When the student shows you their initial model allocate them 2 marks for part a) if it is correct.
If not, tell them that a scale factor of 2 means to enlarge the length, width, and height to twice their original size. Get them to have another go at building the model.
If they can do this on the second go allocate 1 mark to part a).
If they still cannot achieve the task, help them build a correct model, and get them to go on to part b).
Students enlarge a shape made of cubes and explore the relationship between the scale factor and volume.
Curriculum Links:
Key competencies
This resource involves thinking and solving a problem and explaining the solution which relates to the Key competency: Using language, symbols and text.
Gets model correct at first attempt
Gets model correct after the concept of scale factor is explained.
1 mark
b)
24
1 mark
1 mark
c)
i)
ii)
8
Any 1 of:
The volume increases by the cube of the scale factor (2).
Volume = length × width × height so for each square this is 2 × 2 × 2 = 8.
Other correct statements.
1 mark
1 mark
d)
i)
ii)
3000
Any 1 of:
The volume increases by the cube of the scale factor (103).
Volume = length × width × height so for each square this is 10 × 10 × 10 = 1000.
Other correct statements.
NOTE: Do not accept "The volume is 1000 times as much" (without explaining where the 1000 comes from), as this is already clear from the answer of 3000 for d) i).
Diagnostic and formative information:
Common error
Likely calculation
Likely reason
a)
Enlarges incorrectly
Does not know 3-D enlargement.
c) i)
21
24 - 3
Uses additive increase rather than multiplicative.
