In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
There are nasty versions of this dice game but we'll start with the nice ones...
How can we help students make sense of addition and subtraction of negative numbers?
Can you hang weights in the right place to make the equaliser
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Find the sum of all three-digit numbers each of whose digits is
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
What is the sum of all the three digit whole numbers?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you substitute numbers for the letters in these sums?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
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.
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Use the number weights to find different ways of balancing the equaliser.
Investigate what happens when you add house numbers along a street
in different ways.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Who said that adding couldn't be fun?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Find a great variety of ways of asking questions which make 8.
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Are these domino games fair? Can you explain why or why not?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Investigate the different distances of these car journeys and find
out how long they take.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three