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the the ZZ strategy strategy

Relating Multiplication Relating Multiplication with Divisionwith Division

the the ZZ strategy strategy

Relating Multiplication Relating Multiplication with Divisionwith Division

Let’s Remember:• We know our fact families:

– 5 x 7 = 35 35 = 5 x 7– 7 x 5 = 35 35 = 7 x 5– 35 ÷ 7 = 5 5 = 35 ÷ 7– 35 ÷ 5 = 7 7 = 35 ÷ 5

We also can reverse a multiplication or division number sentence. For example:

5 35

7

We can reverse a multiplication sentence to make a division number sentence. For example:

9 x 11 = 99

99 ÷ 11 = 9

Let’s See that Again45 ÷ 9 = ____

Now, was that so hard?

You TryWrite a Related Multiplication or

Division Sentence:3 x 12 = 36 5 x 4 = 20

45 ÷ 9 = 5 77 ÷ 11 = 7

What if the equation is the “wrong” way?

15 = 3 x 5 7 = 28 ÷ 4• You can still use the Z strategy!• Just rewrite the equations:

3 x 5 = 15 28 ÷ 4 = 7

• And Z it up!!!

You TryRewrite the equation and use the Z

strategy to create a related x or ÷ sentence:

24 = 6 * 4 2 = 10 ÷ 5

5 = 25 ÷ 5 40 = 4 x 10

Problem SolvingA division problem that

you can solve with multiplication

During the 2009-2010 school year there were a total of 78 students in the 4th grade classes of Encarnacion, Boynton and Hamme. If each class has the same number of students, how many students were in each class?

Think – “Zzzz”There are a total of 78 students in the 4th

grade classes of Encarnacion, Boynton and Hamme. If each class has the same number of students, how many students are in each class?

Division – I know the total78 ÷ 3 = ?

? x 3 = 78

Jacob solved the following multiplication equation:

23 x 8 = 184

What number sentence could he use to check his answer?

23 x 8 = 184

184 ÷ 8 = 23

or 184 ÷ 23 = 8

Tutters says, “Meowwww… it’s your turn!”

Gabrielle solved the following math problem:32 x 4 = 128

What number sentence could she use to check her answer?

128 128 ÷ 4 = 32÷ 4 = 32

32 x 4 = 128

Final Check-Up for Today

Use the Z strategy to create a related multiplication or division equation:

9 x 12 = 108 380 = 95 x 4

45 = 450 ÷ 10 132 ÷ 11 = 12

the the ZZ strategy strategycontinued…continued…

the the ZZ strategy strategycontinued…continued…

Write a related equation for the following number equations:

36÷6 = 6 72 = 9x8 25÷5 = 5

6x7= 42 8 = 56÷7 4 = 12÷3

• Now – don’t let the variables in the next problems scare you!

36 ÷ x = 6 72 = 9x s

6 x 7 = m y = 56 ÷ 7

• Find the value of the variable (unknown letter).

YOU TRY - Write a related equation for the following number sentences:

y ÷ 4 = 5 3 x b = 6

c = 8 x 2 d ÷ 10 = 9

• Find the value of the variable (unknown letter).

If 48 ÷ n = 6

What does 6 x n = ?

48because using the Z strategy

I can see that

n = 8

and 48 ÷ 8 = 6

6 x 8 = 48

48 ÷ n = 6

6 x n = 48

True or False

The following statement is correct:

If n x 3 = 18, then n = 18 ÷ 3

True

because…

If n x 3 = 18, then n = 18 ÷ 3

n = 6

6 x 3 = 18

6 = 18 ÷ 3

ZZZZ

N x 3 = 18

True or False

The following statement is correct:

If 5 x f = 35, then 35 = 5 ÷ f

False

because…

If 5 x f = 35, then f = 7

And 35 = 5 ÷ 7?

NO WAY!

ZZZZZZ

5 x f = 35

Focused and alert, no sleeping now!

So… if all I have to do is reverse the number sentence?

• What is another way to write the equation 308 ÷ n = 14 ?

a. 14 + n = 308b. 14 x 308 = nc. 14 x n = 308d. 308 – 14 = n

Let’s just reverse the number sentence in the question.

14 x n = 308

so CC is our answer!

Well, how about with the variable N ?

What is another way to write the equation N x 24 = 120?

a. N = 24 ÷ 120

b. N = 120 ÷ 24

c. N = 24 x 120d. N x 120 = 24 Let’s just reverse the number

sentence in the question. 120 ÷ 24 = N, so B is our answer!

What is another way to write the

equation 54 ÷ n = 6?

a. n = 9 x 6b. n = 54 x 6c. n = 54 ÷ 6d. n = 54 x 9

(THINK – What number could n be? Which answer choice makes sense for that number?)

Which statement is correct?

A. If a ÷ 3 = 7, then a = 7 x 4

B. If 5 x 6 = b, then 6 x b = 5

C. If 14 ÷ y = 2, then y = 14 x 2

D. If d = 24 ÷ 6, then d x 6 = 24

D 500