South Carolina ETV

Manipulating Multi-step Equations (Grade 8)

Master Teacher

Wakesha Fogle

Time Allotment

One 90-minute class period

Overview

"Manipulating Multi-Step Equations" is an interactive, media-rich lesson in which students examine solving equations with variables on both sides of the equal sign through hands-on, online, and multimedia activities.

Subject Matter

Mathematics

Learning Objective

Students will be able to:

Solve equations with variables on both sides of the equal sign.

South Carolina Standards

(These Standards are available online at

http://www.myscschools.com/offices/cso/standards/math/default.cfm.)

A.II.D.2 (8 th grade)

Students will be able to recognize and generate equivalent forms for simple algebraic expressions and solve linear equations. That is, students will be able to:

Use strategies that involve inverse operations to solve one-step and two-step linear equations and inequalities in one variable.

Media Components

Video

Operation Algebra: Solving Equations with Variables on Both Sides of the Equal Sign (ax + b = cx + d) The video clips used in this lesson are “A Real Life Example: Who’s Faster, Men or Women?” (three minutes and 30 seconds long); “Solving Equations with Variables on Both Sides” (three minutes and 19 seconds long); and “Another way to Solve Equations with Variables” (one minute and 56 seconds long).

To access these video clips, log on to your account at ETV’s StreamlineSC Web site (http://etv.streamlinesc.org). In the search by keyword box, type, Operation Algebra: Solving Equations with Variables and hit go. Click on the program title which will take you to a list of video clips. Download the three video clips listed above to your computer desktop and preview them.

(Note to Teacher: If you don’t have an account with ETV’s StreamlineSC, check with your media specialist or Instructional Technologist about signing up for your own account.)

Web Site

Virtual Manipulative: Algebra Balance Scales

http://matti.usu.edu/nlvm/nav/frames_asid_201_g_4_t_2.html

This is a site authored by the National Library of Virtual Manipulatives (Utah State University) which offers mathlets. This page specifically 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.

Materials

Student’s Notes Handout
Internet Activity Sheet
Tying It All Together Activity Sheet
Overhead transparency of Student’s Notes Handout

Equipment

Computers
Overhead projector
Averkey to project computer on the television or use a LCD projector

Prep for Teachers

Prior to teaching the lesson, bookmark the Web site used in the lesson on each computer in your lab or classroom. Load the Shockwave plug-in, available at http://www.macromedia.com, onto each computer, too.

Play each of the online games prior to teaching the lesson, so you are aware of the flow and how to use the supplements provided.

Download the video clips “A Real Life Example: Who’s Faster, Men or Women?”; “Solving Equations with Variables on Both Sides”; and “Another Way to Solve Equations with Variables on Both Sides.” Cue each clip to its beginning. Always use PAUSE instead of STOP when you want to temporarily stop the video. Otherwise, the clip will restart from the beginning when you press STOP and then PLAY.

Copy all the handouts for each student and make an overhead transparency of the Student’s Notes Handout.

Write the three questions found on the Student’s Notes handout on your board or a transparency.

When using media, provide students with a Focus for Media Interaction, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites, or other multimedia elements.

Introductory Activity

Step 1: Distribute the Student’s Notes handout.

Step 2: CUE the video to the beginning of the clip “A Real Life Example: Who’s Faster, Men or Women?” You will see a woman standing outside in front of a hill. Provide your students with a Focus for Media Interaction by asking them to read the first two questions on their Student’s Notes handout. Tell them to be prepared to answer them at the end of the segment.

Step 3: PLAY the entire clip.

Step 4: Review questions 1 and 2 from the Student’s Notes handout and check for understanding. The questions and answers are below.

Question 1: The equation for finding the number of years it takes after 1928 for the men and women’s teams to be equal is: 136.8 - .280y = 111.8 - .136y. What is different about this equation than others we have solved in the past? (It contains variables on both sides.)

Question 2: In order to solve this equation, what must you be able to do? In other words, what is our learning objective for today based on the video you just viewed? (Solve equations with variables on both sides of the equal sign.)

Step 5 : Explain to your students that in this lesson, you will examine solving equations with variables on both sides.

Learning Activities

Step 1: CUE the video “Solving Equations with Variables on Both Sides” to the beginning. You will see the same woman from the last video segment. Provide the class with a Focus for Media interaction by asking them to listen for the answer to question three on their Student’s Notes handout. Tell them to be prepared to answer it at the end of the segment.

Step 2: PLAY the video until the woman on screen finishes listing the two basic things to do when solving equations with variables on both sides. She will say: “Here, let’s do an example.” Now PAUSE the video.

Step 3: Check for student understanding by making sure everyone has recorded on their Student’s Notes handout:

1. Collect the variable terms on one side of the equation.

2. Solve the equation by “undoing” the operations.

Step 4: Provide students with a Focus for Media Interaction by telling them to watch the video and be prepared to copy and discuss the first step involved in solving the equation.

Step 5: PLAY the video until the woman finishes explaining the first step. She will say: “Now, this should look familiar, a regular two-step equation with the variable on one side.” Now PAUSE the video.

Step 6: Give students time to fill out Step 1 under Method One on their Student’s Notes handout. Check for student understanding by making sure everyone has recorded the two-step equation 8 = 2x + 12 and left written in the blank.

Step 7: Ask students to look at their neighbor’s paper and confirm that they also have this step recorded on their handout.

Step 8: Provide students with a Focus for Media Interaction by telling them to watch the video and be prepared to copy and discuss the second step involved in solving the equation.

Step 9: PLAY the tape until they have finished explaining the second step in the problem. PAUSE the tape as soon as the woman says, “Since twelve minus twelve is zero, we are left with two x.”

Step 10: Give students time to fill out Step 2 under Method One on their Student’s Notes handout. Check for student comprehension by answering any questions the students may have.

Step 11: Ask students to look at their neighbors’ paper and confirm that they also have this step recorded on their handout.

Step 12: Provide students with a Focus for Media Interaction by asking them to look for the third step in solving the problem and tell them to indicate it on their handout.

Step 13: PLAY the video until you see a sign saying: the answer is right. PAUSE the video when you hear the music stop.

Step 14: Give students time to fill out Step 3 under Method One on their Student’s Notes handout. Have students check the solution by plugging in the solution -2 into the original equation.

Step 15: Provide students with a Focus for Media Interaction by telling them to check their work with the video to determine if what the solution is makes a true statement.

Step 16: CUE the video “Another way to Solve Equations with Variables on Both Sides” to the beginning. You will see the same woman from the last video segment. Explain to students that they will learn another way to solve the same equation from the previous video.

Step 17: Provide students with a Focus for Media Interaction by telling them to watch the video and be prepared to copy and discuss the first step involved in solving the equation.

Step 18: PLAY the video until the woman finishes explaining the first step. She will say: “Now, we have a regular two-step equation with the variable on the left side of the equation.” Now PAUSE the video.

Step 19: Give students time to fill out Step 1 under Method Two on their Student’s Notes handout. Check for student understanding by making sure everyone has recorded the two step equation -2x + 8 = 12 and right written in the blank.

Step 20: Provide students with a Focus for Media Interaction by telling them to watch the video and be prepared to copy and discuss the second step involved in solving the equation.

Step 21: PLAY the tape until they have finished explaining the second step in the problem. PAUSE the tape as soon as the woman says, “leaving us with twelve minus eight or four on the right.”

Step 22: Give students time to fill out Step 2 under Method Two on their Student’s Notes handout. Again, check for student comprehension by answering any questions the students may have. Ask students to look at their neighbors’ paper and confirm that they also have this step recorded on their handout.

Step 23: Provide students with a Focus for Media Interaction by asking them to look for the third step in solving the problem and tell them to indicate it on their handout.

Step 24: PLAY the video to the end of the segment. Give students time to fill out Step 3 under Method Two on their Student’s Notes handout. Check for student comprehension by answering any questions the students may have and seeing that the students have all steps for this method written out on their papers.

Step 25: Have students fill in the blanks in the Summary Statement on their handout.

Culminating Activity

Step 1: Distribute the Internet Activity Sheet. Tell your students that they will now have the opportunity to use their knowledge of solving equations with variables on both sides of the equal sign by solving a variety of problems by visiting the Web site Virtual Manipulative: Algebra Balance Scales. Have your students log on to the National Library of Virtual Manipulatives Web site at http://matti.usu.edu/nlvm/nav/frames_asid_201_g_4_t_2.html. Provide your students with a Focus for Media Interaction, asking them to click on the instructions tab at the top of the screen. Go over how to use the balance with the class. Have students complete several problems using the virtual manipulative along with Internet Activity Sheet.

Step 2 : Once the students have completed the six questions and you’ve checked their answers, distribute the Tying It All Together Activity Sheet and have students form pairs to complete this activity. (Note toTeacher: If some students are having difficulty, you can have them go to work on some additional problems with a partner.)

Cross-Curricular Extensions

Social Studies: Have your students conduct research on stamps from various countries. Have them set up equations representing the value of the stamps and quantity. Students are to determine how many stamps would be needed for the values to be equal.

Language Arts: Have students write a proposal discussing why the particular deal in “Tying It All Together,” More applications problem #1 is the best option.

Community Connections

Invite an Event Planner or Wedding Planner to come to your class and discuss how they determine the best deals when planning an event. Have students solve some of the Planner’s scenarios using their knowledge of solving equations like the ones discussed today.

Student Materials

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