Solve comparison and change problems using division | Maths

Starter quiz

Which word or phrase completes the sentence: The green ribbon is ___ times the length of the white ribbon.
- three
- two
- one third ✓
- one half
If the white ribbon is 39 cm long, how long is the green ribbon? The green ribbon is ______ cm long.
- '13' ✓
The longer white ribbon is 36 cm long. How long is the shorter red ribbon? The red ribbon is ______ cm long.
- '18' ✓
The white ribbon is 36 cm long. How long is the shorter red ribbon?
- 33
- 18
- 12 ✓
- 10
The longer white ribbon is 36 cm long. How long is the red ribbon?
- '9' ✓
Which statements are represented by this image?
- The blue ribbon is eight times the length of the white ribbon.
- The blue ribbon is one eighth times the length of the white ribbon. ✓
- The white ribbon is one eighth times the length of the blue ribbon.
- The white ribbon is eight times the length of the blue ribbon. ✓

Exit quiz

A pencil was 15 cm long when it was new. It has been used and is now one third times its original size. Which image represents the change?
The length of a model car is one tenth of the length of the real car. The real car is 4 m long. Which table represents the lengths of the cars?
Compare the height of the tree and the sunflower and the height of the dog. Which sentences could describe the image?
- The dog is four times the height of the sunflower.
- The sunflower is four times the height of the dog. ✓
- The dog is ${1}\over{4}$ times the height of the sunflower. ✓
- The sunflower is ${1}\over{4}$ times the height of the dog.
A pencil was 15 cm long when it was new. It has been used and is now one third times its original size. The pencil is now ______ cm long.
- '5' ✓
The length of a model car is one tenth of the length of the real car. The real car is 4 m long. Which calculations could you use to work out the length of the model car?
- 4 m × 10 = 40 m
- 4 m ÷ 10 = 0.4 m ✓
- 4 m × ${1}\over{10}$ = 0.4 m ✓
- 400 cm × ${1}\over{10}$ = 40 cm ✓
$The dog is <Math>{1}\over{4}</Math> times the height of the sunflower. Match the possible heights of the dog and the sunflower.$

The dog is ${1}\over{4}$ times the height of the sunflower. Match the possible heights of the dog and the sunflower.
- Dog is 24 cm tall.
  
  ⇔
  
  Sunflower is 96 cm tall. ✓
- Dog is 45 cm tall.
  
  ⇔
  
  Sunflower is 180 cm tall. ✓
- Dog is 19 cm tall.
  
  ⇔
  
  Sunflower is 76 cm tall. ✓
- Dog is 25 cm tall.
  
  ⇔
  
  Sunflower is 100 cm tall. ✓
- Dog is 51 cm tall.
  
  ⇔
  
  Sunflower is 204 cm tall. ✓

Worksheet

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Lesson Details

Key learning points

A change in length can be described using division.
Division can be represented as multiplication by a unit fraction.
The stem sentence, 'The ___ is ___ times the length of the ___' can be used to support understanding.
Comparison and change problems can be represented visually to support understanding.

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.