Scale factor and dimensions
Y10 (05/2007)  
a) 

6  very difficult 
b) 
i) 
9 3 
moderate 
c) 
i) ii) 
8 2 
moderate 
Common error  Likely misconception  
a) b) i) or b) ii) c) i) or c) ii) 
250 [300 – 50] 1200 [1350 – 150] 2800 [3200 – 400] 
Uses an additive model (may be unfamiliar with "scale factor") Student gives the absolute amount that the length, area, or volume has increased, rather than using a multiplicative model. 
b) ii) c) ii) 
9 8 
Unfamiliar with "scale factor" and its effects Confuses the increase of area or volume with the scale factor, which is a linear measure of increase. 
a) b) ii) c) ii) 
×6, 50×6, etc. ×9, 150×9, etc. ×8, 400×8, etc. 
Unfamiliar with "scale factor" and its effects Student expresses the number of times the original shape has increased by. 
a) b) ii) c) ii) 
16, ^{1}/_{6} , 1:6, ^{50}/_{300} , ^{6}/_{1} etc. 19, ^{1}/_{9} , 1:9, ^{150}/_{1350} , ^{9}/_{1} etc. 18, ^{1}/_{8} , 1:8, ^{400}/_{3200} , ^{8}/_{1} etc. 
Unfamiliar with "scale factor" and its effects Student expresses a movement (16 or 1→6), a fraction, or a ratio to describe the relative amount the original shape has increased by. 
Mathematical language – scale factor
Students need to know and use the correct mathematical language of enlargement, otherwise ambiguity arises. In particular, they need to know and use the term scale factor, and that it describes linear change. This is the clearest and most unambiguous way to describe the degree of an enlargement.
Uses an additive model
Students need to look carefully at the language clues in the question. The phrase "how many times bigger … compared with" in parts b)ii) and c)ii) needs to be interpreted as a multiplicative question. If students have misinterpreted the question this way, see if they can perform the question once this has been clarified.
Unfamiliar with the term "scale factor" or of the concept of enlargement
Work with students to understand that enlargement increases each dimension linearly by an amount known as the scale factor. Get the students working with enlargement on grid paper. Enlarging shapes describes the process without using the term scale factor. Use keywords enlargement AND scale factor for further resources that assess this. Also look at the Figure it out resource Enlargement Explosion (Geometry, L4+, Book 2, page 12).
Students firstly need to know that "scale factor" is a linear measure. They then need to explore the relationship between scale factor and area.
 The increase in area goes up by the square of the scale factor. This is because area is a square measure (m^{2}, cm^{2} etc). Resources Enlargement, length and area, Enlarge the arrow, and Projecting with a scale factor are particularly useful for exploring invariant properties. Also look at the Figure it out resource Growing Changes (Geometry, L3, page 24).
 The increase in volume goes up by the cube of the scale factor. This is because area is a cubic measure (m^{3}, cm^{3} etc).
 Enlarging on a grid
 Scale factor enlargements
 Lengths and angles
 Enlarging diagrams
 Enlargement and area
 Enlargement, length and area
 Using the centre of enlargement
 Enlarge the arrow
 Isometric drawings
 School extensions
 Finding the centre of enlargement
 Length and scale factor
 Reducing the logo
 Using the centre of enlargement II
 Predicting resizing
 Enlarging animals
 Enlarging road signs
 Enlarging blocks