# 2.10 Equivalent number sentences

Lesson

## Ideas

Do you remember how to  make a target number  ?

### Examples

#### Example 1

Find the missing number to equal the number 98.

a

89 + ⬚ = 98

Worked Solution
Create a strategy

Use the number line below to count how many jumps are between the starting number and the target number.

Apply the idea

Locate where 89 is.

Jump to the right of 89 and count the number of spaces until we reach 98.

We have jumped 9 spaces to the right of 89. So 89 + 9 = 98

b

20 + ⬚ = 98

Worked Solution
Create a strategy

Use the number line below to count how many jumps are between the starting number and the target number.

Apply the idea

Locate where 20 is.

Jump to the right of 20 and count the number of spaces until we reach 98.

We have jumped 78 spaces to the right of 20. So 20 + 78 = 98

c

28 + ⬚ = 98

Worked Solution
Create a strategy

Use the number line below to count how many jumps are between the starting number and the target number.

Apply the idea

Locate where 28 is.

Jump to the right of 28 and count the number of spaces until we reach 98.

We have jumped 70 spaces to the right of 28. So 28 + 70 = 98

Idea summary

We can use number lines to make a target number by plotting the beginning number and the target number, and counting how many spaces are between them.

## Equivalent number sentences

For our number sentences to be equivalent, both sides need to be equal. Let's see how to check if this is true, as well as how we can make it true.

### Examples

#### Example 2

Complete the number sentence: 31 - ⬚ = 16

Worked Solution
Create a strategy

Use a number line.

Apply the idea

Locate 31 in a number line.

Jump back from 31 and count the number of units until we reach 16.

We have jumped back 15 units from 31, so the complete number sentence would be: 31 - 15 = 16

Idea summary

We can use number lines to make a target number using subtraction by plotting the beginning number and the target number, and counting how many spaces are between them.

## Find a missing number

If we need to find a missing number, we can use things such as bridge to 10, and number lines to help us. Let's see how we can do this for an addition and a subtraction problem, to make a sentence equal.

### Examples

#### Example 3

Complete the number sentence: 48 - ⬚ = 19 + 16

Worked Solution
Create a strategy

Find the right hand side of the equation first then use a number lin to complete the number sentence.

Apply the idea

Add the numbers in the right hand side of the equation in a vertical algorithm. \begin{array}{c} & &1 &9 \\ &+ &1 &6 \\ \hline \\ \hline \end{array}

Add the ones column first: 9 + 6 = 15. Bring down the 5 and carry the 1 to the tens column. \begin{array}{c} & &\text{}^1 1 &9 \\ &+ &1 &6 \\ \hline & & &5 \\ \hline \end{array}

Add the tens column: 1 + 1 + 1 = 3. \begin{array}{c} & &\text{}^1 1 &9 \\ &+ &1 &6 \\ \hline & &3 &5 \\ \hline \end{array}

The simplified number sentence would be: 48 - ⬚ = 35

Locate 48 in the number line.

Jump back from 48 and count the number of units until we reach 35.

We have jumped back 13 units from 48. So the complete number sentence would be: 48 - 13 = 19 + 16

Idea summary

For number sentences to be equivalent, or balanced, both sides must equal the same amount.

### Outcomes

#### MA2-5NA

uses mental and written strategies for addition and subtraction involving two-, three-, four and five-digit numbers