Making Fraction Strips

1. Making Fraction Strips NO LABELING OF FRACTION STRIPS! • Pink: whole • Green:halves, fourths, eighths • Yellow: thirds, sixths, ninths • Blue:twelfths Note relationships among the fractions as you fold.

2. Fraction Equivalency…Is it easier than it sounds? Academic Coaches – Math Meeting February 1, 2013 Beth Schefelker Bridget Schock Connie Laughlin Hank Kepner Kevin McLeod

3. Learning Intention and Success Criteria Learning Intention: We are learning to develop understanding of fraction as numbers. Success Criteria: We will be successful when can explain equivalence of fractions.

4. Focusing on Unit Fractions • Fold each fraction strip to show the unit fraction for each strip. • Arrange these unit fractions from largest to smallest. • What are some observations you can make about unit fractions?

5. Standard 3.NF.1. Unit Fractions Read 3.NF.1 Complete the standards interpretation guide. 3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

6. Fractions Composed of Unit Fractions • Use your fourths strip to show . • How do you see this fraction as composed of unit fractions?

7. Attending to Precision in Language In pairs, practice using the language of the standard to describe non-unit fractions. 3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

8. 0 2 Number Line as a Linear Model • Draw a number line from 0 to 2 that shows fourths. • Locate the number on your number line. • Explain to a partner how you decided upon the placement of this number.

9. NF Progressions Document • What are the CCSSM expectations for number lines? • Read: “The Number Line and Number Line Diagrams”on page 3 of the Progression Document. • Read: Standard 3.NF.2, parts a and b. • With a partner, explain this standard to each other while referring to your drawing.

10. Standard 3.NF.2 3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

11. Fraction Equivalence

12. Making Sense of Equivalency Explain why is equivalent to Use fraction strips or a number line to explain your reasoning.

13. Standard 3.NF.3, Parts a, b, & c 3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

14. Puzzled Penguin My teacher asked me to show two fractions that was equivalent to Is my answer correct?

15. Fraction Equivalencies Equivalent fractions show the same size. Equivalent fractions show the same point on the number line.

16. Making Connections in Classroom • Use the fraction strips to make a number line from 0 to 1, so that the whole is the same length as the whole fraction strip. • Line up the fraction strips under the number line, one at a time, and mark the equal-sized parts. • Label the marks with fraction symbols. Don’t forget to also label fractions such as 0/4 and 4/4. What are some observations you hope students would make about fraction relationships to help them decide if two fractions are equivalent?

17. How do you know if fractions are equivalent?

18. Standard 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a) / (n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

19. Progressions Document Read the progressions document • Grade 3 • Equivalent Fractions • Read pp. 3-4; • study margin notes and diagrams. • Study standard 3.NF.3. Grade 4 Equivalent Fractions Read p. 5; study margin notes and diagrams. Study standard 4.NF.1. Go back to the interpretation guide to add any more information you’ve learned from the progressions.

20. Learning Intention and Success Criteria Learning Intention: We are learning to develop understanding of fraction as numbers. Success Criteria: We will be successful when can explain the equivalence of fractions.

21. Reflection How will the study of the fractions standards progression and their application to the classroom help your work with teachers? If you could choose a Math Practice Standard for this session, which standard would you choose and why? Use specific examples to support your reasoning. 21

22. Professional Practice Use the task “Closest to Half” with 2-5 students. Bring back student work samples Be prepared to share out 22