Compare and describe lengths using knowledge of division | Maths

Starter quiz

A piece of elastic stretches to 3 times its original length. Which bar model represents this?
The original piece of elastic was 50 cm long. How long is it now it has stretched to three times it's original length?
- 50 cm
- 100 cm
- 150 cm ✓
- 53 cm
Hamish the cat is 4 times as tall as a mouse. If the mouse is 8 cm tall, how tall is the cat? The cat is ______ cm tall.
- '32' ✓
How many 20s are there in 140?
- '7' ✓
45 is 15 times the size of ______
- '3' ✓
What number is ten times the size of 12?
- 102
- 22
- 112
- 120 ✓

Which image represents this statement? The green ribbon is one-half times the length of the white ribbon.
If the white ribbon is 14 cm long, how long is the green ribbon if it is one-half times the length?
- 16
- 12
- 28
- 7 ✓
Which equations show that one half of 14 cm is equal to 7 cm?
- 14 ÷ 2 = 7 ✓
- 7 ÷ 2 = 14
- 14 × ${1}\over{2}$ = 7 ✓
- 7 × ${1}\over{2}$ = 14
Lucas has spent half of his money. He has £13 left. How much money did he have to start with?
- £6.50
- £26 ✓
The white ribbon is the whole. Which sentence describes the length of the shorter red ribbon?
- The red ribbon is one half the length of the white ribbon.
- The red ribbon is the same length as the white ribbon.
- The red ribbon is one third the length of the white ribbon. ✓
The red ribbon is one third times the length of the white ribbon. If the white ribbon is 60 cm long, how long is the red ribbon?
- 180 cm
- 120 cm
- 30 cm
- 20 cm ✓

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Lengths can be compared using division.
The stem sentence, 'The ___ is ___ times the length of the ___' can be used to compare and describe lengths.
Comparisons of length can be represented as multiplication equations with a fractional multiplier.

Children are more familiar with multiplication resulting in an increase and so may not accept that it can also result in a decrease.

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.

Times the length/height/depth - Times the length/height/depth is a phrase that is used to compare and describe lengths or heights. For example, one tree might be three times the height of another tree; it is three times as tall.
Unit fraction - A unit fraction is a fraction where the numerator is one.