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### Number and algebra

### Geometry and measure

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### Working mathematically

### For younger learners

### Advanced mathematics

# Particular to the General - Masterclass

### Summing Consecutive Numbers

### Marbles in a Box

### Route to Infinity

### What's Possible?

### Painted Cube

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The problems in this masterclass package are intended to offer students the opportunity to engage in a key mathematical activity: moving from particular instances to general cases. Along the way, students can notice patterns, make conjectures and choose representations to help justify and prove.

Age 11 to 14

Challenge Level

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?

Age 11 to 16

Challenge Level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Age 11 to 14

Challenge Level

Can you describe this route to infinity? Where will the arrows take you next?

Age 14 to 16

Challenge Level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Age 14 to 16

Challenge Level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?