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1. Fractions with Bars, Area Model and Number Line Mathematics Learning, Teaching and Leading Collaborative

2. The Structure of Fractions 3.NF 1. Understand a fraction 1/B as the quantity formed by 1 part when a whole is partitioned into Bequal parts; 0/6 1/6 Mathematics Learning, Teaching and Leading Collaborative

3. The Structure of Fractions 3NF1. Understand a fraction A/B as the quantity formed by A parts of size 1/B.” 1/b 1/B = 1/6 A= 4 4 parts of 1/6 = 4/6 A=0 and B=6 0/6 = 0 A=6 and B=6 6/6 = 1 A = 4 B = 6 4/6 Mathematics Learning, Teaching and Leading Collaborative

4. The Structure of Fractions 3NF 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.” 1/B = 1/12. The length of the blue line is A (in this case 4) parts of 1/B or 4 equal parts of 1/12; 1/12 + 1/12 + 1/12 + 1/12 = 4/12 • 1 Math Learning TLC Mathematics Learning, Teaching and Leading Collaborative

5. The Structure of Fractions3NF2a. 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.3NF2b. 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. 0/6 1/6 1=6/6 Starting at 0, 1/6 it is reproduced 6 times to get a long segmentequal to 6/6 or 1.

6. The Main Topics of 4th Grade 4.NF A big idea in 4th grade is the fundamental facts about equivalent fractions (a fraction is not changed when its numerator and denominator are multiplied by the same nonzero whole number.) Spend time comparing, adding, and subtracting fractions with common denominators and the meaning of multiplying a fraction by a whole number. Math Learning TLC Mathematics Learning, Teaching and Leading Collaborative

7. The fraction value is not changed when its numerator and denominator are multiplied by the same nonzero whole number. Or why 2/3 = 8/12 Mathematics Learning, Teaching and Leading Collaborative

8. (n × a)/(n × b) example: (4X2)/(4X3) = 8/12 2 = 4 X 2 2 = 8 3 4 X 3 3 12 2/3 2/3 8/12 4/4 Mathematics Learning, Teaching and Leading Collaborative

9. Grade Four FractionsExamples from CCSS Content Standards for Mathematics • Break apart a fraction into smaller fractions with the same denominator, or bottom number, in more than one way. For example: 3⁄8 = 1 ⁄ 8 + 1 ⁄ 8 + 1 ⁄ 8 = 2 ⁄ 8+ 1 ⁄ 8 2) Explain why a fraction is equal to another fraction 3) Add and subtract mixed numbers (whole numbers mixed with fractions, such as 1 1/5) with the same denominators 4) Multiply a fraction by a whole number Mathematics Learning, Teaching and Leading Collaborative

10. Mathematics Learning, Teaching, & Leading Collaborative

11. Fraction BarsIndividual Work 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ . . . • Lay the 1/4 bar on your desk and then find bars with more parts but with the same amount of shading. Write down a number sentence to describe your actions. • Repeat this with the 1/2, 3/4, and 2/3 bars. When done, choose bars of your own choice, continue writing down number sentences that describe your actions. • Be ready to share your thinking and noticings. Mathematics Learning, Teaching and Leading Collaborative

12. Fraction Bars: Work and discuss in pairs, and then in your small group. 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ . . . • Find the 1/2 bar. With your bars, show that 1/2 = 2/4 = 3/6 = 6/12 What do you notice? • Sketch a bar for 2/5. Divide the parts of your bar to show that 2/5 = 5/10. • Sketch a bar for 3/8. Divide the parts of your bar to show that 3/8 = 6/16. • What are some general methods you found for forming equivalent fractions? Be ready to report out to the large group. Mathematics Learning, Teaching and Leading Collaborative

13. Fraction Bars 4.NF.2 Compare 2 fractions with different numerators and different denominators . . . . . . . Locate the 1/3 fraction bar and the 1/4 fraction. Privately decide which fraction is greater and write down a number sentence that matches your thinking, using greater than or less then notation. Mathematics Learning, Teaching and Leading Collaborative

14. Fraction Bars 4.NF.2 Compare 2 fractions with different numerators and different denominators . . . . . . . Locate and lay out the following pairs of fraction bars. • 1/2 and 4/6 • 5/12 and 2/3 • 5/6 and 7/12 • 2/3 and 3/4 Write down a number sentence for each pair using greater than or less than signs. Mathematics Learning, Teaching and Leading Collaborative

15. Fraction Bars Devise ways to use fraction bars to find these sums. Be ready to share your thinking. 4.NF.B Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. • 1/5 + 2/5 = • 3/4 + 2/4 = • 3/6 + 4/6 = Mathematics Learning, Teaching and Leading Collaborative

16. Grade Five FractionsExamples from CCSS Content Standards for Mathematics • Interpret a fraction as division of the numerator (the top number) by the denominator (the bottom number) • Add and subtract fractions with different denominators • Multiply a fraction by a whole number or another fraction • Dividefractions by whole numbers and whole numbers by fractions Mathematics Learning, Teaching and Leading Collaborative

17. Fraction Bars Devise ways to use fraction bars to find these sums. Be ready to share your thinking. 5.NF.A Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. • 2/3 + 3/4 = • 2/3 + 5/6 = • 3/4+ 3/12 = Mathematics Learning, Teaching and Leading Collaborative

18. Fraction Bars Devise ways to use fraction bars to find these differences. 5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. • 3/4 - 2/3 = • 5/12 - 1/6 = • 3/4 - 3/12 = • 1 ½ - ⅚ = Mathematics Learning, Teaching and Leading Collaborative

19. Mathematics Learning, Teaching, & Leading Collaborative

20. StopGo to “What is the product of 4 x 2/3? Mathematics Learning, Teaching, & Leading Collaborative

21. Grade Five FractionsExamples from CCSS Content Standards for Mathematics • Interpret a fraction as division of the numerator (the top number) by the denominator (the bottom number) • Add and subtract fractions with different denominators • Multiplya fraction by a whole number or another fraction • Dividefractions by whole numbers and whole numbers by fractions Mathematics Learning, Teaching and Leading Collaborative

22. Mathematics Learning, Teaching, & Leading Collaborative

23. Fraction MultiplicationMethod Two: Area Model 2/3 X 3/4 Mathematics Learning, Teaching and Leading Collaborative

24. Fraction MultiplicationMethod Two: Area Model 2/3 X 3/4 Mathematics Learning, Teaching and Leading Collaborative

25. Fraction MultiplicationMethod Two: Area Model 2/3 3/4 Mathematics Learning, Teaching and Leading Collaborative

26. Fraction MultiplicationMethod Two: Area Model 3/5 X 2/3 The whole is 15 and the part is 6 so the answer is 6/15 Mathematics Learning, Teaching and Leading Collaborative

27. Method Two Area ModelFraction Multiplication 3 1/2 X 4 = 14 AND 4 X 3 1/2 = 14 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1+ ½ + ½ + ½ + ½ = 12 + 4 (1/2) = 12 + 2 = 14 Math Learning TLC Mathematics Learning, Teaching and Leading Collaborative

28. CCSS Math Task, Fraction Multiplication Rob is calculating the area of this rectangle. His strategy is to multiply the whole numbers first and then multiply the fractions. Since 6 X 7 = 42 and 1/2 × 6 = 3, he concludes that the area of the rectangle is 42 + 3 = 45 sq. units. Is he correct? If your answer is yes, explain why he correct. If you answer is no, write down the correct answer and tell why it is correct. 6 7 1/2 Math Learning TLC Mathematics Learning, Teaching and Leading Collaborative

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34. Fraction Multiplication, Method Three Egg Carton Fractions. Use your egg cartons and yarn to solve a selection (your choice) of the following. Mathematics Learning, Teaching, & Leading Collaborative Mathematics Learning, Teaching and Leading Collaborative

35. CCSS, 5th Grade Stuffed with Pizza Tito and Luis are stuffed with pizza! Tito ate one-fourth of a cheese pizza. Tito ate three-eights of a pepperoni pizza. Tito ate one-half of a mushroom pizza. Louis ate five-eights of the chees pizza. Louis ate the other half of the mushroom pizza. All the pizzas were the same size. Tito says he ate more pizza than Luis, because Luis did not eat any pepperoni pizza. Luis says they ate the same amount of pizza. • Who is correct? • Show all your mathematical thinking. Mathematics Learning, Teaching and Leading Collaborative