Year 8 Being resilient

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...

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?

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

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

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?

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

How many different differences can you make?

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

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: ×2 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.

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

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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.

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? 

Four friends must cross a bridge. How can they all cross it in just 17 minutes?