Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Choose a symbol to put into the number sentence.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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 task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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.
If you have only four weights, where could you place them in order
to balance this equaliser?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Here is a chance to play a version of the classic Countdown Game.
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
There are nasty versions of this dice game but we'll start with the nice ones...
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?
This is an adding game for two players.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
A game for 2 players. Practises subtraction or other maths
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.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Who said that adding couldn't be fun?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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?
Can you be the first to complete a row of three?
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 substitute numbers for the letters in these sums?
Delight your friends with this cunning trick! Can you explain how
Can you explain the strategy for winning this game with any target?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
How can we help students make sense of addition and subtraction of negative numbers?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Ben has five coins in his pocket. How much money might he have?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?