# Table Building/Patterns and Equations

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```					Name _______________________________ Date ________________ Period _____________

Matthew’s Party
Donna is planning a surprise birthday party for her son, Matthew. She has rented a tent for the
backyard and plans to set up hexagonal tables for the dinner. Each table seats 6 people.
6, 12, 18, 24, 30, 36…
1. Complete the table below to show the relationship between the number of hexagonal tables
and the number of people who can be seated for dinner.

# of Hexagonal              # of People
Verbal                                        Process
Picture                                                    Tables                  (Value of
Description                                     Column
(Position/Term #)                Term)
When 1 hexagonal table is set up, 6
1                        6
people can be seated.

When 2 hexagonal tables are set
2
up, ___ people can be seated.

When 3 hexagonal tables are set
3
up, ___ people can be seated.

4

5

6

When n hexagonal tables are set
n
up, ___ people can be seated.

Rule: ____________                       Equation: ____________

Use the table above to answer the following questions.

2. How did you find the rule which describes the relationship between the number of hexagonal
tables and the number of people who can be seated in the vertical table?

3. If Donna sets up 22 hexagonal tables in her backyard, how many people can be seated for
dinner?

4. Donna wants to invite 58 people to the birthday party and plans to set up 9 hexagonal tables.
Will there be enough seating if all 58 people come to the party? Explain.
Matthew’s Party
Donna is planning a surprise birthday party for her son, Matthew. She has rented a tent for the
backyard and plans to set up hexagonal tables for the dinner. Each table seats 6 people.

6, 12, 18, 24, 30, 36…

5. Complete the graph below to show the relationship between the number of hexagonal tables
and the number of people who can be seated for dinner.
# of People

# of Hexagonal Tables

Use the graph above to answer the following questions.

6.   Write a sentence describing the relationship between the number of hexagonal tables and
the total number of people who can be seated for dinner.

7.   Would the ordered pair (0, 0) make sense for this scenario? Explain.

9.   Donna wants to invite 80 people to Matthew’s birthday party, including Matthew and his
immediate family. Donna plans to set up 14 tables. Will there be enough seating if all 80
people show up for the party? Explain.

```
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