Starter quiz
- Variables are in proportion if they have a constant ______ relationship.
- additive
- different
- multiplicative ✓
- division
-
- How many centimetres are in 1 metre?
- '100' ✓
- How many centimetres are in 1 kilometre?
- '100 000' ✓
- If 1 cm = 5 km, how many kilometres are represented by 6 cm?
- '30 km' ✓
- If 1 cm = 5 km, how many centimetres represent 45 km?
- '9 cm' ✓
- If 1 cm = 5 km, how many kilometres are represented by 4.5 cm?
- '22.5 km' ✓
Exit quiz
- Variables are in proportion if they have a ______ relationship.
- constant additive
- different additive
- constant multiplicative ✓
- different multiplicative
-
- If 1 cm = 20 km, how many kilometres are represented by 6 cm?
- '120 km' ✓
- If 1 cm = 20 km, how many centimetres represent 60 km?
- '3 cm' ✓
- The scale on a map is 1 : 300 000. The distance between two places on the map is 4 cm. What is the distance in real life in kilometres?
- '12 km' ✓
- The scale on a map is 1 : 400 000. The distance between two places in real life is 14 km. What is the distance between them on the map?
- '3.5 cm' ✓
- The scale of a model building is 1 : 200. The height of a model church is 6.5 cm. How tall is the church in real life?
- '13 m' ✓
Worksheet
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Presentation
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Video
Lesson Details
Key learning points
- Maps are a practical example of a multiplicative relationships.
- The scale factor is the multiplier.
- The multiplicative relationship can be written as a ratio.
- Real-life scaling involves writing a ratio involving the parts which are dependent on each other.
Common misconception
Misinterpreting a scale, particularly if given with no units.
Encourage pupils to carefully convert the scale into a more useful scale. E.g. writing 1 : 20 0000 as 1 cm = 2 km
Keywords
Proportionality - Variables are in proportion if they have a constant multiplicative relationship.
Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
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