Problem Solving 7 : Complex Diagrams
Objective
This lesson will consolidate the pupils’ knowledge of various
ways to represent data and outline some problem situations
where they can discuss and apply their knowledge.
1.
Circle Sums
Arrange the numbers 1 to 5 so that the total number in each
of the blue, red and black circles are the same.
There is a pattern to each of these solutions.
The numbers in the circles at each end contain the two
largest numbers.
2.
Teaching
Ask the pupils to make a list of the different ways to
represent (show or display) data. Here are some examples:
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tally charts and frequency tables
Venn diagrams
Carol diagrams
pictographs
bar charts
pie
line graphs
Ask the pupils to describe how each of these work or give
an example of each method. This will promote a class
discussion on the advantages and disadvantages of each of
these methods.
3.
How Far Is It?
This is a straightforward set of questions involving the
interpretation of maps. However, it will quickly identify
any problems with reading diagrams or interpreting what is
required in narrative style questions.
4.
Neighbours
The real task here is to recognise a more unusual diagram
and determine what is required to solve the problem.
There are lots of solutions because each set of numbers can
be reflected vertically and horizontally to give further
solutions.
5.
Rebecca’s Favourite School Day
To find Rebecca’s favourite day, the pupils work through a
set of clues which are used to eliminate days until the
pupils reach the required day of Friday.
Sam’s day may need some discussion about which days can be
safely eliminated.
6.
Plenary
These diagrams were created using computer software.
Only one of these diagrams is appropriate.
Which three diagrams are not appropriate?
Discuss why each of the three diagrams is unsuitable.
chart 1
This is suitable to show the average amount of milk, but
the units could be improved to read litres per day.
chart 2
This is not appropriate because the width of the bottle
is increased as well as the height. When the height is
doubled, the volume of the bottle is increased by a scale
factor of 2 x 2 x 2 = 8. This technique is often used to
mislead people. Compare the size of D(8) and J(16) and
you can see that bottle J looks much more than twice D.
chart 3
This is a line graph which implies continuity of data
with valid in-between values. It would be the correct
diagram to use if both axes measured continuous variables
such as time and temperature. But the breed of cow is
not continuous. You cannot have a cow between Ayrshire
and Dexter.
chart 4
Pie charts are excellent for comparing the relative sizes
of milk yield for each breed of cow but no information is
given to indicate the quantity of milk produced.
This question was taken from Year 9 SATs Paper 2 (2005) levels 5-7