Measuring road signs

Measuring road signs

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Working with Students
This task is about working out the circumference, circular and square area of a road sign.
The figure below shows a circular 50 km/h sign, punched out of a square sheet of metal of sides 60 cm. (Use = 3.14 approx.)

a) What is the circumference of the outer circle? __________ cm
 
b) What is the area of the circular sign? __________ cm2
 
c) What is the total area of sheet metal wasted in the four corners, after the sign is punched out?

__________ cm2
 
d) The shaded ring has an inner diameter of 40 cm, and an outer diameter of 60 cm.

What is its area? __________ cm2

 

Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
area, circumference, composite shapes, circles
Description of task: 
Students calculate circumference, circular and square area of a road sign.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 7-8
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  

Y9 (10/1996)
a) 188.4 cm (3.14 × 60)
[Accept answers between 188.3 – 188.6.]		 difficult
b) 2 826 cm2 (3.14 × 900)
[Accept answers between 2 825 – 2 830.]		 difficult
c) 774 cm2 (3 600 - 2 826)
[Accept answers between 770 – 775.]		 difficult
d) 1 570 cm2 (3.14 × 500)
[Accept answers between 1 570 – 1 572.]

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Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
d) 1 256 cm2
 
125.6 cm2		 3.14 × 202 Misinterprets question (i.e., gives the area of
inner circle, not shaded ring).
Misinterprets question, and makes error in
the magnitude of the answer.