What changes?

What changes?

Auto-markingPencil and paperOnline interactive
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.

Question 1Change answer

enlarging-triangles-2.png
 
Harry enlarged a triangle by a scale factor of 2. He wrote down the lengths (base and height), the areas and the angles before the enlargement.
In the table below write down the lengths (base and height), the areas and the angles after the enlargement.
  Property Before the enlargement After the enlargement
a) length (base/height) 5 units  units
b) area 12.5 units2  units2
c) angles 45° (degrees)  °(degrees)
Task administration: 
This task can be completed with pencil and paper or online (with auto marking displayed to students).
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Transformation
Keywords: 
invariant properties, enlargement, resizing
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
Geometric thinking, sets 4-5
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.