The purpose of this activity is to support students in finding the structure of one shape within a growing pattern. Relating parts of the single shape to the shape number offers possibilities for creating function rules.
Shape number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Number of squares | 7 | 13 | 19 | 25 | 31 | 37 | 43 | 49 | 55 | 61 |
Change in number of squares | +6 | +6 | +6 | +6 | +6 | +6 | +6 | +6 | +6 |
Gather the students to share strategies.
Which strategy is the most efficient? Explain why.
Can you create a general rule?
If I give you any shape number, you can work out the number of squares?
Students should call on their recognition of structure in the diagrams, and table of values.
Can you draw a diagram for Shape n?
Write an expression for the number of squares in Shape n.
Students might need to be told of the convention that 6n represents “n multiplied by six.”
6n+1.
Next steps
Words | Symbols |
The number two less than n. | n-2 |
The number three more than n. | n+3 |
The number that is n multiplied by five. | 5n |
The number that is n divided by three. | n/3 |
N multiplied by itself | n2 |
Printed from https://nzmaths.co.nz/resource/reasoning-one-shape at 6:40pm on the 7th May 2024