Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Try out this number trick. What happens with different starting numbers? What do you notice?

Find the sum of all three-digit numbers each of whose digits is odd.

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

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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?

Here are two kinds of spirals for you to explore. What do you notice?

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

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?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

This task follows on from Build it Up and takes the ideas into three dimensions!

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

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?

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.

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

This challenge asks you to imagine a snake coiling on itself.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

This challenge is about finding the difference between numbers which have the same tens digit.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

This activity involves rounding four-digit numbers to the nearest thousand.

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

What happens when you round these three-digit numbers to the nearest 100?

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?