What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you substitute numbers for the letters in these sums?
Can you replace the letters with numbers? Is there only one
solution in each case?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Follow the clues to find the mystery number.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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.
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?
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
What happens when you round these numbers to the nearest whole number?
How many different journeys could you make if you were going to
visit four stations in this network? How about if there were five
stations? Can you predict the number of journeys for seven
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Have a go at balancing this equation. Can you find different ways of doing it?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
An investigation that gives you the opportunity to make and justify
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
How many triangles can you make on the 3 by 3 pegboard?
Find out about Magic Squares in this article written for students. Why are they magic?!
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
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...
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.