List

Working Systematically

 

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

Secondary Working Systematically header


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.

 



 

Two and Two
problem
Favourite

Two and Two

Age
7 to 16
Challenge level
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How many solutions can you find to this sum? Each of the different letters stands for a different number.

1 Step 2 Step
problem
Favourite

1 Step 2 Step

Age
11 to 14
Challenge level
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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?
ACE, TWO, THREE...
problem

ACE, TWO, THREE...

Age
11 to 14
Challenge level
filled star empty star empty star
Can you picture how to order the cards to reproduce Charlie's card trick for yourself?
Isosceles Triangles
problem
Favourite

Isosceles Triangles

Age
11 to 14
Challenge level
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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?
m, m and m
problem
Favourite

M, M and M

Age
11 to 14
Challenge level
filled star empty star empty star

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

Can they be equal?
problem
Favourite

Can they be equal?

Age
11 to 14
Challenge level
filled star empty star empty star
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Sticky Numbers
problem
Favourite

Sticky Numbers

Age
11 to 14
Challenge level
filled star empty star empty star
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Shifting Times Tables
problem
Favourite

Shifting Times Tables

Age
11 to 14
Challenge level
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Can you find a way to identify times tables after they have been shifted up or down?

Charlie's delightful machine
problem
Favourite

Charlie's delightful machine

Age
11 to 16
Challenge level
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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

American Billions
problem
Favourite

American Billions

Age
11 to 14
Challenge level
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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...