Colours on the flag

Colours on the flag

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about working out the area and perimeter.
The figure below shows a flag. It has three equal-sized rectangular panels of blue, gold, and red. The gold panel has a black circle in the centre of it.
 


[NOT DRAWN TO SCALE]

 Useful Formula

a =r2 where:
      a = area of a circle
      = 3.14
      r = radius of a circle
 
a)
 
What would be the length of stitching required to go right around the flag?
 
__________ m

 
b) What is the area of the blue panel? __________ m2
 
c) What is the area of the black circle, if it has a diameter of 5.0 m? __________ m2
 
d)
What is the area of gold cloth remaining in the centre panel, if the black circle was cut from it?
 
__________ m2
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
area, perimeter, composite shapes, circles, rectangles
Description of task: 
Students calculate area of colours and the perimeter of a flag.
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: 
    Y10 (12/1997)
a) 60.0 m easy
b) 72.0 m2 easy
c) 19.63 [Accept if ± 0.2 m2] difficult
d) 52.38 m2 [Accept if ± 0.2 m2]
NOTE: Accept answer to b) - answer to c).		 moderate
Diagnostic and formative information: 
  Student response Likely calculation Likely reason
a) 30 18 + 12 Half of perimeter only.
a)
b)		 216
36 (or 18)		 18 × 12
2 × 12 + 2 × 6		 Confuses area and perimeter.
a)
b)		 46 656
5184		 12 × 12 × 18 × 18
12 × 12 × 6 × 6		 Multiplies too many dimensions to get area.
c) 15.7 5 × 3.14 Confuses circumference and area.
c) 78.5 3.14 × 52 Usesd2 rather thanr2.