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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
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
