Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?
What do you notice about these squares of numbers? What is the same? What is different?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
If the answer's 2010, what could the question be?
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!
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 next number in this pattern: 3, 7, 19, 55 ...
Investigate what happens when you add house numbers along a street in different ways.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.
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.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
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!
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?
Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
Find a great variety of ways of asking questions which make 8.
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
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?
Number problems for you to work on with others.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
This number has 903 digits. What is the sum of all 903 digits?
Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
What is the sum of all the three digit whole numbers?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?