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One Big Triangle

Age 5 to 7
Challenge Level

One Big Triangle

Here are nine triangles.  Each one has three numbers on it.


Your challenge is to arrange these triangles to make one big triangle, so the numbers that touch add up to 10.

You can print out this copy of the triangles and cut them out, then try arranging them.  
If you prefer, here is a printable version of the triangles with the numbers represented on tens frames.

Let us know how you go about trying to make the big triangle.
How did you get started?
What did you do next?

Why do this problem?

This problem is useful for recalling and learning all the pairs of numbers with a total of 10 and working out the corresponding subtraction facts. The novel context is likely to appeal to learners and encourage them to persevere. Children who are fluent with number bonds to ten will still be challenged as the approach is not obvious, but logical reasoning will help them be more efficient in their search for a solution. If using the cards rather than the interactive, learners will also need to visualise triangles in different orientations in order to solve the problem.

Possible approach

You could show the images of the small triangles on the board and ask children to look in silence for a few minutes and think about what they can see.  Then encourage them to share with a partner before taking some suggestions as a whole group.  Welcome all contributions, even if they don't seem relevant to the mathematics - children will need to get all sorts of observations 'off their chests'!  

Using some already cut out pieces, place a few triangles in the big triangle, making sure that touching faces add to 10. Invite children to gather round to see and ask them to think about what they notice.  Again, take some contributions and then introduce the task itself.
Children can work in pairs on the problem with cards made from this sheet so that they are able to talk through their ideas with a partner. (If these are printed onto thin card and laminated you will have a permanent set that can be used for other purposes as well.) 

You could facilitate as many mini plenaries as you feel is helpful in order to share ideas that are being worked on around the room, including possible ways of getting started on the task.  Learners' suggestions might include, for example, working top down, or bottom up, or hexagon out, matching colours, making pairs first, noticing the three 5s and therefore reasoning that one of these will have to be on an outer edge...  
During the final plenary, encourage the children to talk about the strategies they have used. Did they guess and then check? Or did they have a more systematic approach to the problem? Did they imagine what a triangle would look like in a particular position before placing it there? You might find learners have used visualisation to plan which piece will go where.

Discuss the solutions that have been found. Are they all the same? If not, have they found all the possiblities?

Key questions

Tell me what you have done so far.
What do you need to put with ... to make 10?

Can you find a different card with that number on it?
What might be helpful to try next?

Possible extension

Children could be asked whether they can find more than one solution.  How will they know whether another solution is the same or different to any they have already got?  How will they know that they have found all the solutions?
Leaners could also use the cards to make a shape (not necessarily a triangle) where the touching numbers add to 9 (or 8 or 11). Alternatively, they could add their own choice of numbers to blank triangular pieces to create their own activity.

Possible support

Children could use the cards to make a different shape (not necessarily a triangle) where the touching numbers add to 10, and/or these cards could be used in which the numbers are represented by tens frames. Some children may find it difficult to cope with matching more than one pair of numbers at a time, in which case a domino activity would be more accessible. A set of nine-spot dominoes would be useful for this and you can find one for printing here. The task could be to join the dominoes together so that the 'match' adds to 10 or any other number of the children's choice. This will then give them plenty of practice in identifying and remembering number bonds.