1. No… not of the romantic kind … Relationships of the algebraic kind

2. Seating Arrangements How many people can sit around a row of 9 tables?
How many tables would be needed for a party of 30 people?
A giant street party has 49 tables in a row. How many people can sit round this?
My street has 258 people living in it. How long would the row of tables need to be?

3. What does many tables look like? Continuing the pattern

4. Make up a table showing the number of tables and people around the tables1 2 3 4 5

5. Draw a graph showing the number of people versus the number of tables for up to 10 tables
What should be the label on the horizontal axis?
What should be the label on the vertical axis?
Where should you put the numbers on the horizontal axis?
Can we start each axis at zero?
Do you have the same gap between each number on your horizontal axis?
Approximately how high does the vertical axis need to go?
If there were 6 people around every table how many people would there be for 10 tables?
Will the vertical axis need to be taller or shorter than this?

6. Draw a graph showing the number of people versus the number of tables for up to 10 tables
If we use one square per person the graph will be VERY tall and skinny.
How can we make the graph fit on the page?
For 2 tables how many people are there? Where should this point go?
Can you draw a straight line through your points?
If one of your points is not on the straight line, what does this suggest?

7. Draw a graph showing the number of people versus the number of tables for up to 10 tables
Use your graph to find how many people can sit around a row of 9 tables. Use your graph to find how many tables would be needed for a party of 30 people.
Where is the point representing the number of people for 9 tables? Can you mark this on the line? Can you trace across to the vertical axis to find how many people?
Where is the point representing the number of tables for 30 people? Can you mark this on the line? Can you trace down to the horizontal axis to find how many tables?
Can you use your graph to find how many people fit around 49 tables?

8. Coming up with a relationship between the number of people and the number of tables
What is the relationship between the number of people and the number of tables?
Think about people at the ends of the tables….
Think about people on the sides of the tables…
Joneen has written p = 4t + 2 and Melissa has written p=6+4(t-1). Who is correct?

9. Coming up with a rule to describe the relationship between the number of people and the number of tables
What letter shall we write instead of “number of people”? What letter shall we write instead of “number of tables”?
Use your equation to find how many people can sit around 9 tables, 49 tables.
Use your equation to find how many tables are needed for 258 people.