Fitting Together II

Fitting Together II

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about tessellating shapes.

Practical task

Colour the four shapes on the last page red, and then cut out.

a)
Arrange the four shapes so that they fit exactly on the grid with the red sides facing up.
Then draw around each shape to show where it fits on the grid.
 
 
b)
Arrange the four shapes so that they fit exactly on the grid with the white sides facing up.
Then draw around each shape to show where it fits on the grid.
 

 
c)
Arrange the four shapes so that they fit exactly on the grid.
There must be at least one red side facing up and at least one white side facing up.
Then draw around each shape to show where it fits on the grid.  
d) Arrange the four shapes so that they fit exactly on the grid. There must be at least one red side facing up and at least one white side facing up and you must find a way of arranging the shapes that is different from what you did before. Then draw around each shape to show where it fits on the grid.
Shapes
               
Task administration: 
This task is completed with pencil and paper, and other equipment.
 
Equipment: Scissors; red coloured pencils, felt pens or crayons.

If a student produces an answer in part d) that is the same as that produced in part c), only in a different orientation, point this out to the student and ask him/her to try and find another way of arranging the shapes that is completely different from that used in part c).

Copyright: 
Copyright: NZCER
Level:
3
Curriculum info: 
Maths, Geometry and Measurement, Transformation
Key Competencies: 
Thinking
Keywords: 
tessellations
Description of task: 
Students colour and cut out 4 shapes and fit them together to make tessellating patterns.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, sets 3-4
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

a)

b)

c)

Any 1 of:

d)

Any 1 of the above that has not been drawn for part c) and is not a different orientation of an arrangement drawn in part c).
 

Note: A shape tessellates (covers the plane) only using translation or rotation on that shape. This means that the patterns in part c) are not tessellations of a single shape but of two closely related shapes.