In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
An old game but lots of arithmetic!
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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 hang weights in the right place to make the equaliser
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.
A game for 2 players. Practises subtraction or other maths
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Use the number weights to find different ways of balancing the equaliser.
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Choose four of the numbers from 1 to 9 to put in the squares so
that the differences between joined squares are odd.
Ben has five coins in his pocket. How much money might he have?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Here is a chance to play a version of the classic Countdown Game.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
This challenge extends the Plants investigation so now four or more children are involved.
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
If you hang two weights on one side of this balance, in how many
different ways can you hang three weights on the other side for it
to be balanced?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Choose a symbol to put into the number sentence.
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?
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.
There are nasty versions of this dice game but we'll start with the nice ones...
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!
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.