56 406 is the product of two consecutive numbers. What are these two numbers?
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 the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you work out what a ziffle is on the planet Zargon?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
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. . . .
What is the least square number which commences with six two's?
Can you replace the letters with numbers? Is there only one solution in each case?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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 complete this jigsaw of the multiplication square?
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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
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?
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?
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?
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?
Number problems at primary level that require careful consideration.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
If the answer's 2010, what could the question be?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Number problems at primary level that may require determination.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Choose a symbol to put into the number sentence.
What is happening at each box in these machines?
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!
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 number has 903 digits. What is the sum of all 903 digits?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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 pile.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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,. . . .
Find the next number in this pattern: 3, 7, 19, 55 ...
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.