Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Given the products of adjacent cells, can you complete this Sudoku?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
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
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
56 406 is the product of two consecutive numbers. What are these
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
Here is a chance to play a version of the classic Countdown Game.
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
A game that tests your understanding of remainders.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you work out what a ziffle is on the planet Zargon?
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.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
What is happening at each box in these machines?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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 the number which has 8 divisors, such that the product of the
divisors is 331776.
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?
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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,. . . .