How many winning lines can you make in a three-dimensional version of noughts and crosses?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Can you describe this route to infinity? Where will the arrows take you next?
If you move the tiles around, can you make squares with different coloured edges?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Can you maximise the area available to a grazing goat?
Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Explore the effect of reflecting in two parallel mirror lines.
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Explore the effect of combining enlargements.
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Can all unit fractions be written as the sum of two unit fractions?
Which set of numbers that add to 10 have the largest product?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Use the differences to find the solution to this Sudoku.
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Can you work out the dimensions of the three cubes?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
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 pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?