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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Break it Up!

## You may also like

### Let's Investigate Triangles

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 5 to 11

Challenge Level

You have a stick of seven interlocking cubes (or a tower of seven Lego blocks). You cannot change the order of the cubes.

You break off a bit of it leaving it in two pieces.

Here is one of the ways in which you can do it:

Here is another way you can do it:

**In how many different ways can it be done?**

**Now try with a stick of eight cubes:**

**What about with a stick of six cubes?**

**What do you notice?**

Now predict how many ways there will be with five cubes.

Try it! Were you right?

How many ways with 20 cubes?

**Will your noticing always be true? Can you create an argument that would convince mathematicians?**

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?