Transcript Investigate and Describe Patterns

Investigate and Describe Patterns
Discover the Math
8.1
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.
6
10
14
1 Table
2 Tables
3 Tables
How many guests
can sit in each arrangement?
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
1 Table
2 Tables
3 Tables
18
22
4 Tables
5 Tables
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.
Do you notice any
patterns?
Can you use that
pattern to predict the
number of guests at
10 and 20 tables?
Number Number
of
of
guests
tables
6
1
2
10
3
14
+4
+4
+4
4
18
+4
5
22
10
42
82
20
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
1 Table
2 Tables
3 Tables
18
22
4 Tables
5 Tables
Sports Banquet Pattern
What is constant or the same in every picture?
6
10
14
1 Table
2 Tables
3 Tables
18
22
4 Tables
5 Tables
Sports Banquet Pattern
How does the number of blue chairs relate to the table number?
6
10
14
1 Table
2 Tables
3 Tables
18
22
4 Tables
5 Tables
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
Let’s test this
expression with our
information
4t + 2
Is this
the pattern?
Test the expression
with our organized information
4t  2
Replace " t"
with our table number
and solve!
41  2  6
42   2  10
43  2  14
44   2  18
45  2  22
410   2  42
420   2  82
Number of
tables
1
2
3
4
5
10
20
Number of
guests
6
10
14
18
22
42
82
Now let’s graph it!