During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
A game that tests your understanding of remainders.
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Can you replace the letters with numbers? Is there only one
solution in each case?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
This article for teachers suggests ideas for activities built around 10 and 2010.
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?
Unmultiply is a game of quick estimation. You need to find two
numbers that multiply together to something close to the given
target - fast! 10 levels with a high scores table.
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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.
Here is a picnic that Chris and Michael are going to share equally.
Can you tell us what each of them will have?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
Ahmed is making rods using different numbers of cubes. Which rod is
twice the length of his first rod?
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,. . . .
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
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.
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?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Choose a symbol to put into the number sentence.
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 work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
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!
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
Can you complete this jigsaw of the multiplication square?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
Here is a chance to play a version of the classic Countdown Game.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you arrange 5 different digits (from 0 - 9) in the cross in the
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Resources to support understanding of multiplication and division through playing with number.
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Imagine a pyramid which is built in square layers of small cubes.
If we number the cubes from the top, starting with 1, can you
picture which cubes are directly below this first cube?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
What is the sum of all the three digit whole numbers?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.