Problem Solving for Lower, Middle and Upper Primary
Each of the problems in this series has teacher notes that
include a problem solving guide, suggestions for how to reflect on the solutions
that the children find, and extensions that take the problem a bit further.
The following example is taken from the Middle Primary set and
encourages a systematic approach to problem solving at the same time as
providing plenty of practice in mental arithmetic.
The Problem
|
Place the numbers 2 - 10 in the circles on the diagram.
Find the total along each line.
Find the total around the outside.
Can you find a way of placing the number in the circles so
that the total along each line and around the outside are all the same?
|
Teacher Guide
Read the first part of the first part of the problem with the
children and allow time for them to randomly place the numbers 2 - 10 onto the
circle and to find the totals of each diagonal and the perimeter. When they have
done this ask them what the largest/smallest total they found was. Some children
will be surprised that the totals can range from 14 to 36.
Then set the children the challenge of placing the numbers so
that the totals are all the same.
Note: There is a logical way to work out what this total
should be. Since each number is either on 2 lines or on a line and a circle, it
will appear in 2 of the totals. We can find the total by adding all the numbers
together, multiplying by 2 and then dividing by 4 (which is the number of totals
to be found). Thus
(2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) ´
2 = 108
108 ¸ 4 = 27
Thus the common total will be 27. Since it really helps to
know this number, you may want to give children a hint by telling them this
total.
Reflection
Ask the children to explain how they approached this problem,
and whether earlier experience with puzzles like Number Star helped them to work
out a way of finding where to place the numbers. Since not all children will
have been successful with this puzzle, help them to feel good by showing them
how much good work they did.
Extension
There are many ways in which the total can be found, but only one of them has
the special property that the four numbers round the trapezium-shaped areas
(marked * below) also add to the same total of 27. Those children who didn’t
find this arrangement can be challenged to look for it.
