In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Number problems at primary level that require careful consideration.
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.
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.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Number problems at primary level that may require determination.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Use the information to work out how many gifts there are in each
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
What is happening at each box in these machines?
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
If the answer's 2010, what could the question be?
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?
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?
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
This activity focuses on doubling multiples of five.
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?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
This task combines spatial awareness with addition and multiplication.
Are these statements always true, sometimes true or never true?