Integrated Mathematics II
Unit 2: Equations and Inequalities
Abstract
In this unit students will learn how to solve linear equations and inequalities involving one variable. Linear equations are a common model for real world problem solving and many such problems are incorporated in the unit. As students work through the unit, they progress from solving one and twostep equations to multistep equations. Students then extend these concepts to solving one and twostep linear inequalities. They will also draw connections between algebraic solutions to linear equations and inequalities with their graphical solutions.
Essential Question: How do patterns and functions help us to describe data and physical phenomena and solve a variety of problems?
Focus Questions

How are equations and inequalities used to solve a variety of problems? (ARCore:1.3a)

How can realworld problems be modeled using equations and inequalities? (ARCore:1.3a)
Benchmarks
The student will be able to:

Solve and check solutions of linear equations involving one or more steps, identifying and correcting errors as necessary. (F1, ARCore:1.3a.1, 1.3a.2)

Solve and check solutions of linear inequalities involving one or more steps, identifying and correcting errors as necessary. (F1, ARCore:1.3a.1, 1.3a.2)

Simplify an algebraic expression. (F1, ARCore:1.3a.2)

Analyze a realworld problem by developing an algebraic representation, solving it, and evaluating the solution in writing. (F2, ARCore:1.3a.1)
Technology Education Framework Connection
Content Standards 5, 7
Required Activities (Common Experiences)

Use algebra tiles or colored index cards as visual aids to model and solve algebraic equations. (F1, ARCore:1.3a.1, 1.3a.2)

Students will model a “breakeven” type of problem by generating a table of values based on an equation or inequality. Students will solve the problem and defend their approach and solution in writing. (e.g. CAPT release Fame and Fortune) (F2, ARCore:1.3a.1)

Students model the depreciation of a vehicle with an algebraic equation. Students use the model to calculate car value over time. (e.g. 2004 CAPT release item, “Car Depreciation”) (F2, ARCore:1.3a.1)
Suggested Activities

Using construction software students experiment with a sketch that graphically illustrates the distributive property in order to simplify algebraic expressions. Exploring Algebra with Geometers’ Sketchpad, p. 2426. See appendix. (F1, ARCore:1.3a.2)
Assessment Tasks

Required activities above.

Teacher generated tests and quizzes that align to unit benchmarks, focus questions and the essential question.
Instructional Resources and Materials
Calculator (TI30XIIS)
Algebra Tiles
Exploring Algebra with Geometers’ Sketchpad
Geometers’ Sketchpad software
Prentice Hall Mathematics Course 3
Connections
Science  Apply formulas to natural phenomena
Accounting  Modeling profit
Pacing
This unit is expected to take approximately seven class periods under the block schedule.
Notes to Teachers:
Approved by Instructional Council 6/05/06.
