1. This shape is made from two identical squares overlapping.
Expressions
A2.2 Extension Starter
This shape is made from two identical squares overlapping.
(a) Find an expression for the perimeter of the shape.
Both squares have sides 10 cm long.
(b) Find an expression for the perimeter of the shape using b.
(c) Find an expression for the perimeter of the shape using a.
Preamble
An activity involving some relatively difficult algebraic manipulation. Some support
may well be needed, particularly in parts (b) and (c).
Possible content
Algebraic simplification, revision of perimeter.
Resources
None.
Solutions/Notes
Perimeter is 6a + 8b (opportunity to stress importance of simplification).
Perimeter is 6(a + b) + 2b = b (since a + b = 10).
b = 10 − a so the perimeter can be written as (10 − a) = 80 – 2a