Sitting Round the Party Tables
1 out of 3
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Problem
Sitting Round the Party Tables printable sheet
Some children are at a party. They are sitting around a square table like this:
What do you notice?
You might like to focus on:
- The number of sweets that are given out altogether
- The total number of sweets that children sitting opposite each other are given
- The total number of sweets that children sitting diagonally opposite each other are given
- Or something else!
There are other similar parties happening at the same time. They have bigger square tables with more children sitting around them - perhaps 3 children on each side, or maybe more.
Draw some of these tables. What do you notice? You can choose one of the areas above to focus on, or you might have your own ideas about what to investigate.
Once you've thought about that, you might like to explore what happens with five- and six-sided tables like these:
Getting Started
You could use some practical equipment to help you work on this problem, such as counters.
Are there any special things you notice about the seats in particular places?
Student Solutions
We had some really good ideas sent in, some that were illustrated well using the computer. From Kent College we had Primrose and Charlotte, Sophie and Nia, Stephanie, Nandini and Hazel.
Well here we have a superb piece of work, sent in by Abi and Charlotte from the same school, that I would advise people to look at for working investigatively on this activity.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This activity gives pupils the opportunity to explore some simple number relationships, from which they can be encouraged to make some generalisations. It may also be a good context in which to help pupils ask their own questions - "I wonder what would happen if we ...?" showing their curiosity. You will be aware that a lot of perseverance is helpful in solving this challenge. The "Teacher Support" at the bottom of this page is recommended in regard to the curiosity aspect of this task.
Possible approach
With younger pupils or those with little experience of exploration in mathematics and talking about their mathematical thoughts, it would be good to act out the problem as first described.
With more experienced pupils you could just present the challenge orally and ask them to explore further. Encourage learners to write down all the things they notice. It might also be appropriate for you to bring everyone together after some time to discuss how they are recording their work.
Invite pupils to ask and begin to answer their own questions: "I wonder what would happen if I ...?". You could use some of the suggestions in the problem itself to prompt those who may not be used to doing this.
Key questions
Tell me about what you have noticed about the numbers of sweets.
What else are you going to explore?
Tell me about what's going on at the other party tables.
Are there any special things you notice about the seats in particular places?
Possible extension
Some pupils might look at generalisations that they can say about tables of ANY size or of ANY shape.
Possible support
Some pupils may find it helpful to approach the problem using practical equipment, for example using counters to represent the sweets and having 'tables' made out of paper or card.
Teacher support
This task was created to help in the pursuance of curiosity within mathematics lessons.
Help may be found in the realm of curiosity in watching parts of these excellent videos.
Firstly "The Rise & Fall of Curiosity", particularly the extract [23.50 - 37.15] on "adult encouragement answering and teacher behaviour."
Secondly, "The Hungry Mind: The Origins of Curiosity", particularly the extract [8.22 - 12.29] on "Children asking questions."