What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Can you draw a square in which the perimeter is numerically equal to the area?

An investigation that gives you the opportunity to make and justify predictions.

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?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

This task follows on from Build it Up and takes the ideas into three dimensions!

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?

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Number problems at primary level that require careful consideration.

Can you substitute numbers for the letters in these sums?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Find out what a "fault-free" rectangle is and try to make some of your own.

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?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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!

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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?

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?

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?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?