In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
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.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Number problems at primary level that require careful consideration.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Number problems at primary level that may require determination.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Use the information to work out how many gifts there are in each
Find the next number in this pattern: 3, 7, 19, 55 ...
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
What is happening at each box in these machines?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?
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?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Have a go at balancing this equation. Can you find different ways of doing it?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This task combines spatial awareness with addition and multiplication.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This activity focuses on doubling multiples of five.
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
Take the number 6 469 693 230 and divide it by the first ten prime
numbers and you'll find the most beautiful, most magic of all
numbers. What is it?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?