In the playground
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Age
5 to 11
Challenge level
Problem
It might be helpful to have someone else to collaborate with on
this activity, as it will be good to talk about your ideas.
Here is the question we would like you to work on:
Of course this will depend on your school but we would like to hear about the statements you make and how you come up with them.
Here is the question we would like you to work on:
What can you say about the child who is first onto the playground tomorrow morning break time?
Of course this will depend on your school but we would like to hear about the statements you make and how you come up with them.
Getting Started
Is there anything you know for certain about the child who is first
on the playground?
Do you know whether it will be a boy or a girl?
Do you know whose class s/he is in?
Do you know whether it will be a boy or a girl?
Do you know whose class s/he is in?
Student Solutions
We had a good many responses to this question that showed a great variety.
During 2015 we had these suggestions from Squirrels class in Meadowbrook Primary School who said
We think the class who sit nicest in assembly will go first to break.
We think that the person who sits at the end of the row will go first to the playground.
The person who sits near the door might go to the playground first.
Livvy thinks it will be a girl because boys get sent back because they are running!
Elbadri disagrees because he can walk super fast in a stealthy way and not get caught!
We hope you like our ideas!
Mrs Barbour and Squirrels class
Thank you very much for these interesting ideas.
We had Ajit from Visakha Valley School in South East India remarking that;
1. If the child is a boy then he jumps in the playground with joy. He thinks what will he receive as a prize.
2. If the child is a girl then she runs around the playground shaking hands in the air like a fan.
We had Freddy from Bansted Junior School (UK) who said that it would be a child who finished his work quickly.
Other responses took into consideration their own school special circumstances. So for example, James from Loughview School in Belfast (Northern Ireland), wrote;
The answer depends on the day of the week because each day a different group gets sent out first. It also depends on whether the other class comes out before our class.
Also considering their school was Aaron from St. Munchins in the Republic of Ireland who wrote;
I think it is Calvin because he is sitting next to the door.
The fifth class teacher always lets her class out on time.
I also think it is a boy in fifth class because they are the first class upstairs so they have a better chance of getting out first before any other class in the school.
The majority of the class has dark hair so it is most likely to be a boy with dark hair.
I think it is a boy because we are excluding girls because it is an all boys school.
Henry from Moulsford on Thames in England thought about his school situation and said;
I think it might be a boy in 3c because they finish early and race off. It could be Toby because he always likes to be first. The first boy in the playground won't have had his drink and biscuits.
Ben and Niall from Pownall Hall School in England gave it some hard thinking and said;
We thought of lots of ideas about who would be in the playground first.
We wrote them on pieces of paper and then we put the ideas in order with the most likely one first.
Here are our ideas:
1 It may be a person with the nearest classroom.
2 It may be someone energetic.
3 It may be someone who is a quick worker.
4 It could be someone who knows when breaktime is.
5 It could be someone who wants to start playing.
6 It could be someone really quick.
Well done to all of you who sent in your suggestions, I am sorry there is not room for them all. They all showed good thinking around this question that required no arithmetic skills. Please do keep trying the challenges and sending in your responses.
Teachers' Resources
Why do this problem?
This activity is very appropriate when starting off the topic of probability with young children. It gives pupils the opportunity to make their own decisions, and discover some important issues in this area of mathematics.
Possible approach
This task is probably best approached through a whole-group discussion. Learners will need to listen to each other's ideas and decide on the features of the school that affect the question. So, you will probably need to act as a catalyst and then a chairperson to allow pupils' ideas to flow.
Pose the question: "What can you say about the child who is first onto the playground tomorrow morning break time?", adapting it appropriately to suit your circumstances. You are likely to hear comments like:
"It will be someone in Miss Brown's class because she always lets her children out a little early."
"It will be a girl because I think there are a lot more girls than boys in this school."
"It will be a tall child because I've seen several tall children push their way to the front."
"It will be someone from Class 3 because their classroom is nearest the play ground." etc ...
Encourage pupils to justify their suggestions. Is there anything we know for certain about the child? Is there anything we can say is very likely? Very unlikely? How do we know? You could also challenge children to explain how they could become more certain about the 'characteristics' of the child first in the playground.
(I did, on one occasion, have the discussion come to a sudden stop when one girl said, "I know who it will be ? it'll be me because it's my turn to go onto the playground and ring the hand bell!")
It may be appropriate to record the group's ideas on individual strips of paper. (You could then order them from which they think are certain to be true and which they think are unlikely to be true.) The children will want to watch out at the appropriate time the next day to see who it is and then you can have a discussion about which predictions were correct.
Key questions
Tell me about your thoughts.
Can you tell me why you think that?
How could we be more certain?
Possible extension
The pupils themselves are likely to come up with some further ideas for investigation. It may be that some want to conduct a survey about the first person on the playground over a few days so that they can make more accurate predictions on a future date. (See also The Car that Passes.)
Possible support
Some pupils may need help expressing their thoughts so you may need a few particular questions to get them started, such as "will it be a boy or a girl?"; "do we know which class s/he is in?" etc.You can read about some of the issues which might arise when teaching probability in this article.