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### Number and algebra

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### Working mathematically

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# Noticing Patterns

### 1 Step 2 Step

### Summing Consecutive Numbers

### Pick's TheoremLive

### What's Possible?

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The key to solving these problems is to notice patterns or properties. Organising your work in a systematic way will allow you to notice what might not otherwise be obvious.

Age 11 to 14

Challenge Level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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 14 to 16

Challenge Level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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?