In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
If you have only four weights, where could you place them in order
to balance this equaliser?
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 six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
There are nasty versions of this dice game but we'll start with the nice ones...
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Here is a chance to play a version of the classic Countdown Game.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
An old game but lots of arithmetic!
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Can you hang weights in the right place to make the equaliser
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
Use the number weights to find different ways of balancing the equaliser.
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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?
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.
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?
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?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Choose a symbol to put into the number sentence.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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!
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
This challenge extends the Plants investigation so now four or more children are involved.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
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 follow the rule to decode the messages?
Leah and Tom each have a number line. Can you work out where their
counters will land? What are the secret jumps they make with their
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?