Investigate and Describe Patterns

Discover the Math8.1

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

Sports Banquet Pattern

The arrangement pattern is below:The circles show where guests can sit.

How many guests can sit in each arrangement?

1 Table 2 Tables 3 Tables

6 10 14

Sports Banquet PatternCan you draw the next two patterns?What would an arrangement of 4 tables look like? 5?How many people could be seated at each?

1 Table 2 Tables 3 Tables

4 Tables 5 Tables

10 146

18 22

Sports Banquet Pattern

Can you predict how many people can sit at 10 tables? At 20?

Sports Banquet Pattern

Here is the visual for 10 and 20 tables

42 people

82 people

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!

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

10

14

18

22

Do you notice any patterns?

+4

+4

+4

+4

4282

Can you use that pattern to predict the number of guests at 10 and 20 tables?

Sports Banquet PatternCan you describe the pattern you notice in words?Why did I make the chairs at the ends a different colour?

1 Table 2 Tables 3 Tables

4 Tables 5 Tables

10 146

18 22

Sports Banquet Pattern

What is constant or the same in every picture?

1 Table 2 Tables 3 Tables

4 Tables 5 Tables

10 146

18 22

Sports Banquet Pattern

How does the number of blue chairs relate to the table number?

1 Table 2 Tables 3 Tables

4 Tables 5 Tables

10 146

18 22

Is this the pattern?

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

4t + 2Let’s test this

expression with our information

Test the expression with our organized information

Number of tables

Number of guests

1 62 103 144 185 22

10 4220 82

822204

422104222541824414234102246214

solve! andnumber our tablewith

t"" Replace24

t

Now let’s graph it!