problem
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Subtraction Surprise
Age
7 to 14
Challenge level
Try out some calculations. Are you surprised by the results?
problem
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Method in multiplying madness?
Age
7 to 14
Challenge level
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
article
spaces for exploration
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
problem
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Crossed Ends
Age
11 to 14
Challenge level
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
problem
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Can they be equal?
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?
problem
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Keep it simple
Age
11 to 14
Challenge level
Can all unit fractions be written as the sum of two unit fractions?
problem
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How much can we spend?
Age
11 to 14
Challenge level
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
problem
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Charlie's delightful machine
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?
problem
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Your number was...
Age
11 to 14
Challenge level
Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
problem
Favourite
What numbers can we make?
Age
11 to 14
Challenge level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
problem
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Forwards Add Backwards
Age
11 to 14
Challenge level
What happens when you add a three digit number to its reverse?
problem
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Multiple Surprises
Age
11 to 16
Challenge level
Sequences of multiples keep cropping up...
problem
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Polygon Rings
Age
11 to 14
Challenge level
Join pentagons together edge to edge. Will they form a ring?
problem
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Frogs
Age
11 to 14
Challenge level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
problem
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Interactive Spinners
Age
11 to 14
Challenge level
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
problem
Favourite
Cuboid Challenge
Age
11 to 16
Challenge level
What's the largest volume of box you can make from a square of paper?
problem
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Power mad!
Age
11 to 14
Challenge level
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
problem
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Seven Squares
Age
11 to 14
Challenge level
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
problem
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Same Answer
Age
11 to 14
Challenge level
Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?
problem
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Fibonacci Surprises
Age
11 to 14
Challenge level
Play around with the Fibonacci sequence and discover some surprising results!
problem
Favourite
Where can we visit?
Age
11 to 14
Challenge level
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?
problem
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Egyptian Fractions
Age
11 to 14
Challenge level
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
problem
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Farey Sequences
Age
11 to 14
Challenge level
There are lots of ideas to explore in these sequences of ordered fractions.
problem
Favourite
Coordinate Patterns
Age
11 to 14
Challenge level
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
problem
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Stars
Age
11 to 14
Challenge level
Can you work out what step size to take to ensure you visit all the dots on the circle?
problem
Favourite
Route to infinity
Age
11 to 14
Challenge level
Can you describe this route to infinity? Where will the arrows take you next?
problem
Favourite
Consecutive negative numbers
Age
11 to 14
Challenge level
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?