Fingers and hands
How would you count the number of fingers in these pictures?
Age
7 to 11
Challenge level
Problem
Here's something a little different ...
It is an opportunity to work with many aspects of mathematics.
It would be good to work with other people for this challenge.
You'll need to split up into five groups.
Each group will need to have copies of one of the pictures below. (This sheet contains one of each picture.)
In your group, find out how many fingers (including thumbs) there are in the picture you have been given.
Talk to others in your group about how you came to that total and compare your way with other people's ways. Make sure you agree on the number as a whole group.
You may like to record what you have done in some way.
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Swap pictures with another group.
How many fingers, including thumbs, this time? Did you change the way you worked it out?
Once again, talk to others in your group about how you each came to that total.
You could swap your pictures again and keep going until you have had a chance to see all five pictures.
As a class share the different ways that you counted.
Are there some ways that were more popular for particular pictures than others? Why was this, do you think?
There is another activity on NRICH, Alien Counting, which starts like this:-
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Well here are five Aliens, all from different planets.
They all count using one "hand" except the last one who uses his six tentacles.
So let me introduce them:
1st - Serious "Dubo" who counts in twos;
2nd - The two headed "Threebee" who counts in threes;
3rd - The laughing "Quort", who counts in fours;
4th - The green-headed "Chindi" who (you guessed it) counts in fives;
Finally - The four-eyed "Senda" counting in sixes.
What if Dubo, Threebee, Quort, Chindi or Senda had been there in the hand pictures instead of humans?
Which Aliens could be in which pictures if you wanted the total to be the same as with humans?
What numbers of fingers would there be if each human in each picture were to be replaced by an Alien of your choice?
Getting Started
You really need to be able to talk with someone else to do this
activity.
Are there other ways that you could count the fingers?
Are there other ways that you could count the fingers?
Student Solutions
We had many solutions to the numerical questions we posed. From the United Kingdom: Louis, Lucy and Gabriel from Ickford, Taylor from Hillocks, Kieran from Gosforth, Shane and Sameer from Haberdashers, Rohan from Canon Lane.
Charlotte from Laurence Jackson school sent in the following straight-forward ideas that resemble the other solutions sent in.
Solution $1$: count the number of hands and times that number by $5$ which is the number of fingers and thumb on a person's hand.
Solution $2$: simply count the fingers in the picture.
Luke from High Wycombe Maths Master Class sent in,
There are $250$ hands altogether if you count in $5$s it makes it much easier. Hint: the first picture has $30$.
Katrina, Abigail and Aiden from St. Andrew's sent in the solutions clearly as:
Picture $1 - 30$ fingers
Picture $2 - 40$ fingers
Picture $3 - 50$ fingers
Picture $4 - 60$ fingers
Picture $5 - 70$ fingers
We thought the best way to count the fingers was to count the hands in $5$s. You could count pairs of hands in $10$s or count the number of hands and multiply them by $5$ to get the number of fingers.
From the United States of America, solutions were sent in from Conor at Burr Elementary School and Caroline from Estes Hills.
Thank you all for your answers and we welcome any later ones as well.
Did any of you try the last part of the problem, where the challenge was to count using aliens' hands? Do let us know if you've had a go.
Teachers' Resources
Fingers and Hands
Here's something a little different ...
It is an opportunity to work with many aspects of mathematics.
It would be good to work with other people for this challenge.
You'll need to split up into five groups.
Each group will need to have copies of one of the pictures below. (This sheet contains one of each picture.)
In our group, find out how many fingers (including thumbs) there are in the picture you have been given.
Talk to others in your group about how you came to that total and compare your way with other people's ways. Make sure you agree on the number as a whole group.
You may like to record what you have done in some way.
Image
Image
Image
Image
Image
Swap pictures with another group.
How many fingers, including thumbs, this time? Did you change the way you worked it out?
Once again, talk to others in your group about how you each came to that total.
You could swap your pictures again and keep going until you have had a chance to see all five pictures.
As a class share the different ways that you counted.
Are there some ways that were more popular for particular pictures than others? Why was this, do you think?
There is another activity on NRICH, Alien Counting, which starts like this:-
Image
Well here are five Aliens, all from different planets.
They all count using one "hand" except the last one who uses his six tentacles.
So let me introduce them:
1st - Serious "Dubo" who counts in twos;
2nd - The two headed "Threebee" who counts in threes;
3rd - The laughing "Quort", who counts in fours;
4th - The green-headed "Chindi" who (you guessed it) counts in fives;
Finally - The four-eyed "Senda" counting in sixes.
What if Dubo, Threebee, Quort, Chindi or Senda had been there in the hand pictures instead of humans?
Which Aliens could be in which pictures if you wanted the total to be the same as with humans?
What numbers of fingers would there be if each human in each picture were to be replaced by an Alien of your choice?
Why do this problem?
This activity has been designed for pupils to work on in a group so that they share their thoughts and ideas with others.
Possible approach
Split the class into five groups and give each group one of the pictures from this sheet. (It may be useful to have multiple copies of each picture, depending on the number of children in a group.)
To begin with, allow time for everyone individually to work out the total number of fingers, including thumbs, on their picture. Then encourage them to discuss their methods amongst the whole group. You could suggest that each group makes a poster which explains all the different ways of counting that they have used.
Rotate the pictures so that each group now has a new picture. Once again, ask them to work out the total number of fingers, then to share methods again. If new ways of working out the answer have been used, these could be added to the poster.
Once all the pictures have been seen by every group, you can bring the whole class together. They could display their posters and everyone could have time to look at the other groups' posters. Then, ask them to comment on what they have done and seen. Were there some methods that lots of people used? Why do they think that is? Were there some methods that they wouldn't have thought of? Did
any of them change the way they worked out the total number of fingers for different pictures? Why?
It may be that questions arise that can be followed through to a greater depth or you could use the alien context at the foot of the problem to challenge the children to find the totals with some of the aliens' hands.
Key questions
Tell me what you think.
How did you work out the total?
Do you agree with what s/he said?
Why?
Can you tell others about that?
Possible extension
In addition to considering Alien hands, this activity could be extended further into the aliens counting in different bases according to the number of fingers they have on a hand.
Possible support
Some pupils may benefit from having some paper cut-outs of hands.