This is a 'low threshold high ceiling' problem in that all
children will be able to find at least one solution through trial
and improvement, but others will use logical thinking to develop
and try out different strategies for making the sides equivalent.
The actual mathematical knowledge required is to be able to add up
to about 20.

There are different layers to this activity, making it ideal
for a whole class task.

If you have an IWB you could prepare a file with the image and
numbers to drag onto each circle, but if not you could draw a large
version on the board and write the numbers 1-9 at the side. Put
numbers randomly in the circles, crossing them off the 1-9 list as
you do so. When all the circles are full, add up each side of the
triangle and record the answer. Ask the children if they think it's
possible to get the answers closer than yours. Give then some time
to explore, using individual white boards if you have them, (or the
downloadable
sheet ) and see if they can improve on your result.

When someone gets all three sides the same, stop the class and
record the result on the board. Ask if they think this is the only
way we could place the numbers to make the sides equivalent. Allow
some time for exploration and if possible make a part of the wall
space available for recording all the children's answers. If you
encourage the children to record each solution on a separate piece
of paper you can rearrange them during discussion.

You might choose to leave this as a 'simmering' activity over
a period of a few days. Not all children will engage with it but
some will become very enthusiastic. In the plenary discussion draw
attention to families of solutions, and the upper and lower limits
for the side totals.

What's the biggest total a side could have? How do you
know?

What's the smallest? How do you know?

Does thinking about odds and evens help?

Encourage the children to tweak this question by asking 'what
if ...?' Suggestions you could throw in might include:

What if it was a square not a triangle?

What if we had five on each side not four?

What if we only used odd numbers ... even numbers ...
multiples of ten ...

Providing a public space for the children to record their own
investigations makes it a more collaborative activity.

Children could also try this more
challenging version of the problem.

Children who find this difficult could begin with an easier
activity using six circles, three on each side, and the numbers
1-6. Begin by giving them 15 buttons or counters to place in the
circles so that there are the same number of counters on each side.
This gives visual support. Move from there into having a different
number of counters in each circle, and from there to using digits
rather than counters.