Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how
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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you explain the strategy for winning this game with any target?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
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?
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 be the first to complete a row of three?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What are the missing numbers in the pyramids?
This challenge extends the Plants investigation so now four or more children are involved.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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 is an adding game for two players.
Replace each letter with a digit to make this addition correct.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
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
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 gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Choose any three by three square of dates on a calendar page...
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Here is a chance to play a version of the classic Countdown Game.
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?