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GPS Alignment: Instructor Page
Week 5: Algebra - Patterns


Theater Seating (Printable PDF)

The Mathematics Theater has twenty-five seats in the first row, twenty-seven seats in the second row, twenty-nine seats in the third row, and so on. How many seats are in the theater if there are fifteen rows in all?

 

GPS

As seen in Problem Exploration

M6A2: Students will consider relationships between varying quantities.

a. Analyze and describe patterns arising from mathematical rules, tables, and graphs.
 

A spreadsheet or table can be used to consider the relationship between the number of seats in each row and the row number.
 

M7A1: Students will represent and evaluate quantities using algebraic expressions.

a. Translate verbal phrases to algebraic expressions.

b. Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate.
 

The pattern in this investigation can be written in the form of an expression in terms of the row number. The expression is s=25+(2*(n-1)) where s is the number of seats and n is the row number.
 

M7A2: Students will understand and apply linear equations with one variable.

c. Use the addition and multiplication properties of equality to solve one- and two-step linear equations.

The number of seats in each row is an arithmetic pattern, which can be written as a linear equation, s=25+(2*(n-1)) (which is the same as s=2n+23) where s is the number of seats and n is the row number.
 

M7A3: Students will understand relationships between two variables.

b. Represent, describe and analyze relations from tables, graphs, and formulas.
 

The number of seats in each row can be displayed in a table or spreadsheet and then analyzed. The number of seats in each row is an arithmetic pattern and can be expressed as a function. It can be written as s=25+(2*(n-1)) where s is the number of seats and n is the row number.
 

M8A1: Students will use algebra to represent, analyze, and solve problems.

b. Simplify and evaluate algebraic expressions.

c. Solve algebraic equations in one variable, including equations involving absolute values.
 

The number of seats in each row can be expressed as a function, s=25+(2*(n-1)) where s is the number of seats and n is the row number. Summing the values of the function from n=1 to n=15 will result in the solution to this investigation.
 

M8A3: Students will understand relations and linear functions.

i. Identify relations and functions as linear or nonlinear.

The number of seats in each row can be expressed as a linear function, s=25+(2*(n-1)) where s is the number of seats and n is the row number.