Patchwork Cushions

Pupils are asked to find a method for calculating the number of triangles and squares that are needed to make cushions in different sizes.

Practical details

Suitability
National Curriculum levels 6 to 7
Time
30 minutes to 1 hour
Resources
Ruler, pencil and 1cm squared paper

Key Processes involved

Representing
Select an appropriate method for counting and recording the squares and triangles in different sized cushions
Analysing
Vary the size of the cushion systematically and look for invariance and covariance; reason inductively and deductively
Interpreting and evaluating
Examine the data and look for patterns, generalisations and justifications, referring to the structure of the cushion design
Communicating and reflecting
Describe findings clearly and effectively

Teacher guidance

Check that pupils understand the context, for example with questions such as:

• This is a size 3 cushion; can you suggest why I call this “size 3”?
• How many squares and triangles can you see on this cushion?

Pupils can tackle this task in different ways, but those of higher ability might be able to:

• find and describe in words the rule for the next term or the nth term of a sequence where the rule is linear
• find and describe in symbols the next term or nth term of a sequence where the rule is quadratic