A Question of Balance
Materials developed by Paul Dickinson,
Steve Gough & Sue Hough at MMU
Thank you
• Sue, Steve and Paul would like to thank all the
teachers and students who have been
involved in the trials of these materials
• Some of the materials are closely linked to the
‘Making Sense of Maths’ series of books and
are reproduced by the kind permission of
Hodder Education
Note to teacher
This PowerPoint uses the context of a see saw and traditional weighing scales to
encourage students to develop an appreciation of what it means if scales are
balanced, what happens if items are removed from one side of balanced scales and
what strategies can be employed to bring the scales back in balance.
The leaners are asked to draw their own representations of the balance scale pictures
and to consider how shorthand notation such as 3a + 12 = 8a + 2 can be thought of in
the context of weighing scales.
Students are encouraged to operate on their balance pictures by removing items (or
adding items) from both side of the scales. (See slide 19 for Ellie’s method)
The weighing scales context is not a new idea for teaching solving equations with ‘x’
on both sides, but here the context and the images associated with it are embraced in
more detail.
In trials some students were aware that this was giving them a fresh approach to
tackling solving equations with x on both sides, which is a topic they had previously
experienced little success with.
Who is heavier?
How could you balance the see saw?
The human balance
How can you tell these scales are balanced?
What can you say about the flour?
What can you say about the flour?
What can you say about the flour?
Describe what you see in the picture below
What can you say about this bag of flour?
What can you say about this bag of flour?
What about this bag of flour?
Now try the problems on Worksheet A8
Describe
what has
happened
from one
picture to
the next
Draw your own version of this picture
Describe how you can find the weight of one orange
Gary’s method
Describe Gary’s thinking
Ellie’s method
Describe Ellie’s thinking
Now try the problems on Worksheet A9
Explain the short hand
Explain the short hand
What other short hand could you use to
represent this picture?
What’s the shorthand for this situation?
Describe how to find the weight of a grapefruit.
How does the weight of a tomato
compare with the weight of a banana?
Draw a scales picture for this
shorthand
5g + 17 = 9g + 5
Now find the value of the letter g
Draw a scales picture for this
shorthand
7p + 17 = 10p + 2
Find the value of the letter p
Now try the problems on Worksheet A10
Draw a scales picture for this
shorthand
3(t + 2) = 11t + 2
Now find the value of the letter t
Draw a scales picture for this
shorthand
4(x + 3) = 3(x + 5)
Find the value of the letter x
Now try the problems on Worksheet A11
Draw a scales picture for this
shorthand
4t + 1 = 6t – 5
3y – 4 = 5y – 6
10 – p = 2p - 8
Summary
You have used balanced weighing scales as a way
of making sense of solving linear equations like
those shown below. Check to see which of these
equations you can now solve:
1)
2) 4x + 3 = 27
3) 13x + 1 = 11x + 15
4) 3( t + 4) = 21
5) 5y – 4 = 3y + 6
Blank template slide
Information
Question 1
Question 2