Solve problems involving comparison and change | Maths

Starter quiz

A pencil was 20 cm long. It is now one quarter of its original length. Which expression represents its new length?
- 20 ÷ 4 ✓
- 20 × 4
- 20 × ${1}\over{4}$ ✓
Which sentence matches this bar model?
- The blue bar is 6 times the length of the white bar.
- The blue bar is one sixth times the length of the white bar. ✓
- The white bar is 6 times the length of the blue bar. ✓
Compare the heights of the tree and the car. The tree is ______ times the height of the car.
- '5' ✓
A pencil was 20 cm long. It is now ${1}\over{4}$ of its original length. How long is the pencil now?
- 20 cm
- 16 cm
- 10 cm
- 5 cm ✓
The white bar is 360 cm long. How long is the blue bar? The blue bar is ______ cm long.
- '60' ✓
Match the possible heights of the tree to the heights of the car. The car is one fifth times the height of the tree.
- The tree is 50 m tall
  
  ⇔
  
  The car is 10 m tall ✓
- The tree is 5 m tall
  
  ⇔
  
  The car is 1 m tall ✓
- The tree is 500 cm
  
  ⇔
  
  The car is 100 cm tall ✓
- The tree is 50 cm tall
  
  ⇔
  
  The car is 10 cm tall ✓

Exit quiz

Jacob runs 300 m in 1 minute. Izzy walks one third times the distance. How far does Izzy walk?
- 200 m
- 100 m ✓
- 297 m
Jacob runs 300 m in 1 minute. Izzy walks one third times the distance. How much further does Jacob run than Izzy walks?
- 100 m
- 3 m
- 200 m ✓
- 400 m
True or false? 160 x ${1}\over{4}$ = 160 ÷ 4
- True because dividing by 4 is the same as multiplying by one quarter. ✓
- False because when you multiply, the product is always larger.
Which two equations can you write from this bar model to calculate the length of the blue bar?
- 240 x 4 =
- 240 x ${1}\over{4}$ = ✓
- 240 ÷ ${1}\over{4}$ =
- 240 ÷ 4 = ✓
The bus ride to school is 7 km. The bus broke down one half times the distance from school. The bus still had ______ km left to travel.
- '3.5' ✓
Match a multiplication expression to a division equivalent.
- 400 m x ${1}\over{4}$
  
  ⇔
  
  0.4 km ÷ 4 ✓
- 4 km x ${1}\over{4}$
  
  ⇔
  
  4,000 m ÷ 4 ✓
- 400 cm x ${1}\over{4}$
  
  ⇔
  
  4 m ÷ 4 ✓
- 4 m x ${1}\over{4}$
  
  ⇔
  
  400 cm ÷ 4 ✓

Worksheet

Presentation

Video

Lesson Details

Key learning points

A change in length can be described using multiplication or division.
Comparison and change problems can be represented visually to support understanding.
To find ___ times a length, we know we will be multiplying the length by ___.
To find a unit fraction times a length, divide the length into the number of equal parts represented by the denominator.

Common misconception

Children may say 'ten times shorter' which is imprecise. Children are more familiar with multiplication resulting in an increase, and need to appreciate that it can also result in a decrease.

We say, 'ten times the original height' because this is more precise especially when the scale factor is fractional. When we multiply by a unit fraction, it is the same as dividing the whole by the denominator. This results in a decrease in length.

Keywords

Comparison - When a comparison is made, we are determining how different two objects are. In this case, how many times longer, taller or deeper an object is than another.
Change - A comparison can also be made between an object before, and then after, a change. Examples of a change include a change in height of a flower due to growth.
Unit fraction - A unit fraction is a fraction where the numerator is one.