Year 8 Exploring and noticing

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

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

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Draw some isosceles triangles with an area of $9cm^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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.

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?

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

A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Invent a scoring system for a 'guess the weight' competition.

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?

Can you deduce which Olympic athletics events are represented by the graphs?

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

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

How many different number families can you find?

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

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

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

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

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

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

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

Sequences of multiples keep cropping up...

The number in the square is the mean of the four numbers surrounding it. Can you find the missing numbers? 

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

How did the the rotation robot make these patterns?

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.