Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you substitute numbers for the letters in these sums?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
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?
Can you use the information to find out which cards I have used?
Number problems at primary level that require careful consideration.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Investigate the different ways you could split up these rooms so that you have double the number.
There are lots of different methods to find out what the shapes are worth - how many can you find?
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!
When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?