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?
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
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?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
If you move the tiles around, can you make squares with different coloured edges?
Which set of numbers that add to 10 have the largest product?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Can you find the area of a parallelogram defined by two vectors?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
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. . . .
How many different symmetrical shapes can you make by shading triangles or squares?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
What is the same and what is different about these circle
questions? What connections can you make?
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
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.
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?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Explore the effect of combining enlargements.
Explore the effect of reflecting in two parallel mirror lines.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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 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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
Can you describe this route to infinity? Where will the arrows take you next?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Can you maximise the area available to a grazing goat?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
The clues for this Sudoku are the product of the numbers in adjacent squares.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.