There are 94 NRICH Mathematical resources connected to Counting, you may find related items under Place value and the number system.
Broad Topics > Place value and the number system > Counting
Have a look at these photos of different fruit. How many do you see? How did you count?
What do you see as you watch this video? Can you create a similar video for the number 12?
How could you estimate the number of pencils/pens in these pictures?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
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?
In this game, you throw a dice and move counters along the snail's body and in a spiral around the snail's shell. It is about understanding tens and ones.
An activity centred around observations of dots and how we visualise number arrangement patterns.
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?
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.
Dotty Six is a simple dice game that you can adapt in many ways.
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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 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 ...?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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?
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?
Delight your friends with this cunning trick! Can you explain how it works?
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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?
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?
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?
Can you work out how many apples there are in this fruit bowl if you know what fraction there are?
Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?
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 saw 12 legs walk by into the Ark. How many creatures did he see?
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 only?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was thinking of.
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
How many different ways can you arrange the officers in a square?
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?