This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This challenge extends the Plants investigation so now four or more children are involved.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Can you explain the strategy for winning this game with any target?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Can you make square numbers by adding two prime numbers together?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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.

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?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

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?

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.

If you have only four weights, where could you place them in order to balance this equaliser?

Number problems at primary level that require careful consideration.

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?

This Sudoku, based on differences. Using the one clue number can you find the solution?

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 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!

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. . . .

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?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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?

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?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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?

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?