Investigate and Describe Patterns

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Students describe repeating and changing patterns using words.

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Presentation transcript:

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 3 Tables 1 Table 2 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 3 Tables 1 Table 2 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!

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

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

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

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

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

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

Now let’s graph it!