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Broad Topics > Numbers and the Number System > Counting

### Incey Wincey Spider

##### Stage: 1 Challenge Level:

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?

### Tug Harder!

##### Stage: 2 Challenge Level:

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?

### Tug of War

##### Stage: 1 Challenge Level:

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

### Swimming Pool

##### Stage: 1 and 2 Challenge Level:

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?

### 100 Square Jigsaw

##### Stage: 1 Challenge Level:

Can you complete this jigsaw of the 100 square?

### Cunning Card Trick

##### Stage: 3 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

### Diagonal Sums Sudoku

##### Stage: 2, 3 and 4 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

### Ladybird Count

##### Stage: 1 Challenge Level:

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

### Amazing Card Trick

##### Stage: 3 Challenge Level:

How is it possible to predict the card?

### Counting Cards

##### Stage: 2 Challenge Level:

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?

### Neighbours

##### Stage: 2 Challenge Level:

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?

### Birthday Cakes

##### Stage: 1 Challenge Level:

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?

### Making Sticks

##### Stage: 1 Challenge Level:

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

### Buzzy Bee

##### Stage: 1 Challenge Level:

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?

### Next Domino

##### Stage: 1 Challenge Level:

Which comes next in each pattern of dominoes?

### Writing Digits

##### Stage: 1 Short Challenge Level:

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 she wrote?

### Noah

##### Stage: 1 Challenge Level:

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

### Five Steps to 50

##### Stage: 1 Challenge Level:

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

### Snail One Hundred

##### Stage: 1 and 2 Challenge Level:

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

### How Would We Count?

##### Stage: 1 and 2 Challenge Level:

An activity centred around observations of dots and how we visualise number arrangement patterns.

### Some Secret Codes

##### Stage: 2 Challenge Level:

Can you follow the rule to decode the messages?

### All Change

##### Stage: 1 Challenge Level:

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?

### Jumping Squares

##### Stage: 1 Challenge Level:

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.

### Pairs of Legs

##### Stage: 1 Challenge Level:

How many legs do each of these creatures have? How many pairs is that?

### Dotty Six

##### Stage: 1 and 2 Challenge Level:

Dotty Six is a simple dice game that you can adapt in many ways.

### Count the Digits

##### Stage: 1 and 2 Challenge Level:

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

### Pairs of Numbers

##### Stage: 1 Challenge Level:

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?

### Sitting Round the Party Tables

##### Stage: 1 and 2 Challenge Level:

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

### How Odd

##### Stage: 1 Challenge Level:

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?

### Ip Dip

##### Stage: 1 and 2 Challenge Level:

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

### Cube Bricks and Daisy Chains

##### Stage: 1 Challenge Level:

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.

### Sort Them Out (1)

##### Stage: 1 Challenge Level:

Can you each work out the number on your card? What do you notice? How could you sort the cards?

### Lots of Biscuits!

##### Stage: 1 Challenge Level:

Help share out the biscuits the children have made.

### Fingers and Hands

##### Stage: 2 Challenge Level:

How would you count the number of fingers in these pictures?

### Picture a Pyramid ...

##### Stage: 2 Challenge Level:

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?

### Alien Counting

##### Stage: 2 Challenge Level:

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.

### Making Maths: Happy Families

##### Stage: 1 and 2 Challenge Level:

Here is a version of the game 'Happy Families' for you to make and play.

### Building Patterns

##### Stage: 2 Challenge Level:

Can you deduce the pattern that has been used to lay out these bottle tops?

### Binary Sequences

##### Stage: 5 Challenge Level:

Show that the infinite set of finite (or terminating) binary sequences can be written as an ordered list whereas the infinite set of all infinite binary sequences cannot.

### Adding with the Abacus

##### Stage: 1, 2, 3 and 4

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?

### Natural Born Mathematicians

##### Stage: 1

Helen Joyce interviews the neuropsychologist Brian Butterworth whose research has shown that we are all born with a "built-in" sense of cardinal number.

### Numbers and Notation - Ambiguities and Confusions

##### Stage: 1

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. . . .

### Stone Age Counting

##### Stage: 1 Challenge Level:

What could these drawings, found in a cave in Spain, represent?

### Dramatic Mathematics

##### Stage: 1 and 2

This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.

### Queue

##### Stage: 1 Challenge Level:

25 students are queuing in a straight line. How many are there between Julia and Jenny?

### 1 to 8

##### Stage: 2 Challenge Level:

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

### Voting Paradox

##### Stage: 4 and 5 Challenge Level:

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?

### Ruler

##### Stage: 5 Challenge Level:

The interval 0 - 1 is marked into halves, quarters, eighths ... etc. Vertical lines are drawn at these points, heights depending on positions. What happens as this process goes on indefinitely?