Essential Question:  How do proportional reasoning and variation help me determine the relationships between data?

Unit Rationale:  Understanding and applying proportional reasoning and variation is the foundation for solving and modeling linear equations.

As a result of this unit, students will be able to:

Ø  Set up, solve, and use proportions to identify an unknown number or to make predictions from data.

Ø  Use direct and indirect variation equations, tables, and their graphs to solve real-world problems, including problems involving units of measure and rates.

Ø  Solve equations using the “undoing” method

Vocabulary:

·         Accuracy

·         Constant

·         Direct Variation

·         Expression

·         Inverse variation

·         Proportion

·         Proportional

·         Rate

·         Ratio

·         Rational number

·         Term

·         Variable

 

Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements. 

Focus Standards:

*A1.1.A Select and justify functions and equations to model and solve problems.

Supporting Standards:

*A1.1.B  Solve problems that can be represented by linear functions, equations, and inequalities.

*A1.2.B  Recognize the multiple use of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables.

A1.2.D  Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection.

*A1.3.B  Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations.

*A1.2.B  Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables.

*A1.4.A  Write and solve linear equations and inequalities in one variable.

Reasoning, Problem Solving, and Communication Standards:

A1.8.A  Analyze a problem situation and represent it mathematically.

A1.8.D  Generalize a solution strategy for a single problem to a class of problems, and apply a strategy for a class of related problems to solve specific problems.