Fractions: Beyond Pizzas and Pies

2. Fractions: Beyond Pizzas and Pies

3. What fraction of the large square is shaded… NumberSense 4-6, Dale Seymour 1997

6. Consider this…. 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

8. Misunderstanding

9. Simply Procedural

10. These are just two examples of what we want our students to be able to do.So how do we get there?

11. Today’s Objectives: • Enhance understanding of strategies for developing “fraction sense” • Identify material for professional development of fraction instruction

12. 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?

13. 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).”

14. 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

15. Common Core Standards Fractions as standards… Grade 3 = Which Grade Has The Greatest Concentration of Fractions? Grade 4 = Grade 5 =

16. Common Core Standards Fractions as standards… Grade 3 = (24% or 43.2 days of school) Grade 4 = (38% or 68.4 days of school) Grade 5 = (34% or 61.2 days of school)

17. Think - Pair - Share What are some strategies you use for comparing fractions?

18. Compare the following fractions. • Talk with your table how you compared the fractions. • We will share our ideas with the group.

19. A. E. B. F. C. G. D. H.

20. 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 Strategies for Comparing Fractions

21. With a partner, create 3 sets of fractions that can be compared with the listed strategy.

22. What’s the Math? • Alternative reasoning about comparison also supports reasoning about the size of fractions.

23. 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.

24. Guess My Number… My number is between 0 and 1

25. 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.

26. 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

27. Evaluation