Fractions: Beyond Pizzas and Pies

What fraction of the large square is shaded…

NumberSense 4-6, Dale Seymour 1997

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….

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

be able to do.

So how do we get there?

Today’s Objectives:

• Enhance understanding of strategies for developing “fraction sense”

• Identify material for professional development of fraction instruction

Talk With Your Table…• What aspects of fractions do the

students/teachers at your school do well with?

• What challenges with fractions do your students/teachers face?

• 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 StandardsFractions as standards…

€

937Grade 3 =

€

1437Grade 4 =

€

1441Grade 5 =

Common Core StandardsFractions as standards…

€

937Grade 3 = (24% or 43.2 days of school)

€

1437Grade 4 = (38% or 68.4 days of school)

€

1441Grade 5 = (34% or 61.2 days of school)

Think - Pair - Share

What are some strategies you use for comparing fractions?

• 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!

With a partner, create 3 sets of

fractions that can be compared with the listed strategy.

What’s the Math?

• Alternative reasoning about comparison also supports reasoning about the size of fractions.

What’s the Research?• Students rarely used one-half as a

benchmark for solving problems.

• Students indicated that using a common denominator is “doing the math”

• Students have difficulty being able to reason about an estimate without being able to find the exact answer.

Guess My Number…

My number is between 0 and 1

What’s the Math?What’s the Research?

• Review your group’s chapter.

• Go to http://mst.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