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.
Replace each letter with a digit to make this addition correct.
Find a great variety of ways of asking questions which make 8.
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?
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
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
What are the missing numbers in the pyramids?
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?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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.
Can you explain how this card trick works?
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
Can you substitute numbers for the letters in these sums?
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.
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?
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.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Find the numbers in this sum
Delight your friends with this cunning trick! Can you explain how
Find the sum of all three-digit numbers each of whose digits is
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
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. . . .
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?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Who said that adding couldn't be fun?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Are these statements always true, sometimes true or never true?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
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. . . .
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
If the answer's 2010, what could the question be?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
An environment which simulates working with Cuisenaire rods.
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
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?
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?
Investigate the different distances of these car journeys and find
out how long they take.
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?
Can you make square numbers by adding two prime numbers together?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.