Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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,. . . .
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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?
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?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
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?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Here is a chance to play a version of the classic Countdown Game.
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!
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 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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
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.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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 happens?
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 lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
What is happening at each box in these machines?
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 require careful consideration.
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Find the next number in this pattern: 3, 7, 19, 55 ...
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
What is the sum of all the three digit whole numbers?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
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?
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 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?