1. Grade Three: Fractions Unit 7 Finding Fair Shares

2. Let’s Start with some MATH! If the whole square is equal to 1, label each part with the appropriate fraction

3. What makes work with fractions so difficult for students? (p. 109)

4. CCSS.Math.Content.3.NF.A.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. CCSS.Math.Content.3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. CCSS.Math.Content.3.NF.A.2a 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. CCSS.Math.Content.3.NF.A.2b 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. CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. CCSS.Math.Content.3.NF.A.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. CCSS.Math.Content.3.NF.A.3b 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. CCSS.Math.Content.3.NF.A.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. CCSS.Math.Content.3.NF.A.3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 1 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.

5. CCSS.Math.Content.3.NF.A.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. CCSS.Math.Content.3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

6. Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.

7. Overview of our Sessions 1. Investigation 1: Sharing Brownies 2. Investigation 2: Many Ways to Make a Share 3. CMS Unit: Fractions on a Number Line

8. One Brownie to Share Take 1 brownie. How can you cut the brownie so that two people can have equal shares?

9. Fraction Notation What would you call the share of the brownie that one person gets? This piece is _____ of the whole. What does the number on the top stand for? What does the number on the bottom stand for?

10. Fraction Notation Read Math Note 3: Vocabulary on page 25 Turn and Talk: What is most important here?

11. Sharing Brownies Using the sheet of large brownies, create the “fair shares” on the activity sheet. SAB 1-2

12. Key Discussion: Are your shares equal?

13. Making Fair Shares – Key Discussion Are these shares equal? How do you know? How could you prove it?

14. Why focus on “fair” shares? ¼ 1/3 1/3

15. Common Core State Standards What standards are evident in this lesson? How can I ensure that this lesson is about mathematics and not about cutting and pasting?

16. Making Fraction Sets -Get with a partner and take 5 sheets of the same color paper -Fold into equal pieces, then draw lines to separate them -Label each piece with the fraction name -Cut into equal pieces 1 st sheet: 2 equal pieces 2 nd sheet: 4 equal pieces 3 rd sheet: 8 equal pieces 4 th sheet: 3 equal pieces 5 th sheet: 6 equal pieces discuss the difference between the two ways to make sixths and how to prove they are equal

17. Aarrgghh, I know some of my students… What challenges may arise as students create fraction sets? What can you do that will not interfere with student learning?

18. Smallest to Largest ½ 1414

19. True or False? “The Larger the Denominator, the _________ the fraction” 1 or 1 7 5

20. What about now? “The Larger the Denominator, the __smaller__ the fraction” 3 Or 4 7 5

21. A student’s fraction models What do you know about Billy’s understanding of fractions based on his models?

22. Common Core State Standards What standards are evident in this lesson? How can I ensure that this lesson is about mathematics and not about coloring?

23. Make a new set of fraction cards with one piece missing You will need 5 sheets of paper. 1. Fold one paper into fourths. 2. Cut away 1 piece. Label it ¼. 3. Label the remaining piece ¾. 4. Continue until you have made representations for all of these fractions:

24. NO Common Denominators! Which is larger 5/6 or 7/8

25. NO Common Denominators! Which is larger, 5/6 or 7/8

26. Many Ways to Make a Whole With your partner, find different ways to make a whole. Record on FRACTION FACTS Chart

27. Common Core State Standards Do 3 rd Graders need to add fractions with unlike denominators in the Common Core? Do they need to add fractions at all? Why keep this lesson?

28. Sharing Seven Brownies Imagine there are seven brownies to share equally among four people. About how many brownies do you think each person will get? Work with a partner to find out exactly how many brownies each person will get. Record your work on a sheet of paper.

29. Gallery Walk What do you notice about our solutions?

30. Common Core State Standards Do students need to consider quantities greater than one? 3.MD.4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

31. Session 1.5: SAB 11 Which fraction standard is this about? What do these students understand about it? What else comes up for us in this work? Should we read something from the fraction book?

32. Exit Ticket How did the facilitation of today’s session work for you? What did not work for you? What recommendations do you have for future sessions?

33. Welcome Back! How’s it going?