Lining up time
Page 1 
CANVAS & STRETCHER Lining up time: how many ways can you arrange the people in a portrait? 

Here is the portrait of David Garrick and his wife Eva Maria. The artist only has 2 ways to arrange them:
or


Now look at this picture with 3 men, each wearing a different coloured coat. The artist has shown them like this:
but he could have done:

Find the other ways he could have done it: 
green 


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How many different ways are there to arrange 3 people? 
Do you think one man looks more important than the other two or do all three look about equal? 

Here you have got:
The artist could have done
now find all the other ways: 
How many different ways are there to arrange 4 people? 
Charles is the smallest person in the picture. Where has the artist put him to make him look important? What else has the artist done to help you notice him? 
Page 3 

Work out some of the other ways they could sit. 
Now guess how many different ways they could sit (don't try to work out all of them). 
I guess  different ways 
Why did the artist choose Charles to be in the middle, do you think? 
Page 4 
Extension  

You are now going to look at some portraits with more people in. Don't try to count all the different ways to arrange them as there are hundreds of ways! For 6 look at the Tyers family. 

For 7 look at the Capel family. 

For 8 look at Guy Fawkes and the Gunpowder Plot conspirators. 
There is a way to work out how many ways to arrange a set number of people. 
Page 5 
Fill in this chart using the information you already have: 
1 person can be arranged 
1 
way  
2 people can be arranged in 
2 
ways  
3 people can be arranged in  ways  
4 people can be arranged in  ways  
5 people can be arranged in 
120 
ways 
How good was your guess for 5 people? 
Can you find a pattern which links the number of people with the number of ways they can be arranged? (CLUE  it's to do with multiplying, and you always use your last answer in the next sum). 
Page 6 
The pattern you have found is called the factorial for each number and is written !2. So !5 means 1 x 2 x 3 x 4 x 5 = 120

The Tyers family 
The Capel family 
The Gunpowder Plot 
The Tyers family, 6 people, can be arranged in  ways  
The Capel family, 7 people, can be arranged in  ways  
The 8 Gunpowder Plot conspirators can be arranged in 

ways 
If you arranged all the people in your class in a line, how many different ways could you do it?  you will need a calculator for this! 
Now make a portrait of a group of people in your class  how will you arrange them? 
Join and Support
Canvas & Stretcher:
The Capel's garden
William Jones & circles
William Hogarth's self portrait