Year 8 Conjecturing and generalising

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

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

Can all unit fractions be written as the sum of two unit fractions?

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?

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

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?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

What happens when you add a three digit number to its reverse?

Sequences of multiples keep cropping up...

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

How many moves does it take to swap over some red and blue frogs? Do you have a method?

We usually use squares to measure area, but what if we use triangles instead?

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

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

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

How well can you estimate 10 seconds? Investigate with our timing tool.

Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

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

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?

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.

Play around with sets of five numbers and see what you can discover about different types of average...

There are lots of ideas to explore in these sequences of ordered fractions.

Isometric Areas explored areas of parallelograms in triangular units. Here we explore areas of triangles...

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

How did the the rotation robot make these patterns?

Can you work out what step size to take to ensure you visit all the dots on the circle?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Can you describe this route to infinity? Where will the arrows take you next?

What's the largest volume of box you can make from a square of paper?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?