Mental Math Multiples of Ten

Module 5- 5.01-5.02

Multiplication

Solve 5 x 20 = ____.

To solve this equation using mental math, we will make the equation simpler. We will expand each number so that we can do the math in our heads.

Here are the steps we can use to solve this problem mentally.

Change the multiple of 10

The first step is to expand the number that is a multiple of 10.

We expand 20 into 2 x 10 because we know that 2 x 10 = 20.

We did all of this just using mental math.

Now we have 5 x 2 x 10 = ____.

Our equation is now 5 x 2 x 10 = ____.

We have created this new equation because the parts are now simpler to multiply using mental math. You can now multiply 5 x 2 in your head. 5 x 2 = 10.

Now we have 10 x 10 = ____.

Multiple Choice

Solve:

5*50=

• 250

• 550

• 2500

Multiple Choice

Solve:

4*30=

• 120

• 430

• 1200

Expressions

By practicing your mental math skills, you will get better at math sooner than you think. Keep growing your brain by learning how to write an expression to represent a number.

Let's write an expression...

Write an expression that can be used to find the product of 350.

To complete this task using mental math, we will use what we know about multiples of 10, as well as our multiplication facts, to write a multiplication problem that will equal 350.

Step 1:

The first step is to observe the number 350. What do you notice about the last digit?

Since 350 ends with a 0 we know it is a multiple of 10.

Step 2:

We can use mental math to rewrite 350 as 35 x 10.

So, 35 x 10 is an expression that can be used to find a product of 350.

Step 3:

We can use multiplication fact families to help us find more expressions that give a product of 350. Do you see any other multiplication problems hiding inside of 35 and 10?

35 can be written as 5 x 7.

Now, the expression is 5 x 7 x 10. We can use the commutative property to change the order of the factors and come up with new expressions that equal 350, like 5 x 70 and 7 x 50.

So, we have found three expressions that can be used to find a product of 350.

35 x 10

5 x 70

7 x 50

Multiple Choice

Write a multiplication problem that can be used to find the product of 180.

• 6*30=

• 4*30=

Multiple Choice

2*40=

• 80

• 240

Multiple Choice

7*40=

• 280

• 2800

• 210

Multiple Select

What is an expression for 540? Click all that apply.

• 9*60=

• 54*10=

• 10*54=

Multiple Select

Write an expression for 120.

• 6*20=

• 12*10=

• 4*30=

• 12*1=

Area Models

The part of the rectangle showing the area of the tens was larger than the part of the rectangle showing the area of the ones. This is because the area representing the tens will be larger than the area representing the ones.

Expand

To solve the equation 17 x 30 = ___, we can simplify it by expanding the number that is a multiple of ten.

30 can be expanded into 3 x 10 because we know that 3 x 10 = 30.

Area Model

We will use an area model to solve this part of the equation. First, we expand the two-digit number into tens and ones. 17 expands to become 10 + 7. We now draw a rectangle and partition it into two parts, one for the tens and the other for the ones. There is one row for the 3 that we are multiplying by.

Complete Area Model

Next, we find the product of each row and each column. The rectangle is partitioned into two parts in this area model. This means we are finding two products: 10 x 3 = 30 and 7 x 3 = 21. To find the solution to the equation, we add all of the products in the area model. There are two numbers to add because we found two products.

30 + 21 = 51.

Last we solve 51 times 10=

Next, we find the product of each row and each column. The rectangle is partitioned into two parts in this area model. This means we are finding two products: 10 x 3 = 30 and 7 x 3 = 21. To find the solution to the equation, we add all of the products in the area model. There are two numbers to add because we found two products.

30 + 21 = 51.