This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
This task follows on from Build it Up and takes the ideas into three dimensions!
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
My coat has three buttons. How many ways can you find to do up all the buttons?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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.
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?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
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?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Can you use the information to find out which cards I have used?
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
Can you find out in which order the children are standing in this line?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
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.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Ben has five coins in his pocket. How much money might he have?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing 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?
Find out what a "fault-free" rectangle is and try to make some of your own.
Number problems at primary level that require careful consideration.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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?
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!