Topics
2. Addition and subtraction
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AustraliaVIC
Level 4

2.10 Equivalent number sentences

Lesson
Practice
Lesson

Are you ready?

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.

87888990919293949596979899100
Apply the idea

Locate where 89 is.

87888990919293949596979899100

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

87888990919293949596979899100

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.

2030405060708090100
Apply the idea

Locate where 20 is.

2030405060708090100

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

2030405060708090100

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.

2030405060708090100
Apply the idea

Locate where 28 is.

2030405060708090100

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

2030405060708090100

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.

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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.

05101520253035

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

05101520253035

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.

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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.

303132333435363738394041424344454647484950

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

303132333435363738394041424344454647484950

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

VCMNA153

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

VCMNA163

Use equivalent number sentences involving addition and subtraction to find unknown quantities

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