In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Find the sum of this series of surds.
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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.
Which set of numbers that add to 10 have the largest product?
If you move the tiles around, can you make squares with different coloured edges?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
What is the same and what is different about these circle questions? What connections can you make?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
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?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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?
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.
The sums of the squares of three related numbers is also a perfect square - can you explain why?
If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
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?
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. . . .
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Can you maximise the area available to a grazing goat?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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?
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Can you describe this route to infinity? Where will the arrows take you next?
Explore the effect of reflecting in two parallel mirror lines.
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?
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Explore the effect of combining enlargements.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .
Can you work out how to produce different shades of pink paint?
A jigsaw where pieces only go together if the fractions are equivalent.
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...