Can You Solve the Mystery of the Variable?

Learning Resource Type

Lesson Plan

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

The lesson will make the connection between isolating a guilty person in a “who-dun-it” with isolating a given variable in an equation. In addition, this lesson will involve students creating a list of procedures to use when solving for a given variable. At this time it is not necessary for students to know the formal names for the properties. It is important for students to understand the concepts and take part in creating a set of procedures for isolating a variable and solving equations.

This lesson results from the ALEX Resource Gap Project.

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Vocabulary

Literal equations
Variable
Constant

Knowledge

Students know:

Properties of equality and inequality

Skills

Students are able to:

Accurately rearrange equations or inequalities to produce equivalent forms for use in resolving situations of interest.

Understanding

Students understand that:

The structure of mathematics allows for the procedures used in working with equations to also be valid when rearranging formulas, The isolated variable in a formula is not always the unknown and rearranging the formula allows for sense-making in problem solving.

Primary Learning Objectives

The student will be able to solve an equation for a given variable in an equation.

The student will be able to create a set of procedures to serve as a reference when solving an equation for a given variable as demonstrated by creating three procedures to use when solving an equation.

Procedures/Activities

Before:

Compare solving for a variable to solving a mystery. Show the clip https://www.youtube.com/watch?v=c6Vu-QzPgHU of the investigator “isolating” or identifying the guilty person. Stop the clip before the detective solves the mystery and ask students to try to solve the case based on the clues provided. Make the connection with “isolating” the given variable in the equation and “isolating” the guilty person in the clip. At this time, discuss as a class what the word isolate means to ensure that everyone understands the meaning. Good detectives use the same procedures every time. Good mathematicians use the same procedures to solve equations each time. Ask students to think back and explain how the detective was able to solve the crime in the clip we just watched. Explain to students that they will create a set of procedures to solve equations for a given variable.

During:

Students will have one to two minutes to work alone on a problem (introductory problem;) requiring them to solve an equation for a given variable. At the end of that time, the student will compare their work with their partner’s work. The teacher will then display the correct answer. At this time, instruct the students that each pair should work together to create a set of procedures explaining how they solved the problem. Allow students 5-10 minutes to do this, then as a class let each pair share the procedures they created with the class. Each pair of students will then be given six problems to solve (worksheet, using the procedures they just created with their partner. Ask students to make a note if any changes need to be made to their procedures. Provide highlighters to each student and encourage them to highlight the variable being isolated as a further visual aid if they find it helpful.

After:

Allow students to check their answers to the problems they just worked on. Then, as a class, create one set of procedures for solving equations and isolating the variable in question. Each group should participate and help edit and improve the procedures until there is one document everyone can agree on. The teacher will write the procedures on poster/chart paper. The teacher will keep the procedures posted in the room throughout the year. If desired, the formal properties can be introduced in a subsequent lesson.

Conclude with an exit pass requiring students to solve for a given variable using the newly created procedures.

Assessment Strategies

Formative:

pre-assessment
discussion during the video clip
the introductory problem (teacher will walk around and make note of the responses)
worksheet (teacher will walk around and make note of the responses)

Summative:

exit pass

Acceleration

Pair up students who finish early. Each student will create a problem consisting of an equation containing multiple variables with a specific variable to isolate. Each student will solve the problem that they created. Students will then exchange the problem they created with their partner. After each student has had a chance to work on the problem created by their partner, they will discuss their answers.

Khan Academy activity (link below)

-Students will complete Practice: Manipulate Formulas found on Khan Academy. This can be a paper and pencil activity, which can be turned in. The activity allows students to check their answers as they go. If students are having difficulty, they can watch the videos provided on the same page. This activity can extend students' understanding of this concept by allowing them to apply what they have learned to area, perimeter, and temperature formulas.

https://www.khanacademy.org/math/algebra2/modeling-with- algebra/manipulating-formulas/v/rearrange-formulas-to-isolate-specific-variableshttps://www.khanacademy.org/math/algebra2/modeling-with-algebra/manipulating-formulas/v/rearrange-formulas-to-isolate-specific-variables

Intervention

The teacher will use the information from the students' pre-assessments to provide assistance as necessary for students who need extra preparation.

Provide highlighters for students to visually isolate the variable in question.

Work with a peer to provide extra assistance.

For extra assistance after the lesson, students can complete the activity on https://www.ixl.com/math/algebra-1. Students will need to click on Algebra I- I.8 (Rearrange Multiple Variable Equations).

* IXL is an adaptive program that allows students to practice math skills. IXL has a paid subscriber option, however, it allows for free practice as well. Students will be allowed to practice 10 problems for free.

Total Duration

91 to 120 Minutes

Background/Preparation

Students should be able to multiply a binomial by a monomial (distribute). Students should be able to apply the additive identity property, multiplicative identity property, and the multiplicative inverse property. It is not necessary that the students know the names of the properties.

Teachers should carefully consider how to help students create a useful reference for solving equations. Also, teachers should consider ahead of time how to help guide students to the correct answer without explicitly telling students the answer. For instance: perhaps ask a student how they intend to isolate the variable in question.

Teachers should review the "Possible Procedures" document to be aware of students' potential answers.

The teacher will give the pre-assessment the last ten minutes of class the day prior to teaching this lesson. The teacher will examine the responses before teaching this lesson. This will allow the teacher to anticipate where students might have difficulty. The teacher will use the pre-assessment to assign students a partner to work with during the lesson. Students will be assigned to work with partners with similar abilities.

The teacher should view the video clip prior to teaching the lesson, so he or she can pause the video at the appropriate time.

Materials and Resources

Pre-Assessment (make a copy for each student)

Movie clip: https://www.youtube.com/watch?v=c6Vu-QzPgHU

Introductory problem (make a copy for each student or project for all students to see)

Worksheet (make a copy for each student)

Exit Pass (make a copy for each student)

Highlighters

Colored paper for students to write their procedures on

poster paper/chart paper

Technology Resources Needed

Projector

Access to Internet

Approved Date

2017-08-23