Year 8 Reasoning, convincing and proving

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

These Olympic quantities have been jumbled up! Can you put them back together again?

What are the possible areas of triangles drawn in a square?

Sequences of multiples keep cropping up...

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

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

Can you find triangles on a 9-point circle? Can you work out their angles?

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

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?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Which countries have the most naturally athletic populations?

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!

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

How did the the rotation robot make these patterns?

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

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

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

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