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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
Can you explain how this card trick works?
There are nasty versions of this dice game but we'll start with the nice ones...
Delight your friends with this cunning trick! Can you explain how
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.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Here is a chance to play a version of the classic Countdown Game.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
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.
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
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?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
What are the missing numbers in the pyramids?
Choose any three by three square of dates on a calendar page...
Replace each letter with a digit to make this addition correct.
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
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Here is a chance to play a fractions version of the classic
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
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?
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
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. . . .
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?
Find a great variety of ways of asking questions which make 8.
How can we help students make sense of addition and subtraction of negative numbers?
What is the sum of all the digits in all the integers from one to
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.
How is it possible to predict the card?
This article for teachers suggests ideas for activities built around 10 and 2010.
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.