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Fractions: Beyond Pizzas and Pies

John SanGiovanni

http://jsangiovanni.hcpss.wikispaces.net

jsangiovanni@hcpss.org

What fraction of the large square is shaded…

NumberSense 4-6, Dale Seymour 1997 http://jsangiovanni.hcpss.wikispaces.net

http://jsangiovanni.hcpss.wikispaces.net

http://jsangiovanni.hcpss.wikispaces.net

There are 3 different bags of oranges at the grocery store.

Estimate the sum of the 3 bags.

Is the combined weight of the 3 bags greater than 10 pounds?

Nimble with Numbers 4-6, Dale Seymour, 1998

Consider this….

http://jsangiovanni.hcpss.wikispaces.net

These are just two examples of what we want our students to

be able to do.

So how do we get there?

http://jsangiovanni.hcpss.wikispaces.net

Today’s Objectives:

• Enhance understanding of strategies for developing “fraction sense”

• Identify resources to provide instructional support for teachers in your building

Talk With Your Table…

• What aspects of fractions do your students do well with?

• What challenges do you or your students face when teaching or learning about fractions?

• Why is it important for our students to understand fractions?

National Math Panel, 2007

• “A major goal for K - 8 mathematics education should be proficiency with fractions (including decimals, percents) for such proficiency is foundational for algebra (p.20).”

• Teachers should not assume that children understand the magnitudes represented by fractions, even if they can perform arithmetic operations with them, or that children understand what the operations mean (p. 28).”

PSSM Expectations

Students should be able to:

Work flexibly with fractions, decimals, and percents to solve problems

Understanding the meaning and effects of arithmetic operations with fractions, decimals and percents.

Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the answers.

- P. 214

Common Core Standards

• Compare the following fractions.

• Talk with your table how you compared the fractions.

• We will share our ideas with the group.

€

27

3

5

€

89

2

6

€

1418

14

20

€

1314

15

16

€

36

15

20

€

56

5

8

€

1617

30

34

€

712

9

20

Strategies for Comparing Fractions

• Common Denominator

• Cross Multiplying

• Same number of parts of different sizes

• More and less than one-half or one whole

• Close to one-half or one whole

€

14

2

3

€

28

2

3

€

14

2

3

€

67

11

12

€

14

is less 1

2

€

12ths are

smaller

than 7 ths.

€

14

2

3 (1 x 3 < 2 x 4 )€

Duh!

What’s the math?What’s the research?

What’s the Math?What’s the Research?

• Review your group’s chapter.

• Go to http://jsangiovanni.hcpss.wikispaces.net

• Record your thoughts about the chapter.

• Be prepared to share.

Chapter 1: The Problem With Partitioning

Chapter 2: Top or Bottom: Which One Matters?

Chapter 3: Understanding Equivalency: How Can Double Be the Same?

Chapter 4: Fraction Kits: Friend or Foe?

Chapter 5: Is 1/2 Always Greater Than 1/3?

Chapter 6: How Come 1/5 ≠ .15? Helping Students Make Sense of Fraction and Decimal Notation

Chapter 7: The Multiple Meanings of Fractions: Beyond Pizzas and Pies

Evaluation