Smallest perimeter

Smallest perimeter

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources

Practical Task 

Take four multi-link cubes and arrange these on a sheet of paper to make as many different shapes as you can.
All four cubes need to be flat on the piece of paper and have sides touching. Reflections or rotations of a shape do not count as different shapes.
 
a)
 
Draw around each shape as you make it.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
b) Circle the shape that has the smallest perimeter.
 
c)		  
What do you notice about the area of all the shapes you have drawn?

 

 
Task administration: 
Equipment:
Four multi-link cubes and an A4 sheet of paper per person.
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Key Competencies: 
Thinking
Keywords: 
perimeter, drawing, area
Description of task: 
In this practical task, students make different shapes with four multi-link cubes, draw them, identify the smallest perimeter, and explain what happens to the area.
Curriculum Links: 
This resource can help to identify students' developing understanding of invariant properties.
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: 
 
a)
b) Circles the square.
c) The area is the same (but the perimteter varies)
Next steps: 
Extension
Make the different 3-dimensional shapes from the four cubes. Reflections of shapes count as separate.
Compare all your shapes with the shapes in the SOMA cube.