Collaborating Teachers

Grade 3September 10, 2013

Rosie’s Multiplicative Situation

Rosie has 3 friends. She bakes 15 cookies. She gives each friend 5 cookies.

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?

Rosie’s Multiplicative Situation

Rosie has 3 friends. She gives each friend 5 cookies. How many cookies does Rosie bake?

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

Rosie’s Multiplicative Situation

Rosie has 3 friends. She bakes 15 cookies. How many cookies does Rosie give to each friend?

Rosie’s Multiplicative Situation

Each multiplication or division situation involves three quantities, each of which can be the unknown.

3 x 5 = 15

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

Apples in a Store Window

Equal Groups?Array?

Apples in a Store Window

Equal Groups?Array?Both!

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.

Array

2 x 4 = 84 x 2 = 8

Rotate an array to illustrate the commutative property for multiplication.

Array Connects Equal Groups to Area Measurement

Array Area

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.

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?

Multiplication and Division in 3rd 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.

• Analyzing Word Problems Involving Multiplication - http://www.illustrativemathematics.org/illustrations/365

• Gifts from Grandma, Variation 1 - http://www.illustrativemathematics.org/illustrations/262

• Two interpretations of Division - http://www.illustrativemathematics.org/illustrations/344

• Fish Tanks (assess understanding of meanings of division)http://www.illustrativemathematics.org/illustrations/1531

• The Square Counting Shortcut - http://www.illustrativemathematics.org/illustrations/516

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