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Solving Linear Equations by Balancing (using technology)


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Keywords: Linear Equations, Algebra, Balance, Math
Subject(s): Math, Special Needs
Grades 6 through 8
School: IS 166 George Gershwin, Brooklyn, NY
Planned By: Jossie Espinal
Original Author: Jossie Espinal, Brooklyn
Learning Objective: Students will solve a complicated equation by making it simpler while keeping two sides of the equation equal.

Standards addressed:
Standard MST1: Analysis, Inquiry, and Design
*Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.


Materials: Impact Mathematics Course 2 (chapter 6), Geometer’s sketchpad (solve by balancing.gsp), balance scale, paper bags, blocks, Solving the Equation handout, play money, chart paper, markers, rubrics, assessment

Time for lesson: 3 days

Vocabulary: Balance, Equation, Variable

Day 1:
Motivation: Have 2 students come to the front of the room and tell them that they must come to the front of the room. Using play money, give both students $5.00. Have students stand on either side of an equal sign that is prewritten on the board. Ask students: If I take away $2.00 from student A, what must I do mathematically with Student B? (Students will offer different suggestions, but the correct one is to take away from the other student.) Let’s explore this concept further…

Mini Lesson: Open Solve by Balancing : Use from Geometer’s Sketchpad. Model experimentation by dragging objects from the storage area (on the left of the dividing bar) to the left or right balancing pan.
Q1 Which objects weigh a pan down, and which ones pull it up?
Q2 What happens as each item is dragged across the page?

Explore Time: Allow students to experiment with the Solve by Balancing. Students must write in their math journals any patterns they see, what happens as they move the objects around and why do they think this happens (make a hypothesis). No more than 10 minutes for this activity.

Mini lesson: Have students open to page 402 in Impact (problem set F). Using the equation 3n+8=5n+2, set up the balance to solve equation (NB: The variable will be named x in Geometer’s Sketchpad, review vocabulary: variable). Take away the same number of variables from both sides (3x) and then take away the same number from both sides (2). The new equation will be 8=2x+2. Now subtract 2 from both sides, and the new equation will be 6=2x+0, which is the same as saying 6=2x. Now you have a simpler equation that you can do. Divide both sides by 2 and you will have 3=1x, which is the same as 3=x.

Worktime: Students will solve the #2 in Problem Set F.

Closing: Review student work.
Assessment: Observation, student work
Homework: Do #3 &4 in Problem Set F on page 402. Write a step by step procedure on how you solved the equations.
Day 2:
Motivation: Create a KWL chart on solving equations by balancing.

Mini Lesson: Using a balance scale, blocks and paper bags, I will set the equation: 3n+8=5n+2. Solicit input from the students building on the previous lesson. Ask how this activity is different from previous lesson (expected responses: not on a computer, able to touch objects). Make the statement that the steps that we take are the same. Review with students the scoring rubric: http://rubistar.4teachers.org/index.php?screen=ShowRubric&module=Rubistar&rubric_id=1433630&

Create Time: Students (within their groups) will make a “How To Solve an Equation” poster using the rubric as a checklist.

Closing: Students will share their finished projects.
Homework: Complete Solving the Equation handout.

Day 3:
Motivation: Solve this equation: 6x+6=9x-6
Step 1: Combine integers (6+6=12) New equation: 6x+12=9x
Step 2: Combine variables on the other side of the “=” sign (9x-6x=3x) New equation: 12=3x
Step 3: Divide both sides by 3 (12/3=4) Solution is 4=1x or 4=x

Students will complete powerpoint: Solving equations by balancing powerpoint

Homework: Write a reflection on this topic. Using an equation, solve and explain each step of the process. Draw a model to show how you would balance a linear equation.

Reflection Rubric: Rubric

Create a rap that summarizes information.

Behavioral Reward System: Points given and calculated for inclusion for the rewards wheel.

Differentiation is built in lesson plan:
Verbal Intelligence-Writing a reflection, Designing bulletin board
Materials: Digital SLR, Special Education, Math, Flash/USB Drives, Batteries