# Multiplication strategies

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##### Intros
###### Lessons
1. Introduction to Multiplication Strategies:
2. Using addition and arrays to understand multiplication
3. Breaking down multiplication facts into smaller groupsr
4. A product can be found using a smaller product and a sum
5. A product can be found using a bigger product and a difference
6. Patterns to know for memorizing multiples of 9
7. Finger method of 9 times tables
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##### Examples
###### Lessons
1. Understanding products using smaller products
Turn the product into the sum of two smaller group products.
1. 8 × 4 = (5 × 4) + ( __ × 4)
$\qquad \qquad$ = _____ + _____
$\qquad \qquad$ = _______
2. 12 × 12 = (10 × 12) + ( __ × 12)
$\qquad \qquad$ = _______ + _______
$\qquad \qquad$ = _______
3. 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

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.
1. 5 × 3 = ( __ × 3) + 3
$\qquad \qquad$ = _______ + 3
$\qquad \qquad$ = _______
2. 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.
1. 9 × 6 = ( __ × 6) - 6
$\qquad \qquad$ = _______ + ____
$\qquad \qquad$ = _______
2. 9 × 27 = ( __ × 27) - 27
$\qquad \qquad$ = _______ - ____
$\qquad \qquad$ = _______
5. Relating multiplication and addition concepts
Find the answer using the given product.
1. If 6 × 86 = 516 , what is 7 × 86 = ?
2. 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.
1. If you put down the fourth finger, what is the 9-times tables multiplication sentence that is represented?
2. 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
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##### Practice
###### Topic Notes

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