1. Investigate and Describe Patterns
Discover the Math
8.1

2. Sports Banquet Pattern
Gilles and Aceena are arranging an academic and sports banquet.
They want to know how many guests can be seated in different table arrangements

3. Sports Banquet Pattern
The arrangement pattern is below:
The circles show where guests can sit. 6 10 14
3 Tables
1 Table
2 Tables
How many guests
can sit in each arrangement?

4. Sports Banquet Pattern
Can you draw the next two patterns?
What would an arrangement of 4 tables look like? 5?
How many people could be seated at each? 6 10 14
3 Tables
1 Table
2 Tables 18 22
4 Tables
5 Tables

5. Sports Banquet Pattern
Can you predict how many people
can sit at 10 tables? At 20?

6. Sports Banquet Pattern
Here is the visual for 10 and 20 tables
42 people
82 people

7. Sports Banquet Pattern
Is there a way to figure this out
without drawing the pattern?
Organize the information you have?
Yeah! …and look for a pattern in the numbers!

8. Do you notice any patterns?
Let’s arrange the information we already have for this pattern in a table.
Number of
tables
Number of guests 1 2 3 4 5 10 20 6 +4 10 +4 14
Do you notice any patterns? +4 18 +4 22
Can you use that pattern to predict the number of guests at 10 and 20 tables? 42 82

9. Sports Banquet Pattern
Can you describe the pattern you notice in words? Why did I make the chairs at the ends a different colour? 6 10 14
3 Tables
1 Table
2 Tables 18 22
4 Tables
5 Tables

10. Sports Banquet Pattern
What is constant or the same in every picture? 6 10 14
3 Tables
1 Table
2 Tables 18 22
4 Tables
5 Tables

11. Sports Banquet Pattern
How does the number of blue chairs relate to the table number? 6 10 14
3 Tables
1 Table
2 Tables 18 22
4 Tables
5 Tables

12. Sports Banquet Pattern
So…4 chairs for each table plus the 2 on the ends!
Can we write this symbolically?
4 x the number of tables + 2
Let’s use “t” to stand for the number of tables
Is this
the pattern?
4t + 2
Let’s test this expression with our information

13. with our organized information
Test the expression
with our organized information
Number of
tables
Number of guests 1 6 2 10 3 14 4 18 5 22 42 20 82

14. Now let’s graph it!