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?

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?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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

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

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

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

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?

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?

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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?

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

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!

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

Is there an efficient way to work out how many factors a large number has?

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

Surprise your friends with this magic square trick.

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

Make some loops out of regular hexagons. What rules can you discover?

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

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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?

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?

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

These tasks give learners chance to generalise, which involves identifying an underlying structure.

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

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

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

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

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

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

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

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?

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

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

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

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

Can you figure out how sequences of beach huts are generated?

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