UNIT: Prentice Hall Course 2, Chapter 2

Title: Solving One Step Equations: 2.3 and 2.4

By: Coral Quackenbush

Grade Level: 6th Grade Advanced Mathematics
Classroom Layout: A lab setting would be preferred. Students can share laptops, or if laptops are not available, the teacher can model the dynamic worksheets using the LCD and their computer.

Pre-requisite Knowledge: Students should have a basic understanding of Geogebra Dynamic Worksheets and how to use sliders.Teachers should understand how to utilize Power Point and Geogebra in the classroom. Students should know the order of operations, as well as operations with integers.

Students should also know how to combine like terms.

Summary:Students will investigate balancing equations using the sliders on the dynamic worksheet. They will then make a conjecture based on their observations.

Objective: Students will learn to solve one-step equations with inverse operations.

Content: Use the provided power point presentation to begin class with Warm Up and Homework correction. Introduce the lesson using the Dynamic Worksheet as a hyperlink from the Power Point Presentation. If you do not have individual laptops for the students, you can have them interact with the Dynamic Worksheet using the LCD projector. Students will use the slider to change the value of the variable until the equation is balanced. Each equation has a slider that will be moved to illustrate the solution to the equation. During this investigation, students will make generalizations about balancing an equation and inverse operations.

Materials:LCD projector, Laptop (teacher), Student Laptops (optional). If students do not have laptops, the teacher can model the activity with the LCD projector.

SunshineState Standards:

MA.A.3.3.1 The student understands and explains the effects of addition, subtraction, multiplication, and division on whole numbers, fractions, including mixed numbers and decimals, including the inverse relationships of positive and negative numbers

MA.A.3.3.3The student adds, subtracts, multiplies, and divides whole numbers, decimals, and fractions including mixed numbers to solve real-world problems using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

MA.D.2.3.1The student represents and solves real-world problems graphically, with algebraic expressions, equations, and inequalities.

MA.D.2.3.2The student uses algebraic problem-solving strategies to solve real-world problems involving linear equations and inequalities.

Key Words: Equation, Inverse Operation

LESSON PLAN

Introduction to the Lesson

Historical Background

Equations that have exactly the same solution or solutions are called equivalent equations. Solving a given equation is essentially a process of writing a series of equivalent fractions until the variable is isolated by itself on one side of the equal sign. The equivalent equations that will achieve this goal are determined by a thoughtful application of the properties of equality. The properties of equality are sometimes summarized informally as follows: Whatever you do to one side of an equation, you must do to the other.

Anticipatory Set

To introduce students to this lesson, begin a discussion of friends borrowing and paying back money. Discuss that when they are “paid back” they have balanced out the equation.

Explanation of Math Involved

At this point, students know the order of operations: PEMDAS. When solving equations they must follow the inverse order of operations: “SADM”, which is undo all subtraction and addition first, then undo the division and multiplication.

Instructional Methods

Step by Step Procedure

  • Introduce the lesson with the United Streaming Video Clip.
  • The first student activity is a dynamic worksheet with Geogebra.

*If you are using student laptops, you must load the files onto each individual computer and be sure the most current Java is loaded.

  • Once students have been introduced to solving one-step equations, follow the Power Point Presentation which includes key concepts and examples.
  • Throughout the lesson, stress the importance of checking a proposed solution by substituting if for the variable in the original equation.
  • Assign students problems to be completed at home.
  • The following day, address any student questions or concerns before proceeding to multi-step equations.

Possible Questions to be asked

When working through this lesson, some questions you can ask your students to help them understand the problem are:

  • Slide 2: ask students for examples of how operations “undo” each other.
  • What are you trying to solve for?
  • What are inverse operations?
  • How can you use inverse operations to solve equations?
  • Why do you used the Division Property of Equality to solve an equation with multiplication, such as 12x = 96?
  • When do you use the Multiplication Property of Equality to solve an equation?
  • On slides 7 and 8, these examples should be done together in class.

Description of Class Activities

  • Dynamic Worksheet with Geogebra – In this activity, students will independently explore one step equations using the four operations and formulate the concept of inverse operations.
  • Power Point Presentation – In this presentation, students will be provided key concepts and examples.

Closure to the Lesson

At the end of the lesson, students will write a paragraph explaining how to solve one-step equations to a student who was absent.

Assignments for the Students

  • Assign homework appropriate for your students. It should be 15 – 20 problems including word problems with real-world application.

Assessments

  • Students will complete the JMatch (HTM file) after completing the lesson.
  • Students will be assessed with teacher-generated assessments.

Plan for Providing Feedback

To provide feedback to students, have them make corrections to their activities and assessments by having them use substitution to check their answers and locate their own errors.

Connections Section

This lesson is a precursor to future problem solving. Students will need to have a strong understanding of solving equations before moving to the next lesson.