TITLE: Solving Systems of Equations 2
TASK DEVELOPER: Barbara L. Schlegel
GRADE AND CONTENT AREA: Grade 9, Algebra I
SCHOOL: Mergenthaler Vocational Technical Senior High School
STANDARDS:

Maryland Core Learning Goals, Expectations, and Indicators

Goal 1 Functions and Algebra: The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions, and algebra.

Expectation 1.2: The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

Indicator 1.2.3: The student will solve and describe using numbers, symbols, and/or graphs if and where two straight lines intersect.

Assessment Limits
  1. Functions will be of the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.
  2. All coefficients will be rational.
  3. Vertical lines will be included.
  4. Systems of linear functions will include coincident, parallel, or intersecting lines.
  5. The majority of these items should be in real-world context.

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PERFORMANCES:
  1. The students will model solving systems of equations using the multiplication-addition method.

  2. The student will solve a system of equations using the calculator and linear regression equations comparing real world data.

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INSTRUCTIONAL ACTIVITIES:

Scaffolding for Success

Activity One: Using the Math Connections Text pages 320-322

  • Go over process used to find point of intersection between two lines on the calculator.

Estimated Time: 15 minutes

  • Step 1: Review writing equations in slope intercept form. Allow students to model this procedure.

  • Step 2: Review entering equations into the Y= screen. Choose volunteers to come to the overhead to show how this is done.

  • Step 3: Allow students to show finding intersection point on the calculator.

Technology: TI-83 calculator with overhead viewscreen.
Materials: TI-83 calculators Math Connections Textbook
Student Product or Performance: Performing correct steps to solve problem and participation in group discussion of problem results.
Scoring Tool: Teacher observation

Activity Two: Solving Equations using Multiplication-Addition Method

Estimated Time: 15 minutes

  • Step 1: Solve the following:

    • 4x+3y=4
    • 2x-y =7

  • Model for the students how this problem is done.

    Step 2: Get the students to model these problems on the board with other students giving guidance:
    • 3x+7y=15
    • x+3y=7
    • 5x+2y=-4
    • 2x-4y=24

Technology: Chalkboard
Materials: Paper and pencil
Student Product or Performance: Correct student modeling of method and group participation in work.
Scoring Tool: Teacher observation

Activity Three: Combining Line of Best Fit with Intersection of two lines

Estimated Time:20 minutes

  • Step 1: Using Math Connections Text- page 325 #3. Have students review orally
    how to find the linear regression equation for Hours and Strain 1 on the calculator. Model the instructions that they give me.

  • Step 2: Choose a volunteer to model how to find the linear regression equation for Hours and Strain 2 on the calculator.

  • Step 3: Choose a volunteer to model how to find the point of intersection between the two strains of bacteria. Have a group discussion on what this point means in context of this problem

Technology: TI-83 calculator with overhead viewscreen
Materials: TI-83 calculator and Math Connections Text
Student Product or Performance: Student Modeling of use of Calculator
Scoring Tool: Teacher observation and student participation

Activity Four: Real world problem - Graded Classwork

Estimated Time: 15 minutes with summary

  • Step 1: Mr Lee has 60 coins in quarters and dimes totaling $10.95.
    • a) Write a system of equations modeling the situation stated in the problem.
    • b) Solve the system explaining the method used and the processes involved in each step.
    • c) Interpret your solutions in terms of the problem in written form.

  • Step 2: Collect papers.

  • Step 3: Use how student s solved the problem as a summary for the lesson.

Technology: TI-83 calculators
Materials: Papeer, pencil, and calculator
Student Product or Performance: Writtten ECR pertaining to real world situation.
Scoring Tool: Classwork paper.

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SCORING:

Scoring Rubric
Score Points
Description
0
 The student did nothing or used information not given in the situation to apply to classwork assigned.
1
 The student wrote the correct system of equations and that was all or student gave correct answers without showing any work or giving any interpretation of the results.
2
 The student wrote correct system of equations, solved them correctly, and put answers in correct form.
3
 The student wrote correct system of equations, solved them correctly, put answers in correct form, and wrote an interpretation of the results in the context of the problem.

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RESULTS:

Organize: I will use the scoring rubric above to show the following data for each time that I assess and score the same learning standard(s), this is a BCR (3 point rubric):

Number of students who performed at or above the proficient level on my scoring tool:

  • 11 out of 15 scored a 3 or 73% of the class
  • 2 out of 15 scored a 2 or 13% of the class

Number of students who performed at or below the proficient level on my scoring tool:

  • 2 out of 15 scored a 1 or 13% of the class

Analyze: I examined the data above to look for trends, contributing factors, and implications of student performance over a series of assessments of the same learning standard.

  • Contributing factors: Students refusal to show work or interpret their results was the reason for the scores of 1 and 2 that I recieved.

Reflect: I will consider using this as a two-day lesson the next time I teach it. The students really enjoyed the practical application problem and wanted to discuss it at greater length than one class period allowed. As a follow-up to this, I would assign as either a project assignment or as extra credit that the students research on the Internet for a situation either in sports, food preparation, or medical research area that could utilize using systems of equations. They could prepare a written report on their findings stating situation, and the processes they used to solve the situation and the interpretationof their results.