Explain how to represent an equation with a bar model | Maths

Starter quiz

8 × f − 6 × g can also be written as:

8 × f − 6 × g

8f − 6g ✓

6g − 8f

f8 − g6
What is the value of the gap marked ? in the bar model? Give your answer in pounds. £______

'40' ✓
What is the value of the gap marked b in the bar model? Give your answer in pounds. £______

'30' ✓
What is the value of the gap marked ? in the bar model? Give your answer in pounds. £______

'240' ✓
What is the value of d in the bar model? Give your answer in pounds. £______

'62' ✓
This pattern is made up of two different-sized squares. What is the length of the longer sided square marked l? ______ cm

'40' ✓

Exit quiz

A bag of soil weighs 3 kg less than a bag of pebbles. If a represents the bag of soil and b represents the pebbles, tick the equation that matches to context.

b − a = 3 kg ✓

a − b = 3 kg

3 kg − b = a

3 kg − a = b
A chocolate bar costs 50 p more than a lolly. 2 chocolate bars and 2 lollies cost £2.20 Which pair of equations show this?

2a + 2b = £2.20; a + b = 50 p

2c + 2l = £2.20; c − l = 50 p ✓

2a + 2b = £2.20; a − b = 50 p ✓
A toy car is 1.5 cm longer than a toy motorbike. 3 toy cars and 2 motorbikes have a total length of 29.5 cm. What is the length of the toy car and motorbike? Tick the appropriate pair of equations.

2a + 2b = 29.5 cm; a − b = 1.5 cm

3a + 2b = 29.5 cm; a − b = 1.5 cm ✓

2a + 3b = 29.5 cm; a − b = 1.5 cm

2a + 3b = 29.5 cm; b − a = 1.5 cm
Solve the following problem. A toy car is 1.5 cm longer than a toy motorbike. 3 toy cars and 2 motorbikes have a total length of 29.5 cm What is the length of a toy motorbike? ______ cm

'5' ✓
Solve the following problem. A toy car is 1.5 cm longer than a toy motorbike. 3 toy cars and 2 motorbikes have a total length of 29.5 cm What is the length of a toy car? ______ cm

'6.5' ✓
A chocolate bar costs 50 p more than a lolly. 2 chocolate bars and 2 lollies cost £2.20 What is the cost of one chocolate bar? What is the cost of one lolly?

Chocolate bar = 80 p; Lolly = 30 p ✓

Chocolate bar = £1; Lolly = 50 p

Chocolate bar = 90 p; Lolly = 40 p

Chocolate bar = 30 p; Lolly = 80 p

Chocolate bar = 85 p; Lolly = 35 p

Worksheet

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Lesson Details

Key learning points

The model can represent a scaling structure with one part being __ times the size of the other.
The model can represent an additive structure.

Common misconception

Pupils opt to represent the problem using two separate bar models that are stacked on top of one another.

Whilst pupils can represent the maths how they wish, these problems tend to be more efficiently represented using a singular bar model with the whole at the top. Further iterations of these bar models can then be represented underneath.

Keywords

Represent - To represent something means to show something in a different way.