Year 8 Conjecturing and Generalising

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Subtraction Surprise

Age

7 to 14

Challenge level

Try out some calculations. Are you surprised by the results?

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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?

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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.

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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?

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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?

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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?

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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?

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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?

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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?

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Multiple Surprises

Age

11 to 16

Challenge level

Sequences of multiples keep cropping up...

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Polygon Rings

Age

11 to 14

Challenge level

Join pentagons together edge to edge. Will they form a ring?

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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?

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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.

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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?

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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?

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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?

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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?

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Fibonacci Surprises

Age

11 to 14

Challenge level

Play around with the Fibonacci sequence and discover some surprising results!

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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?

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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.