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Year 6

Explain how to balance an equation with two unknowns

I can explain how to balance an equation with two unknowns.

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New

Year 6

Explain how to balance an equation with two unknowns

I can explain how to balance an equation with two unknowns.

Download all resources

Share activities with pupils

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Lesson details

Key learning points

The same sum rule can be used to balance equations.
The same difference rule can be used to balance equations.
Understanding of the structure of addition and subtraction can be used to balance equations.

Keywords

Difference - The result of subtracting one number from another number is known as the difference.
Subtrahend - The value used to subtract from the whole is known as the subtrahend.

Common misconception

Pupils use a trial and improvement approach to solve these problems only.

At first, pupils may put numbers into the equation to see what happens each time. Encourage pupils to move beyond this to notice what happens to each example. Pupils should aim to use the relationships between addends or subtrahends to help them.

You could utilise mass as a context to help pupils consider balancing these equations. This may allow pupils to consider the magnitude of how much is needed to be added to each side of the equation in order for the equations to balance.

Teacher tip

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Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Worksheet

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Starter quiz

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6 Questions

Q1.

Match the pairs of missing unknown numbers to find possible solutions.

Correct Answer:5,25

Correct Answer:1,21

Correct Answer:3,23

Correct Answer:2,22

Correct Answer:4,24

Q2.

If one of the unknowns is 60, what would the other unknown be?

Correct Answer: 55, 65

Q3.

Laura has some triangles and squares. She chooses some of the shapes and when she counts the number of sides, she finds that the total is 48 How many of each shape could she have?

Correct answer: 4 triangles and 9 squares

9 squares and 4 triangles

7 triangles and 7 squares

Correct answer: 8 triangles and 6 squares

Q4.

Laura has some squares and pentagons. She chooses some of the shapes and when she counts the number of sides, she finds that the total is 48 How many of each shape could she have?

8 squares and 4 pentagons

Correct answer: 8 pentagons and 2 squares

6 pentagons and 6 squares

Correct answer: 4 pentagons and 7 squares

Q5.

I use two different lengths of wood to make a fence 7 m long. One length of wood is 70 cm and the other is 105 cm. If two 105 cm planks were used, how many of length 70 cm were used? planks

Correct Answer: 7, seven

Q6.

Jun spends 8 hours in maths and science lessons. A maths lesson is 55 minutes,a science lesson is 65 minutes. Jun had the same number of maths and science lessons. How many of each lesson did he have?

Correct Answer: 4, four

Exit quiz

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6 Questions

Q1.

In this problem, the difference between the known addends is 20 Match the expressions correctly.

Correct Answer:When a = 10,the second addend = 30

the second addend = 30

Correct Answer:When a = 15,the second addend = 35

the second addend = 35

Correct Answer:When a = 42,the second addend = 62

the second addend = 62

Correct Answer:When a = 61,the second addend = 81

the second addend = 81

Q2.

If we call the first missing addend a, match the expressions correctly.

Correct Answer:When a = 20 ,the second addend = 34

the second addend = 34

Correct Answer:When a = 31,the second addend = 45

the second addend = 45

Correct Answer:When a = 52,the second addend = 66

the second addend = 66

Correct Answer:When a = 44,the second addend = 60

the second addend = 60

Q3.

If we call the first missing addend a, what is the second addend when a = 10?

Correct Answer: -5, negative 5, minus 5

Q4.

Match the value of the first missing number with the correct value of the second missing number.

Correct Answer:When the first missing value is 50 ,the second missing value is 35

the second missing value is 35

Correct Answer:When the first missing value is 65,the second missing value is 50

the second missing value is 50

Correct Answer:When the first missing value is 62,the second missing value is 47

the second missing value is 47

Correct Answer:When the first missing value is 71,the second missing value is 56

the second missing value is 56

Q5.

Match the value of the second missing number with the correct value of the first missing number.

Correct Answer:When the second missing value is 45,the first missing value is 70

the first missing value is 70

Correct Answer:When the second missing value is 60,the first missing value is 85

the first missing value is 85

Correct Answer:When the second missing value is 75,the first missing value is 90

the first missing value is 90

Correct Answer:When the second missing value is 85,the first missing value is 100

the first missing value is 100

Q6.

If the value of the first missing number is a, what is the value of the second missing number when a = 68?

Correct Answer: 55