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.
This article for teachers suggests ideas for activities built around 10 and 2010.
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. . . .
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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.
Replace each letter with a digit to make this addition correct.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Number problems at primary level that require careful consideration.
If you have only four weights, where could you place them in order to balance this equaliser?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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 put the numbers 1 to 8 into the circles so that the four calculations are correct?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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!
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 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 problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
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?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
What are the missing numbers in the pyramids?
Can you substitute numbers for the letters in these sums?
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
This is an adding game for two players.
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?
Find the sum of all three-digit numbers each of whose digits is odd.
Ben has five coins in his pocket. How much money might he have?
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.
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?
These two group activities use mathematical reasoning - one is numerical, one geometric.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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?
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
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 challenge extends the Plants investigation so now four or more children are involved.
Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?
This number has 903 digits. What is the sum of all 903 digits?