# Multiplication strategies

### Multiplication strategies

In this lesson, we will learn:

• Understanding multiplication using arrays
• Representing a product as either: (1) a smaller product and a sum, or (2) a bigger product and a difference
• Tips and tricks for memorizing the 9 × multiplication table facts

Notes:

• Multiplication is just repeated addition
• Multiplication facts can be shown in an array model with circles/dots
• Using the array model, it shows that multiplication facts can be broken into groups of smaller multiplication facts:
• Using the same array model, we can find the next multiplication fact by adding another row:
• Therefore, a product can be found as a smaller product and a sum
• Or, it could be found as a bigger product and a difference
• The 9 × multiplication tables can be memorized using your fingers!
• Notice that the first ten multiples of 9 are mirrored after the 5-digit in 45
• Ex. 9, 18, 27, 36, 45 $\parallel$ 54, 63, 72, 81, 90

#### Lessons

• Introduction
Introduction to Multiplication Strategies:
a)
Using addition and arrays to understand multiplication

b)
Breaking down multiplication facts into smaller groupsr

c)
A product can be found using a smaller product and a sum

d)
A product can be found using a bigger product and a difference

e)
Patterns to know for memorizing multiples of 9

f)
Finger method of 9 times tables

• 1.
Understanding products using smaller products
Turn the product into the sum of two smaller group products.
a)
8 × 4 = (5 × 4) + ( __ × 4)
$\qquad \qquad$ = _____ + _____
$\qquad \qquad$ = _______

b)
12 × 12 = (10 × 12) + ( __ × 12)
$\qquad \qquad$ = _______ + _______
$\qquad \qquad$ = _______

c)
20 × 35 = (10 × 35) + ( __ × 35)
$\qquad \qquad$ = _______ + _______
$\qquad \qquad$ = _______

• 2.
Describing multiplication array models - 1
Fill in the blanks to describe:
1. the product shown in the array and
2. the sum written with the smaller product
a)

b)

• 3.
Describing multiplication array models - 2
Fill in the blanks to turn the product into a smaller product and sum.
Use an array model to help fill in the blanks.
a)
5 × 3 = ( __ × 3) + 3
$\qquad \qquad$ = _______ + 3
$\qquad \qquad$ = _______

b)
11 × 12 = ( __ × 12) + __
$\qquad \qquad$ = _______ + ____
$\qquad \qquad$ = _______

• 4.
Multiplication and array models with subtraction
Fill in the blanks to turn the product into a bigger product and a difference.
a)
9 × 6 = ( __ × 6) - 6
$\qquad \qquad$ = _______ + ____
$\qquad \qquad$ = _______

b)
9 × 27 = ( __ × 27) - 27
$\qquad \qquad$ = _______ - ____
$\qquad \qquad$ = _______

• 5.
Find the answer using the given product.
a)
If 6 × 86 = 516 , what is 7 × 86 = ?

b)
If 10 × 53 = 530 , what is 9 × 53 = ?

• 6.
Multiplication with 9-times tables strategy: word problems
Use the finger method for 9-times tables to solve.
a)
If you put down the fourth finger, what is the 9-times tables multiplication sentence that is represented?

b)
If you put down the fourth finger, it represents a 9-times table fact. What finger do you need to put down for the opposite answer (when the answer's digits are flipped/mirrored)? Write the multiplication sentence for the 9-times table fact with the opposite answer