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Ledyard Mathematics Department

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 two-step equations to multi-step equations. Students then extend these concepts to solving one and two-step 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

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

  1. How can real-world problems be modeled using equations and inequalities? (ARCore:1.3a)

Benchmarks

The student will be able to:

  1. 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)

  1. 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)

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

  1. Analyze a real-world 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)

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

  1. Students will model a “break-even” 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)

  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

  1. 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. 24-26.  See appendix.  (F1, ARCore:1.3a.2)

Assessment Tasks

  1. Required activities above.

  1. Teacher generated tests and quizzes that align to unit benchmarks, focus questions and the essential question.

Instructional Resources and Materials

Calculator (TI-30XIIS)
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
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Approved by Instructional Council 6/05/06.