School extensions

School extensions

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Copeland College had a staff room that was getting too small so they decided to build an extension.
They wanted the extension to be smaller but exactly the same shape as the original staff room.
 

[Not drawn to scale]

 

a)
What is the scale factor for reducing the size of the original staff room to the extension size? 
 
__________
 
b)
What is the width of the extension (x)?   __________ m.
 
c)
The school offices also needed extending. An extension was built that was smaller but exactly the same shape as the original office.
The scale factor used was \(1 \over 2\).
Draw the new office extension next to the picture of the original office.
 
 
 
 
 

[Drawn to scale]

Task administration: 
This task can be completed with pencil and paper.
Level:
5
Description of task: 
Students calculate the scale factor and length of one side of a building extension, then draw in a different extension from a given scale factor.
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: 

 

Y11 (03/2000)

a)

0.625 [Accept if written as a fraction, e.g., 58.]

very difficult

b)

5

moderate

c)


[Accept if the extension is the correct size and shape but has been drawn in a different position.]

moderate

Diagnostic and formative information: 

 

Common error

Likely calculation

Likely reason

a)

4.5
3.5

12 - 7.5
8 - 4.5

Subtracts dimensions of corresponding sides rather than calculating the ratio of the sides.

b)

1.6

12 ÷ 7.5

Gives inverse of correct ratio.