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

Teaching Multiplication and Division for Meaning Many 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 Schools Jennifer 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 5 x 2 x 4 x 8 x 9 x 3 x 6 x 7 Create Anchor Chart(s) Old Dogs New Math ROB EASTAWAY & MIKE ASKEW

Multiplication Properties Commutative Property: The order in which numbers are multiplied does not change their products. Car analogy:

Multiplication Properties Distributive Property: The product of a sum and any number is equal to the sum of the products of each addend and the number.

Multiplication Properties Associative 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 ArraysArea Modelea

Models for Multiplication & Division The Ratio Table

Strategies for Multiplication & Division Repeated Addition & Subtraction 3 x 4 = 1212 ÷ 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? You16 Your Friend4

Strategies for Multiplication & Division Partial Products

Strategies for Multiplication & Division NCTM illuminations Quotient Cafe Partial Quotients

Strategies for Multiplication & Division Doubling & Halving

Strategies for Multiplication & Division Friendly Products & Quotients Area Model Ratio Table 99 X 8 = 100 X 8 = x 8 = ÷ 8 = 800 ÷ 8 = ÷ 8 =