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### Number and algebra

### Geometry and measure

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### Working mathematically

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### For younger learners

# What Numbers Can We Make?

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### Adding All Nine

### Summing Consecutive Numbers

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Age 11 to 14

Challenge Level

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Begin by exploring what happens when you add two, three, four... numbers chosen from a set of bags containing $2$s, $4$s, $6$s and $8$s. Can you explain your findings?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?