Area Model
The area model is similar to _______?
What is the partial product strategy?
A combination of area models and the distributive property.
How would you write 346 x 4 in standard algorithm?
346 x 4
What is an array?
Items (objects or number) that are arranged in row and columns
What is an area model?
A multiplication strategy using Length x Width = Area, where factors are used for length and width and the product is the area
How would you draw 5 x 3 as an area model?
3 rows of 5 columns
Using the partial product strategy: How would you solve 5 x 127?
Area Model: 5 down, 127 across
Split up 127 into 100, 20, and 7
Multiply: 5 x 100 5 x 20 5 x 7
500 + 100 + 35 = 635
Distributive Property: 5 x (100 + 20 + 7)
(5 x 100) + (5 x 20) + (5 x 7)
500 + 100 + 35 = 635
Using standard algorithm: How would you solve 346 x 4?
2 346 x 4 1,384
the numbers that are multiplied in a multiplication problem
What is Length and Width?
Length defines how long an object is, Width defines how broad an object is.
Using area models: How would you solve 4 x 13?
4 down, 13 across
expand 13 to 3 and 10- split the rectangle into two
multiply 4 and 10, multiply 4 and 3
40 + 12 = 52
Using the partial product strategy: How would you solve 4 x 249?
Area Model: 4 down, 249 across
Split up 249 into 200, 40, and 9
Multiply: 4 x 200 4 x 40 4 x 9
800 + 160 + 36 = 996
Distributive Property: 4 x (200 + 40 + 9)
(4 x 200) + (4 x 40) + (4 x 9)
800 + 160 + 36 = 996
Using standard algorithm: How would you solve 57 x 46
4 57 x 46 342 + 2280 2622
What is the product?
The result, or answer, when multiplying
To break up a number according to its place value and expand it to show the value of each digit is called what?
Expanded Form
Using area model: How would you solve 9 x 135?
9 down, 135 across
Expand 135: 100, 30, 5 - split rectangle into 3
Multiply: 9 x 100 9 x 30 9 x 5
900 + 270 + 45 = 1215
Using the partial product strategy: How would you solve 82 x 43?
Area Model: 82 down, 43 across
Split up 82 into 80, 2 Split up 43 into 40, 3
Multiply: 80 x 40 80 x 3 2 x 40 2 x 3
3,200 + 240 + 80 + 6 = 3,526
Distributive Property: (80 + 2) x (40 + 3)
(80 x 40) + (80 x 3) + (2 x 40) + (2 x 3)
3,200 + 240 + 80 + 6 = 3,526
Using standard algorithm: How would you solve 550 x 3?
1 550 x 3 1,650
What is the commutative property?
Changing the order of the numbers when multiplying does not change the answer
A strategy that is a combination of the area model and distributive property is called what?
Partial Products Strategy
Using area model: How would you solve 12 x 45?
Box method: expand 12 and 45: 10 + 2 40 + 5
Multiply: 10 x 40 10 x 5 2 x 40 2 x 5
400 + 50 + 80 + 10 = 540
Using the partial product strategy: How would you solve 21 x 47?
Area Model: 21 down, 47 across
Split up 21 into 20, 1 Split up 47 into 40, 7
Multiply: 20 x 40 20 x 7 1 x 40 1 x 7
800 + 140 + 40 + 7 = 987
Distributive Property: (20 + 1) x (40 + 7)
(20 x 40) + (20 x 7) + (1 x 40) + (1 x 7)
800 + 140 + 40 + 7 = 987
Using standard algorithm: How would you solve 72 x 43
72 x 43 216 + 2280 3096
What does it mean to decompose?
to split up or divide a number into smaller parts
What is Standard Algorithm for Multiplication?
A multiplication procedure where you follow specific steps and mathematical rules to multiply digits in each place to find a product.