Page 8 - Geometric Patterns

7.6 Writing our plans as flow diagrams

You have already seen this growing pattern in Section 7.4. We will
now look at it again, but in a different way. How will you calculate
the number of squares in Picture 6, Picture 60 and Picture 87?
What is your plan?

Picture 1 Picture 2 Picture 3 Picture 4 Picture 5

Mia writes her plan as a flow diagram:

Picture no. No. of squares

1 6

2 8

3 10
4 × 2 + 4 12

6 ?

60 ?

87 ?

A flow diagram describes a plan (method) using
input → rule → output.

This flow diagram shows that you must first multiply any input
number by 2 and then add 4 to get the output number.
3 × 2 → 6; 6 + 4 → 10
4 × 2 → 8; 8 + 4 → 12

1. First check if Mia’s flow diagram (plan) is correct for the input
and output numbers that we already have. Discuss with your
classmates how you can check her plan.