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- Multiplying and Dividing Numbers

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Try reviewing these fundamentals first

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Get Started Now- Intro Lesson: a4:23
- Intro Lesson: b5:42
- Intro Lesson: c5:35
- Intro Lesson: d3:13
- Intro Lesson: e8:12
- Intro Lesson: f12:21
- Lesson: 1a2:28
- Lesson: 1b3:02
- Lesson: 1c2:16
- Lesson: 2a2:15
- Lesson: 2b2:28
- Lesson: 3a2:09
- Lesson: 3b2:40
- Lesson: 4a2:35
- Lesson: 4b3:10
- Lesson: 5a2:21
- Lesson: 5b3:23
- Lesson: 6a1:55
- Lesson: 6b3:16

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

**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

- IntroductionIntroduction to Multiplication Strategies:a)Using addition and arrays to understand multiplicationb)Breaking down multiplication facts into smaller groupsrc)A product can be found using a smaller product and a sumd)A product can be found using a bigger product and a differencee)Patterns to know for memorizing multiples of 9f)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:- the product shown in the array and
- 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.
**Relating multiplication and addition concepts**

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

4.

Multiplying and Dividing Numbers

4.1

Arrays and factors

4.2

Multiplying by 10, 100, 1000

4.3

Multiplication strategies

4.4

Multiplying multi-digit numbers

4.5

Dividing multiples of 10

4.6

Dividing using place value

4.7

Dividing using area models

4.8

Dividing multi-digit numbers

4.9

Products and quotients: Word problems

4.10

Applications of the four operations