In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Here is a chance to play a version of the classic Countdown Game.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
Number problems at primary level to work on with others.
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
An old game but lots of arithmetic!
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Are these domino games fair? Can you explain why or why not?
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?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Who said that adding couldn't be fun?
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?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Investigate the different distances of these car journeys and find
out how long they take.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Investigate what happens when you add house numbers along a street
in different ways.
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
What is happening at each box in these machines?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?