How many solutions can you find to this sum? Each of the different letters stands for a different number.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
There are nasty versions of this dice game but we'll start with the nice ones...
Here is a chance to play a version of the classic Countdown Game.
Do you notice anything about the solutions when you add and/or
subtract consecutive 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?
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
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.
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.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Find a great variety of ways of asking questions which make 8.
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
Find the values of the nine letters in the sum: FOOT + BALL = GAME
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
What is the sum of all the digits in all the integers from one to
A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how
This challenge is to make up YOUR OWN alphanumeric. Each letter
represents a digit and where the same letter appears more than once
it must represent the same digit each time.
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
Can you be the first to complete a row of three?
This Sudoku, based on differences. Using the one clue number can you find the solution?
An account of some magic squares and their properties and and how to construct them for yourself.
Here is a chance to play a fractions version of the classic
This article for teachers suggests ideas for activities built around 10 and 2010.
This challenge extends the Plants investigation so now four or more children are involved.
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 addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat. . . .
In the following sum the letters A, B, C, D, E and F stand for six
distinct digits. Find all the ways of replacing the letters with
digits so that the arithmetic is correct.
What are the missing numbers in the pyramids?
Find the numbers in this sum