Ben has five coins in his pocket. How much money might he have?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Number problems at primary level that require careful consideration.
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
Can you substitute numbers for the letters in these sums?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
This task follows on from Build it Up and takes the ideas into three dimensions!
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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?
Can you use the information to find out which cards I have used?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Can you replace the letters with numbers? Is there only one solution in each case?
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
In how many ways can you stack these rods, following the rules?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Can you make square numbers by adding two prime numbers together?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?