Nrich maths factors and multiples game

Notice how some questions are open, and some are closed. Some will take a matter of minutes, other a number of lessons. Some will be suitable for one group of students, and others for another group.

But with a bank of these up my sleeve, I can confidently walk around the room, see how different students are getting on with the game, and select the question to give them to challenge and engage them. As I say, if everyone reading this can come up with one question, posted in the comments, we will soon build up a huge collection that could keep this excellent task going for a good few lessons. Feel free to change any aspect of the game, be it the rules, the grid size, whatever you like.

Let you imagination run wild. And at the end of the month, I will compile the activity and questions together into a lovely PowerPoint and share it will you all. So, please spread the word. What is the smallest number of turns before you can choose a number which is neither a factor nor a multiple of the original number?

Just thought of another one myself… What is the longest bigger-smaller-bigger-smaller-bigger-etc sequence you can make? How many prime numbers will automatically end the game when 1 has been removed from play?

Also what is the smallest prime number that will end the game when you have removed 1? What if the grid was only made on even numbers — is the best starting number still the same for your winning strategy?

What if they choose 7? What if they choose 37? Exploring, questioning, working systematically, visualising, conjecturing, explaining, generalising, justifying, proving are all at the heart of mathematical thinking. NRICH promotes the learning of mathematics through problem solving.

NRICH provides engaging problems, linked to the curriculum, with support for teachers in the classroom. Working on these problems will introduce students to key mathematical process skills. They offer students an opportunity to learn by exploring, noticing structure and discussing their insights, which in turn can lead to conjecturing, explaining, generalising, convincing and proof.

They assume that teachers will aim to do for students only what they cannot yet do for themselves. As a teacher, consider how this particular lesson idea can provoke mathematical thinking.

How can you support students' exploration? Which pairs of cogs let the coloured tooth touch every tooth on the other cog?

Which pairs do not let this happen? Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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. In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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. Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers? This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box? Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm?

How about when a friend begins a new rhythm at the same time? If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud? 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? Can you work out how to make each side of this balance equally balanced?

You can put more than one weight on a hook. How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical? Can you find a cuboid that has a surface area of exactly square units. Is there more than one? Can you find them all? Ben, Jack and Emma passed counters to each other and ended with the same number of counters.

How many did they start with? 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?