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

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?

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

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

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?

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

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?

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

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

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

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

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

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?

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

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

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

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?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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

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

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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

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

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

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

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

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

Got It game for an adult and child. How can you play so that you know you will always win?

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

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

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

Ben’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?

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

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

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?

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

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?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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

Watch this animation. What do you see? Can you explain why this happens?

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

Nim-7 game for an adult and child. Who will be the one to take the last counter?