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### Number and algebra

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### Working mathematically

### For younger learners

### Advanced mathematics

# Working Systematically

### Two and Two

### 1 Step 2 Step

### ACE, TWO, THREE...

### Isosceles Triangles

### M, M and M

### Can They Be Equal?

### Sticky Numbers

### Shifting Times Tables

### Charlie's Delightful Machine

### American Billions

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**We have chosen a selection of our favourite NRICH resources that challenge you to work systematically.**

Here are a few questions you might need to ask along the way:

Which piece of information is the most useful to start with? What next?

How will I record my findings?

Will I be confident that I have found all the results by the end?

The problems can be tackled in any order.

Age 7 to 16

Challenge Level

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

Age 11 to 14

Challenge Level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Age 11 to 14

Challenge Level

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Age 11 to 14

Challenge Level

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Age 11 to 14

Challenge Level

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Age 11 to 14

Challenge Level

Can you find a way to identify times tables after they have been shifted up or down?

Age 11 to 16

Challenge Level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Age 11 to 14

Challenge Level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...