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?
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.
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
There are lots of different methods to find out what the shapes are worth - how many can you find?
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. . . .
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?
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?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
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?
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?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
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. . . .
Which set of numbers that add to 10 have the largest product?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Can you find the area of a parallelogram defined by two vectors?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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 ?
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.
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?
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
Use the differences to find the solution to this Sudoku.
How many different symmetrical shapes can you make by shading triangles or squares?
If a sum invested gains 10% each year how long before it has
doubled its value?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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.
If you move the tiles around, can you make squares with different coloured edges?
Is there an efficient way to work out how many factors a large number has?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
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?
Explore the effect of reflecting in two parallel mirror lines.