In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
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?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
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?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Who said that adding couldn't be fun?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
What is happening at each box in these machines?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
If the answer's 2010, what could the question be?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
There are nasty versions of this dice game but we'll start with the nice ones...
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you substitute numbers for the letters in these sums?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Investigate the different distances of these car journeys and find
out how long they take.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Use the information to work out how many gifts there are in each
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Use these four dominoes to make a square that has the same number of dots on each side.
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.