Helen Joyce interviews the neuropsychologist Brian Butterworth
whose research has shown that we are all born with a "built-in"
sense of cardinal number.
While musing about the difficulties children face in comprehending number structure, notation, etc., it occured to the author that there is a vast array of occasions when numbers and signs are used. . . .
In this problem, we're investigating the number of steps we would
climb up or down to get out of or into the swimming pool. How could
you number the steps below the water?
Can you find a path from a number at the top of this network to the
bottom which goes through each number from 1 to 9 once and once
What could these drawings, found in a cave in Spain, represent?
Lee was writing all the counting numbers from 1 to 20. She stopped
for a rest after writing seventeen digits. What was the last number
Which comes next in each pattern of dominoes?
Buzzy Bee was building a honeycomb. She decided to decorate the
honeycomb with a pattern using numbers. Can you discover Buzzy's
pattern and fill in the empty cells for her?
Help share out the biscuits the children have made.
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
A number card game for 2-6 players.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?
How could you estimate the number of pencils/pens in these pictures?
You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?
Some children were playing a game. Make a graph or picture to show
how many ladybirds each child had.
How many legs do each of these creatures have? How many pairs is
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Daisy and Akram were making number patterns. Daisy was using beads
that looked like flowers and Akram was using cube bricks. First
they were counting in twos.
Here is a version of the game 'Happy Families' for you to make and
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?
A game played with a standard pack of cards.
Reasoning based on this Japanese activity.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
25 students are queuing in a straight line. How many are there
between Julia and Jenny?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Dotty Six is a simple dice game that you can adapt in many ways.
Can you follow the rule to decode the messages?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
A game for two people, who take turns to move the counters. The player to remove the last counter from the board wins.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
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?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Can you complete this jigsaw of the 100 square?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?