14: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

Let’s Apply!

Ball Bouncing

Slinky Stretch

Cup Stacking

Party Tables

Page 15: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

Extend and Explain

Page 16: From Concrete to Abstract: Helping ALL Students Develop Algebraic Thinking Skills Heather Sparks, NBCT Taft Middle School Oklahoma City Schools

Heather’s Website:www.hisparks.com