This problem is designed to help children to learn, and to use, the two and three times tables.
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?
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?
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?
What is the sum of all the three digit whole numbers?
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.
56 406 is the product of two consecutive numbers. What are these
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?
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Resources to support understanding of multiplication and division through playing with number.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Number problems at primary level that may require determination.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Find the next number in this pattern: 3, 7, 19, 55 ...
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
What is happening at each box in these machines?
If the answer's 2010, what could the question be?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Number problems at primary level that require careful consideration.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This number has 903 digits. What is the sum of all 903 digits?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Use the information to work out how many gifts there are in each
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out what a ziffle is on the planet Zargon?
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?
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 clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you work out some different ways to balance this equation?
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?