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...
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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 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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Can you substitute numbers for the letters in these sums?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Here is a chance to play a version of the classic Countdown Game.
Choose a symbol to put into the number sentence.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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 information about Sally and her brother to find out how many children there are in the Brown family.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Use the number weights to find different ways of balancing the equaliser.
How would you count the number of fingers in these pictures?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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
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?
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
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?
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?
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
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.
If you have only four weights, where could you place them in order
to balance this equaliser?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
An old game but lots of arithmetic!
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
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?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
This challenge extends the Plants investigation so now four or more children are involved.