Finding the perimeter

Finding the perimeter

Pencil and paper
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This task is about the different perimeters of same-sized shapes.
 
five shapes on a grid
 
On the squared paper above, five different shapes, each made up of 6 unit squares, have been shaded in.
 
a)
Which shape has the smallest perimeter?
 
__________
 
b)
Which shape has the greatest perimeter?
 
__________ 
 
c)
On the squared paper above, draw two shapes each of 9 square units, one with a perimeter of 12 units, and the second with a perimeter of 20 units.
 
d)
Complete the statement:
 
If several figures have an area of 9 squares, the shape which is _____________________ has the least perimeter.
Task administration: 
This task is performed with pencil and paper only.
Levels:
4, 5
Description of task: 
Students calculate the shapes with the largest and smallest perimeter and identify a relationship between the features of a shape and the perimeter.
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: 
   

Y9 (05/1997)

Y10 (07/1997)

a) Shape 1 very easy very easy
b) Shape 5 easy easy
c) 3 × 3
9 × 1 shapes [A variety of shapes possible instead of 9 × 1]
moderate moderate
d) Square (or most compact or most regular) difficult moderate