In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
There are nasty versions of this dice game but we'll start with the nice ones...
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
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 each work out the number on your card? What do you notice?
How could you sort the cards?
Find the sum of all three-digit numbers each of whose digits is
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?
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?
What is the sum of all the three digit whole numbers?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
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?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Can you hang weights in the right place to make the equaliser
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Can you substitute numbers for the letters in these sums?
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?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 15.
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.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
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?
Can you find 2 butterflies to go on each flower so that the numbers
on each pair of butterflies adds to the same number as the one on
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?
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?
Investigate the different distances of these car journeys and find out how long they take.
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?
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?
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 counters?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.