Use knowledge of multiplication and division to solve comparison and change problems | Maths

Starter quiz

One fifth times the value of £450 is ______
- '£90' ✓
A tree is six times the height it was when it was planted. It was 1 m 20 cm when it was planted. How tall is it now in metres and centimetres?
- 6 m 60 cm
- 6 m 120 cm ✓
- 7 m and 20 cm ✓
- 1 m 26 cm
Sam has saved £10.50 Jacob has one tenth times the money that Sam has. How much money does Jacob have?
- £1.00
- £1.50
- £1.05 ✓
- 15 p
Dividing 770 ml by 7 is the same as mulitplying by which fraction?
- ${1}\over{6}$
- ${1}\over{7}$ ✓
- ${1}\over{5}$
- ${7}\over{1}$
Alex can run 100 m in 30 seconds. A cheetah can run this far in one fifth of the time it takes Alex. The cheetah takes ______ seconds to run 100 m.
- 20 m
- 6 seconds ✓
- 20 seconds
- 5 seconds
The dolls house door is ${1}\over{10}$ the height of a real door. The height of a real door is 2 m. What is the height of the dolls house door in cm?
- 0.2 m
- 20 cm ✓
- 2 cm
- 200 cm

Exit quiz

Jacob has a netball that has a mass of 500 g and a tennis ball that is one quarter of the mass of the netball. Does this bar model represent this?
- Yes
- No ✓
Jacob has a netball that has a mass of 500 g and a tennis ball that is one quarter of the mass of the netball. The mass of the tennis ball is ______ g
- '125' ✓
The jug contains a 1 l 500 ml volume of water. This is 3 times the 500 ml volume of water in the glass. Which equations represent this?
- 1 l 500 ml × 3 = 500 ml
- 500 ml × ${1}\over{3}$ = 1 l 500 ml
- 500 ml × 3 = 1 l 500 ml ✓
- 1 l 500 ml × ${1}\over{3}$ = 500 ml ✓
A flight to America takes 12 hours. A flight to Spain takes 3 hours. How many times as long is a flight to America than a flight to Spain?
- ${1}\over{4}$ times as long
- 3 times as long
- 4 times as long ✓
- ${1}\over{3}$ times as long
Lucas is saving to buy a new games console. He needs £240. He currently has £30. He needs ______ times his current amount to buy the new console.
- '8' ✓
Lucas is saving to buy a new games console. He needs £240. He currently has £30. How much more money does he need to save? Does this bar model represent this problem?
- Yes ✓
- No

Worksheet

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Lesson Details

Key learning points

Change can be described using multiplication or division. Division can be represented as multiplication by a fraction.
The sentence 'The __________ is ___ times the size of the __________' supports us to describe a comparison or change.
If units are different, we should convert so that they are the same - this supports us to calculate.
To find a missing factor, we can divide the product by the known factor.

Common misconception

Manipulating equations can result in errors.

To find a missing factor, we can use known facts where applicable, or we can divide the product by the known factor. Always encourage children to describe each part of the equation and what it represents.

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.