Enlarging diagrams

Enlarging diagrams

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
This task is about enlarging length and area by a scale factor.

a) In the box below, redraw Diagram 1 to a scale where 1 cm = 50 m.
 
 
diagram-2--working-space.png
 
b)
 
For each sentence below, fill in the box and circle the appropriate option.
 
  i) Any one length in Diagram 2 is  times longer / times shorter [circle one] than Diagram 1. 
  ii)    The area of Diagram 2 is  times larger / times smaller [circle one] than Diagram 1. 
Task administration: 
This task can be completed with pencil and paper or online.
Copyright: 
Graphic copyright: NZCER
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Transformation
Keywords: 
enlargement, scale factor, invariant properties, length, area, scale
Description of task: 
Students enlarge a diagram to a given scale.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, set 6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (09/1998)
a) Accurate diagram. Students do not have to include measurements.

 easy
b) i)
ii)		 2, longer
4, larger		 moderate
very difficult
Diagnostic and formative information: 
  Common error Likely calculation
b) i)
    ii)
1/2
1/4
 Reduces drawing rather than enlarges it.
b) ii) 2 (or) 1/2 Assumes area increases by same amount as length (instead of by length2).