Pupils are asked to find a method for calculating the number of triangles and squares that are needed to make cushions in different sizes.
- National Curriculum levels 6 to 7
- 30 minutes to 1 hour
- Ruler, pencil and 1cm squared paper
Key Processes involved
- Select an appropriate method for counting and recording the squares and triangles in different sized cushions
- 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
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