List

Year 8 Conjecturing and Generalising

Subtraction Surprise
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Subtraction Surprise

Age
7 to 14
Challenge level
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Try out some calculations. Are you surprised by the results?
Method in multiplying madness?
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Method in multiplying madness?

Age
7 to 14
Challenge level
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Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
spaces for exploration
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spaces for exploration

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
Frogs
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Frogs

Age
11 to 14
Challenge level
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How many moves does it take to swap over some red and blue frogs? Do you have a method?
Interactive Spinners
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Interactive Spinners

Age
11 to 14
Challenge level
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This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Crossed Ends
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Crossed Ends

Age
11 to 14
Challenge level
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Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Can they be equal?
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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
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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 much can we spend?
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How much can we spend?

Age
11 to 14
Challenge level
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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?
Charlie's delightful machine
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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?

Your number was...
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Your number was...

Age
11 to 14
Challenge level
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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?
What numbers can we make?
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What numbers can we make?

Age
11 to 14
Challenge level
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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Forwards Add Backwards
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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?
Multiple Surprises
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Multiple Surprises

Age
11 to 16
Challenge level
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Sequences of multiples keep cropping up...
Polygon Rings
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Polygon Rings

Age
11 to 14
Challenge level
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Join pentagons together edge to edge. Will they form a ring?

Where can we visit?
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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?
Egyptian Fractions
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Egyptian Fractions

Age
11 to 14
Challenge level
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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.
Farey Sequences
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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.
Coordinate Patterns
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Coordinate Patterns

Age
11 to 14
Challenge level
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Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Stars
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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?
Route to infinity
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Route to infinity

Age
11 to 14
Challenge level
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Can you describe this route to infinity? Where will the arrows take you next?
Cuboid challenge
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Cuboid Challenge

Age
11 to 16
Challenge level
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What's the largest volume of box you can make from a square of paper?

Power mad!
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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.

Seven Squares
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Seven Squares

Age
11 to 14
Challenge level
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Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Same Answer
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Same Answer

Age
11 to 14
Challenge level
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Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?
Fibonacci Surprises
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Fibonacci Surprises

Age
11 to 14
Challenge level
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Play around with the Fibonacci sequence and discover some surprising results!
Consecutive negative numbers
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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?