Algebra 1

Unit 1: Representing Functional Relationships

In this unit, students learn about the concept of function and use function notation. Students also develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. All of this work is grounded on understanding quantities and on relationships between them.

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What will my child learn?

Students will:

Understand the concept of a function and use function notation.
F.IF.A.1
Understanding that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.  If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.  The graph of f is the graph of the equation y = f(x).

• Background Info.
• Check for Understanding: Domain of a Function | Range of a Function

• Enrichment Tasks: Domains | Points on a Graph

F.IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

• Background Info.
• Check for Understanding: Evaluating Expressions with Function | Understanding Function Notation

• Enrichment Tasks: Using Function Notation II | Random Walk II

Create equations that describe numbers or relationships.
A.CED.A.2
Create linear equations to represent relationships between quantities; graph equations on coordinate axes with labels and scales (SAT® Content - HOA.01 | HOA.05).

• Background Info.
• Check for Understanding: Modeling with Two-Variable Equations

• Enrichment Tasks: Silver Rectangle | How Much Folate? 

Represent and solve equations and inequalities graphically.
A.REI.D.10
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

• Background Info.
• Check for Understanding: Interpreting Graphs of Linear and Nonlinear Functions

• Enrichment Task: Collinear Points

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What are some signs of student mastery?

• Determines if a given relation is a function.
  
• Evaluates with, uses and interprets with function notation within a context.
• Given a context, writes and analyzes a linear function.
• For linear functions that model contextual relationships, determines and interprets key features, graphs the function, and solves problems.
• Graphs and analyzes the solution sets of equations, linear inequalities and systems of linear inequalities.

Tools and Technology
The Algebra Balance Scale tool (National Library of Virtual Manipulatives) helps reinforce a "sense of balance" when reasoning about equations. This online tool allows you to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, you can choose to perform any arithmetic operation with whole numbers and multiples of the variable 'x', as long as you DO THE SAME THING TO BOTH SIDES, thus keeping the beam balanced. The goal, of course, is to get a single X-box on one side, with however many unit blocks needed for balance, thus giving the value of X.

Note: This tool requires Java.

More 4 U
Watch a portion of a lesson on Modeling Expressions and Equations.

Source: The Teaching Channel

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