1. Collaborating Teachers Grade 3 September 10, 2013

2. Rosie’s Multiplicative Situation Rosie has 3 friends. She bakes 15 cookies. She gives each friend 5 cookies.

3. Rosie’s Multiplicative Situation Rosie has 3 friends. She bakes 15 cookies. She gives each friend 5 cookies. If you covered up one number in the problem, what kind of questions could you ask?

4. Rosie’s Multiplicative Situation Rosie has 3 friends. She gives each friend 5 cookies. How many cookies does Rosie bake?

5. Rosie’s Multiplicative Situation Rosie bakes 15 cookies. She gives each friend 5 cookies. How many friends does Rosie have?

6. Rosie’s Multiplicative Situation Rosie has 3 friends. She bakes 15 cookies. How many cookies does Rosie give to each friend?

7. Rosie’s Multiplicative Situation Each multiplication or division situation involves three quantities, each of which can be the unknown. 3 x 5 = 15

8. Product = Factor x Factor: Questions you could ask How many cookies does Rosie bake? – Unknown Product - multiplication How many cookies does Rosie give to each friend? – Unknown Factor – Group Size Unknown – division How many friends does Rosie have? – Unknown Factor – Number of Groups Unknown – division

9. Apples in a Store Window Equal Groups? Array?

10. Apples in a Store Window Equal Groups? Array? Both!

11. Apples in a Store Window Equal Groups: five groups of two or two groups of five. Array: five columns of two or two rows of five.

12. Array 2 x 4 = 8 4 x 2 = 8 Rotate an array to illustrate the commutative property for multiplication.

13. Array Connects Equal Groups to Area Measurement Array Area

14. Area models are foundational! Area problems where regions are partitioned by unit squares are foundational for Grade 3 because area is used as a model for single-digit multiplication and division strategies in Grade 3, in Grade 4 as a model for multi-digit multiplication and division, and in Grade 5 and Grade 6 as a model for multiplication and division of decimals and of fractions.

15. Grade 3 Number Talk: Array Discussion: 8 x 25 As you watch the number talk in which an 8 x 25 array is used, consider: 1.How does the array model support the student strategies? 2.How does the breaking the factors into friendly numbers promote the goals of efficiency and flexibility? 3.How do the teacher’s questions foster an understanding of multiplication? 4.What math understandings and misconceptions are addressed with this model?

16. Multiplication and Division in 3 rd Grade Begin with repeated addition and with numbers easily skip counted, such as 2, 5, 10, 3, and 4. Explore area by skip counting rows and columns, then multiplying, and later solve problems with area. Develop a solid understanding of the relationship between multiplication and division. Develop strategies for multiplication and division. Use multiplication and division to solve measurement problems. Know all products of two one-digit numbers.

17. Analyzing Word Problems Involving Multiplication - http://www.illustrativemathematics.org/illustrations/365 http://www.illustrativemathematics.org/illustrations/365 Gifts from Grandma, Variation 1 - http://www.illustrativemathematics.org/illustrations/262 http://www.illustrativemathematics.org/illustrations/262 Two interpretations of Division - http://www.illustrativemathematics.org/illustrations/344 http://www.illustrativemathematics.org/illustrations/344 Fish Tanks (assess understanding of meanings of division)http://www.illustrativemathematics.org/illustrati ons/1531http://www.illustrativemathematics.org/illustrati ons/1531 The Square Counting Shortcut - http://www.illustrativemathematics.org/illustrations/516 http://www.illustrativemathematics.org/illustrations/516

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