Multiple Intelligence Lesson Plan

Lesson Plan Title:

Chapter 7 Section 5 – Special Types of Linear Systems

Developed by:

Renee Zomers

Subject Area:



Solving Special Types of Linear Systems

Grade Level:

High School – Algebra II

Time Frame:

50 minutes

Lesson Summary:

The students will work in small groups on an activity.  We will take notes together as a class to show examples of linear systems with one solution, no solution, or infinitely many solutions.


 Before this lesson students should know what slope and intercepts are.  Students should know how to put equations in slope-intercept form, how to graph linear equations, and methods for solving systems of equations.


9-12.A.2.1. Students are able to use algebraic properties to transform multi-step, single-variable, first-degree equations.


9-12.A.2.2A. Students are able to determine the solution of systems of equations and systems of inequalities.


9-12.A.3.1. Students are able to create linear models to represent problem situations.


9-12.A.4.1. Students are able to use graphs, tables, and equations to represent linear functions.


9-12.N.2.1. Students are able to add, subtract, multiply, and divide real numbers including integral exponents.

Lesson Objectives:

Identify linear systems as having one solution, no solution, or infinitely many solutions


Assignment: pages 429-431 problems 12-28, 36-37.  Quiz (to be taken on day following lesson)

Technology to be Used:

 Overhead Projector

Other Materials:

Graph paper; whiteboard

Procedural Activities:

Lesson Opener: Interpersonal intelligence is used during this activity when the students work in small groups and partake in group discussion.  Because students will be solving and graphing the equations themselves, they will be learning by doing therefore demonstrating bodily-kinesthetic intelligence during the activity.

Give each student a piece of graph paper. Divide students into groups of three at their desks.  Give the students the directions for the activity as follows:

  • Each member of the group should choose a different one of the linear equations that will be on the overhead and graph it.
  • Rotate papers once to your left and check the other students work and graph.
  • Everyone should get their own papers back and share your graphs with the other members.  How are the three graphs different?  (How many lines does each graph have?  If there is more than one line, how are the lines related?)
  • Individually, write the equations of your system in the form y=mx+b.
  • Share with your group member what you got for a result.  How are the equations within each system similar or different?
  • Repeat the same steps with the second set of three systems of equations.

We will now have a large group discussion to see what the groups discovered from the activity.  From this activity students should discover the three following ideas:

    1. One solution if each of the equations have different slopes.
    2. No solution if the lines are parallel (same slopes and different


    1. Infinitely many solutions if the equations are of the same line (same slopes and same y-intercepts).

Lecture/Notes:  Verbal-linguistic intelligence is being used during lecture because students will be hearing all the important points and may follow along in the book with vocabulary.  They may also refer to examples in the book for further reading.  Along with this, students should be taking notes as we work problems out on the board.

  • Systems of equations can have either one solution, no solution, or many solutions.  
  • The number of solutions a system has can be determined from the graph or from the equations.

      In each of the following examples, when doing the “solve by graphing” all students will be doing the graphing on their graphing calculators.  Because they will be learning by doing they are using bodily-kinesthetic intelligence.  They are also using visual-spatial intelligence because they are interpreting graphs and determining relationships between lines on the graph.

     Each example will be worked out step-by-step on the board during lecture.  Each steps shows logical progression toward the answer, thus logical-mathematical intelligence will be used.  Following are the examples I will use in class, each step is not written here, but will be written for students notes during class.

  • Example #1 Linear system with one solution

           3x +   y =  2

           2x + 2y = -4

       Solve by substitution:  (-2, 8) is our solution

       Solve by graphing:  see one intersection

  • Example #2  Linear system with no solution

          2x + y = 5

          2x + y = 1

       Solve by substitution:  1=5 is false therefore no solution

       Solve by graphing:  see the lines are parallel

  • Example #3 Linear system with many solutions

                 -2x +   y = 3

                 -4x + 2y = 6

             Solve by linear combination:  0 = 0 always true therefore many solutions                   

             Solve by graphing:  appears like one line because they are the same line


  • Example #4 Identifying the Number of Solutions

              6x – 2y = 10

             -3x +  y = 12

               Solve by substitution:  24 = 10 false so no solution.

               What would the graph look like?  Parallel lines.

               Check by graphing on calculators.

Closing the lesson:  I will reemphasize how we can predict what a graph will look like by comparing the equations.  Students will then be given their homework assignment and have five minutes to get started on it or ask questions.


Activity Problems; Quiz; Quiz Key