The numbers give the design
Area and perimeter
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Multiply multiples 1
Multiply multiples 2
Round the dice decimals 2
What happens when you round these numbers to the nearest whole number?
Multiply multiples 3
Division rules
Factors and multiples game
A game in which players take it in turns to choose a number. Can you block your opponent?
Tumbling down
Watch this animation. What do you see? Can you explain why this happens?
Compare the calculations
Highest and lowest
Abundant numbers
Multiplication squares
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Trebling
Can you replace the letters with numbers? Is there only one solution in each case?
Brush loads
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Route product
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Factor track
Through the window
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Pouring problem
What do you think is going to happen in this video clip? Are you surprised?
Pebbles
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Egyptian rope
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
Make 100
Forgot the numbers
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Numerically equal
Can you draw a square in which the perimeter is numerically equal to the area?
Twenty divided into six
One wasn't square
All the digits
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Reach 100
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Two primes make one square
Cycling squares
Olympic turns
This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.
Ribbon squares
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Four goodness sake
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Fitted
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?