WRITING AND SIMPLIFYING EXPRESSIONS
1. On these diagrams the small letters stand for the lengths of the sides of the shapes:
l= longest side
m = medium side
s = short side
v= very short side
The capital letters stand for the perimeters of the shapes.
l
Write an expression for the perimeter of each shape.
v
l
R
s
l
T
s
s
s
C
s
m
I m
m
s
l
m
v
All the patterns below are made using the shapes above. Use your answers to question 1. Write down
and simplify expressions for the total length of the lines in these patterns.
2
3
4
5
6
7
8
9
10.Find shapes
to make patterns
which have total
lengths equal to
(i) 6m + 6s + l
(ii) 4m + 11s + 3l
(iii)16v + 14l + 4m + 10s?
Another resource from the Bucks KS3 Maths team
WRITING AND SIMPLIFYING EXPRESSIONS 2 Solutions
1. Perimeter of rectangle = 2l + 2r or 2(l+r)
Perimeter of trapezium = l + 3s
Perimeter of isosceles triangle = 2m + s
Perimeter of cross = 2l + 2m + 8v or 2(l + m + 4v)
2. Total length = 3R = 3(2l + 2r) = 6l + 6r = 6(l + r)
3. Total length = 3T = 3(l + 3s) = 3l + 9s
4. Total length = 2R + 3I = 2(2l + 2r) + 3(2m + s) = 4l + 4r + 6m + 3s
5. Total length = 2R + 2T = 2(2l + 2r) + 2(l + 3s) =4l + 4r + 2l + 6s
= 6l + 4r + 6s = 2(3l + 2r + 3s)
6. Total length = 4I + 2T = 4(2m + s) + 2(l + 3s) = 8m + 4s + 2l + 6s
= 8m + 10s + 2l = 2(4m + 5s + l)
7. Total length = C + 2I = 2l + 2m + 8v + 2(2m + s)
=2l + 2m + 8v + 4m + 2s = 2l + 6m +8v + 2s =2(l + 3m + 4v + s)
8. Total length = C + 4I =2l + 2m + 8v + 4(2m + s)
=2l + 2m + 8v + 8m + 4s = 2l + 10m +8v + 4s =2(l + 5m + 4v + 2s)
9. Total length = 2C + 3T =2(2l + 2m + 8v ) + 3(l + 3s)
= 4l + 4m + 16v + 3l + 9s = 7l + 4m + 16v + 9s
10.(i) 6m + 6s +l could be split into 6m + 3s + 3s + l = 3(2m + s) + 3s + l
which is 3 isosceles triangles plus a trapezium = 3I + T
(ii) 4m + 11s + 3l could be 4m + 2s + 3l + 9s = 2(2m + s) + 3(l + 3s)
which is 2 isosceles triangles and 3 trapeziums= 2I + 3T
(iii) 7l + 6m + 10s + 16v could be 4l + 4m + 16v + 3l + 9s + 2m + s = 2(2l + 2m + 8v ) + 3(l + 3s) + 2m+s
which is 2 crosses, 3 trapeziums and an isosceles triangle = 2C + 3T + I
Another resource from the Bucks KS3 Maths team