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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
There are nasty versions of this dice game but we'll start with the nice ones...
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you explain the strategy for winning this game with any target?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
How can we help students make sense of addition and subtraction of negative numbers?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
This challenge extends the Plants investigation so now four or more children are involved.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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?
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.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Here is a chance to play a version of the classic Countdown Game.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Can you use the information to find out which cards I have used?
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?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
Choose a symbol to put into the number sentence.
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you substitute numbers for the letters in these sums?
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?
If you have only four weights, where could you place them in order to balance this equaliser?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
This is an adding game for two players.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Who said that adding couldn't be fun?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how it works?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
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. . . .