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.
Delight your friends with this cunning trick! Can you explain how
Can you explain how this card trick works?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Crosses can be drawn on number grids of various sizes. What do you
notice when you add opposite ends?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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
Find the sum of all three-digit numbers each of whose digits is
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Replace each letter with a digit to make this addition correct.
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?
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?
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.
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
What are the missing numbers in the pyramids?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
What is the sum of all the three digit whole numbers?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
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?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
This is an adding game for two players.
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
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
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?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
This challenge extends the Plants investigation so now four or more children are involved.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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.
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
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. . . .
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 focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Investigate the different distances of these car journeys and find out how long they take.