## One Big Triangle

The small triangles can be moved to fill in the spaces in the big triangle.
Just drag and drop.
The numbers that touch need to add up to $10$.
It is possible to make one big triangle so that all the the numbers on the sides that touch add to $10$.

Full screen version

If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

You can also print out these triangles, cut them out and rearrange them to make the big triangle.

### 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 interactive version will help children to remain engaged with the problem as it is easy to use. However, for children who are fluent with the combinations to ten, this problem is still relevant because of the element of logic. If using the cards rather than the interactivity, learners will also need to visualise triangles in different orientations in order to solve the problem.

### Possible approach

You could start the lesson by asking the children to tell you pairs of numbers that add to $10$. Then you could introduce the interactivity with the whole group on the interactive whiteboard.

After this, 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.) The cards are more difficult to arrange than the interactivity because they can be rotated.

During a 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? Do they look the same as the interactivity? If not, can the children suggest why this should be so?

### Key questions

What do you need to put with $7$ ... to make $10$?
Can you find a different card with that number on it?

### Possible extension

Children who finish quickly could 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 $10$. Alternatively, learners could use the interactivity which will be sure to hold attention and increase persistence and perseverance.
Some children may find it difficult to cope with matching more than one pair at a time in which case using a domino type activity would be more accessible. A set of 9 spot dominoes would be useful for this and you can find one 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.