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# Tables and Seats

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1. Do the problem "Tables and Seats" in this topic. As you work on the problem, see if you can arrive at your solution from several different approaches. Upload your completed solution and methods.

2.Reflect on the aspects of algebraic thinking you discovered in the problem that were applicable to your problem-solving strategies. What algebraic thinking did you engage in when solving this problem? ( at least 200 words)

https://brainmass.com/math/linear-algebra/using-algebraic-thinking-problem-solving-562636

## SOLUTION This solution is FREE courtesy of BrainMass!

Algebraic Thinking

The first question to ask is "What is algebraic thinking?" There are two components to the answer to that question. The first is the development of mathematical thinking tools. The second component is the study of fundamental algebraic ideas. Problem-solving, representation skills, and reasoning skills are all examples of mathematical thinking tools. Fundamental algebraic ideas then represent the framework in which those tools develop.

When looking at the table and chairs problem, mathematical thinking tools were in use. It required the ability to problem solve using the pictorial representation of the tables. Before the equation could be formulated, the picture representation allowed the brain to problem solve how many people could be seated when the tables were pushed together. By visualizing more and more tables being added, the formula was able to be brought together. The formula could then be tested using the pictures provided of the hexagon and trapezoid. Side note: the trapezoid was able to be used to show that the formula works not based on the number of sides of the table, but the number of seats the table accommodates. This allowed the brain to visualize and devise the second equation, which then notated the number of seats in relation to the tables and the number of people total that could be seated.

Solution

4. 2t + 2 = number of people that can be seated, where t is the number of tables

So, going back to the first three questions:

1. Using the equation, 2t + 2 = 12, solve for t

2t + 2 = 12
-2 -2 subtract 2 from both sides
2t = 10
/2 /2 divide both sides by 2
t = 5

Number of tables needed is 5.

2. How many tables for 18? Using the same equation, but have it equal 18:

2t + 2 = 18 Solve the same way as above
t = 8

3. This question already has the number of tables, but it's looking for number of people

2(20) + 2 = number of people
40 + 2 (multiple 2 and 20, then add 2)
42 = number of people

For a hexagon, the equation changes to 4t + 2

For a trapezoid, it changes to 3t + 2

For all tables, you can use the formula:

(s-2)t + 2 = p

Where s is the number of seats at one table by itself, t is the number of tables, and p is the number of people total seated.

Site Source:

Krigler, S. "Mathematics Content Program for Teachers." UCLA Department of Mathematics. January 2000.

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