An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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.
Can you explain how this card trick works?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Delight your friends with this cunning trick! Can you explain how
This challenge extends the Plants investigation so now four or more children are involved.
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?
Find the sum of all three-digit numbers each of whose digits is
Here is a chance to play a version of the classic Countdown Game.
Can you be the first to complete a row of three?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are 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
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
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. . . .
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Replace each letter with a digit to make this addition correct.
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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
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?
This is an adding game for two players.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.