List

Year 8 Working Systematically

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?

Sociable Cards
problem
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Sociable Cards

Age
11 to 14
Challenge level
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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Making a difference
problem
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Making a difference

Age
11 to 14
Challenge level
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How many different differences can you make?
Forwards Add Backwards
problem
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Forwards Add Backwards

Age
11 to 14
Challenge level
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What happens when you add a three digit number to its reverse?
Completing Quadrilaterals
problem
Favourite

Completing Quadrilaterals

Age
11 to 14
Challenge level
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We started drawing some quadrilaterals - can you complete them?

Gabriel's Problem
problem
Favourite

Gabriel's Problem

Age
11 to 14
Challenge level
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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Pocket money
problem
Favourite

Pocket money

Age
11 to 14
Challenge level
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Which of these pocket money systems would you rather have?
American Billions
problem
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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...
Fence it
problem
Favourite

Fence it

Age
11 to 14
Challenge level
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If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Isosceles Triangles
problem
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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?
Triangles in circles
problem
Favourite

Triangles in circles

Age
11 to 14
Challenge level
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Can you find triangles on a 9-point circle? Can you work out their angles?

Can they be equal?
problem
Favourite

Can they be equal?

Age
11 to 14
Challenge level
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Can you find rectangles where the value of the area is the same as the value of the perimeter?
Keep it simple
problem
Favourite

Keep it simple

Age
11 to 14
Challenge level
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Can all unit fractions be written as the sum of two unit fractions?
How steep is the slope?
problem
Favourite

How steep is the slope?

Age
11 to 14
Challenge level
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On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Where can we visit?
problem
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Where can we visit?

Age
11 to 14
Challenge level
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Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Farey Sequences
problem
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Farey Sequences

Age
11 to 14
Challenge level
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There are lots of ideas to explore in these sequences of ordered fractions.
Peaches today, Peaches tomorrow...
problem
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Peaches today, Peaches tomorrow...

Age
11 to 14
Challenge level
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A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Stars
problem
Favourite

Stars

Age
11 to 14
Challenge level
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Can you work out what step size to take to ensure you visit all the dots on the circle?
Shapely pairs
problem
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Shapely pairs

Age
11 to 14
Challenge level
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A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

Weights
problem
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Weights

Age
11 to 14
Challenge level
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Different combinations of the weights available allow you to make different totals. Which totals can you make?
Power mad!
problem
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Power mad!

Age
11 to 14
Challenge level
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Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Consecutive negative numbers
problem
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Consecutive negative numbers

Age
11 to 14
Challenge level
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Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?