Understanding Multiplication & Division Strategies Carissa Connell, Stacey Daly, Jen Maxwell ATOMIC December 2, 2014.

Understanding Multiplication &

Division StrategiesCarissa Connell, Stacey Daly, Jen Maxwell

ATOMICDecember 2, 2014

Teaching Multiplication and Division for MeaningMany children struggle with multiplication and division because it is taught through rote algorithms. This workshop will cover a progression of meaningful steps to teach multiplication and division from a place value perspective. Strategies will be shown for teaching multiplication and division through visual representations of groups and arrays. A progression of strategies leading to the standard algorithm will include skip counting and number line strategies, ratio tables, using strategies such as known facts and doubling and halving. Throughout the presentation, participants will have the opportunity to build the various models and use them to solve varying multiplication and division problems.

Stacey Daly, Madison Public Schools Carissa Connell, Madison Public SchoolsJennifer Maxwell, Madison Public Schools

Conceptual Understanding of Multiplication

● Students begin to make the transition from additive to multiplicative reasoning.

● Unitizing

Multiplication Fact Categories● Zero Property● Identity Property● Times Ten● Half Ten● Doubles● Double- Double● Double-Double-Double● Half Ten Plus A Set● Ten Minus A Set● Doubles Plus One Set

Suggested strategic order in which to learn facts:

x 10 x 5x 2x 4x 8x 9x 3x 6x 7

Create Anchor Chart(s)

Old Dogs New Math ROB EASTAWAY & MIKE

ASKEW

Multiplication PropertiesCommutative Property:

The order in which numbers are multiplied does not change their products.

Car analogy:

Multiplication PropertiesDistributive Property:

The product of a sum and any number is equal to the sum of the products of each addend and the number.

Multiplication PropertiesAssociative Property:

The way in which numbers being multiplied are grouped does not change their product.

Models for Multiplication & Division

Loops & Groups The Number Line

Models for Multiplication & Division

Arrays Area Model ea

Models for Multiplication & Division

The Ratio Table

Strategies for Multiplication & Division

Repeated Addition & Subtraction

3 x 4 = 12 12 ÷ 4 = 34 + 4 + 4 = 12 12 - 4 - 4 - 4= 0

Strategies for Multiplication & Division

Skip Counting

In a problem context: For every ticket you sell, your friend sells 4. You sell a total of 6 tickets. How many does your friend sell?

You 1 6

Your Friend 4

Strategies for Multiplication & Division

Partial Products

Strategies for Multiplication & Division

NCTM illuminationsQuotient Cafe

Partial Quotients

Strategies for Multiplication & Division

Doubling & Halving

Strategies for Multiplication & Division

Friendly Products & QuotientsArea Model

Ratio Table

99 X 8 =

100 X 8 = 800 1 x 8 = - 8 792

792 ÷ 8 =

800 ÷ 8 = 100 8 ÷ 8 = - 1 99