In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Use the information to work out how many gifts there are in each
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?
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
If the answer's 2010, what could the question be?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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.
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Find the next number in this pattern: 3, 7, 19, 55 ...
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Number problems at primary level that require careful consideration.
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?
Number problems at primary level that may require determination.
This number has 903 digits. What is the sum of all 903 digits?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
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?
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?
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?
What is happening at each box in these machines?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
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 sum of all the three digit whole numbers?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you work out what a ziffle is on the planet Zargon?
Can you replace the letters with numbers? Is there only one
solution in each case?
Resources to support understanding of multiplication and division through playing with number.
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
This activity focuses on doubling multiples of five.
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing 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?