Year 8 Conjecturing and generalising

problem

Subtraction surprise

Age

7 to 14

Challenge level

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

problem

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

Polygon rings

Age

11 to 14

Challenge level

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

problem

Isometric areas

Age

11 to 14

Challenge level

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

problem

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

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

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

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

Keep it simple

Age

11 to 14

Challenge level

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

problem

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

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

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

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

Constructing triangles

Age

11 to 14

Challenge level

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

problem

Forwards add backwards

Age

11 to 14

Challenge level

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

problem

Multiple surprises

Age

11 to 16

Challenge level

Sequences of multiples keep cropping up...

problem

More isometric areas

Age

11 to 14

Challenge level

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

problem

Robotic rotations

Age

11 to 16

Challenge level

How did the the rotation robot make these patterns?

problem

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

Rhombus it

Age

11 to 16

Challenge level

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.

problem

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.