What changes?
0
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about identifying what happens to features of a shape when it is enlarged.
Task administration:
This task can be completed with pencil and paper or online (with auto marking displayed to students).
Level:
4
Curriculum info:
Keywords:
Description of task:
Students work out area, length and angles of a shape after enlargement.
Curriculum Links:
This resource can be used to help to identify students' understanding of how features of shapes change under enlargement.
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.Answers/responses:
Y8 (11/2015)  
a)  10  easy 
b)  50  difficult 
c)  45  moderate 
Based on a sample of 107 Year 8 students
Teaching and learning:
Prior knowledge
Students need to know that:
 The scale factor is applied multiplicatively to length;
 The square of the scale factor is applied multiplicatively to area; and
 Angle is invariant under enlargement.
Diagnostic and formative information:
Common error  Likely misunderstanding  
a)
b)

7
12.5

Students apply the scale factor additively. 
b)  50  Students apply the scale factor multiplicatively rather than by the square of the scale factor. 
c)  45 
Students multiply the angle by the scale factor.

Next steps:
Students apply the scale factor additively
Students need to know that the scale factor, by definition, is the number of times each length in the shape is changed by, i.e., New length = original length × scale factor
Students apply the scale factor multiplicatively rather than by the square of the scale factor
Students need to know that scale factor applies to length (see above) and that area is the square of the length. In this problem, encourage the students to use the formula for the area of a triangle (1/2 × base × height). This gives an area of 50 square units, which is the same as the original area (12.5 units) × scale factor squared (2 × 2) ⇒ 12.5 × 4 = 50 square units.
Students multiply the angle by the scale factor
Students could measure the angle in both shapes. They will find that it is equal. They could just look at the two angles to see this. Angles are invariant under enlargement.
Students need to know that the scale factor, by definition, is the number of times each length in the shape is changed by, i.e., New length = original length × scale factor
Students apply the scale factor multiplicatively rather than by the square of the scale factor
Students need to know that scale factor applies to length (see above) and that area is the square of the length. In this problem, encourage the students to use the formula for the area of a triangle (1/2 × base × height). This gives an area of 50 square units, which is the same as the original area (12.5 units) × scale factor squared (2 × 2) ⇒ 12.5 × 4 = 50 square units.
Students multiply the angle by the scale factor
Students could measure the angle in both shapes. They will find that it is equal. They could just look at the two angles to see this. Angles are invariant under enlargement.
 Enlarging on a grid
 Scale factor enlargements
 Lengths and angles
 Enlarging diagrams
 Enlargement and area
 Enlargement, length and area
 Using the centre of enlargement
 Translating points
 Translation and enlargement
 Enlarge the arrow
 Enlarging shapes II
 Isometric drawings
 School extensions
 Finding the centre of enlargement
 Length and scale factor
 Transforming traffic lights
 Reducing the logo
 Using the centre of enlargement II
 Predicting resizing
 Enlarging animals
 Enlarging road signs
 Enlarging blocks
 Scale factor and dimensions
 Transformation properties