Changing perimeter

Changing perimeter

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about perimeter and area of shapes.
A farmer plants 11 square plots with seedlings for hedges. Each plot has at least one side in common with another plot. The farmer wants to protect the seedlings with a deer-proof fence, right around the perimeter of the 11 plots.
 
a) Draw 3 different arrangements for the 11 plots in the box below.
One is already drawn for you, draw 3 more.
 
 
Example:
 i)
 
 
 
 
 
 
ii) iii)
 
 
 
 
 
 
 
b)		  
Draw an arrangement that has the shortest possible perimeter in the box below.
 
 
 
 
 
 
 
 
 
 
 
c)		  
Draw an arrangement that has the longest possible perimeter in the box below.
 
 
 
 
 
 
 
 
 
 
Task administration: 
This task can be completed with pencil and paper.
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
perimeter, unit squares, problem solving
Description of task: 
Students draw shapes to show how the perimeter increases and decreases for different shapes of the same area size.
Curriculum Links: 
This resource can help to identify students' understanding of calculating perimeter.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
   

Y8 (10/1997)
a)
Various possible answers (exclude reflections or rotations), e.g.,
      
NOTE: Accept shapes with 11 squares where some squares are off-centre with others.
 moderate
b) or
or any other shape with a perimeter of 12 units.		 moderate
c)
or any other shape with a perimeter of 24 units.
NOTE: Accept answers between 24 and 32 if their shape has squares which are off-centre with each other or are touching corner to corner.		 easy