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?

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

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

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

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

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?

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

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

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

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

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

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?

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

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?

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

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?

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

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

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

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

What happens when you round these numbers to the nearest whole number?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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?

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

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?

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

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

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

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

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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?

Ben and his mum are planting garlic. Can 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?

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

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

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

It starts quite simple but great opportunities for number discoveries and patterns!

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

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

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

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

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?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

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.