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
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you explain how this card trick works?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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?
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?
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?
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?
Replace each letter with a digit to make this addition correct.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
How many solutions can you find to this sum? Each of the different letters stands for a different number.
What are the missing numbers in the pyramids?
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
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?
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.
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. . . .
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.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
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?
Find the sum of all three-digit numbers each of whose digits is
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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 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.
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?
There are nasty versions of this dice game but we'll start with the nice ones...
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
This challenge extends the Plants investigation so now four or more children are involved.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This task follows on from Build it Up and takes the ideas into three dimensions!
This article suggests some ways of making sense of calculations involving positive and negative 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?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Here is a chance to play a version of the classic Countdown Game.
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?