Are these statements always true, sometimes true or never true?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

An investigation that gives you the opportunity to make and justify predictions.

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Can you find the chosen number from the grid using the clues?

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?

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

Can you find any perfect numbers? Read this article to find out more...

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Number problems at primary level that may require determination.

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Can you complete this jigsaw of the multiplication square?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

If you have only four weights, where could you place them in order to balance this equaliser?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Can you work out some different ways to balance this equation?