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Essay: Solving Linear Equations w/ Two Variables: Lesson Plan

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  • Published: 1 April 2019*
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  • Words: 1,505 (approx)
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Teacher: xxx

Subject: Algebra 2

Topic: Solving Linear Equations with Two Variables

Standards Covered:

The standards listed below relate to the following Standards for Mathematical Content in the Common Core State Standards for Mathematics:

• A-REI: Solve systems of equations.

• A-SSE: Interpret the structure of expressions.

This lesson also places emphasis on Practices 1, 2, 3, and 5 from the common core standards listed above.

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.


Students will be able to identify the characteristic and solutions of a linear equation. Allocating the proper information to solve two separate equations when two unknown variables are present. With this, the students will be able to distinguish the different parts of the equations and the meaning of the algebraic expression by the resultants produced. Also, they should be able to determine what method should be utilized to solve the equations, whether that be substitution or elimination.

Content Knowledge:

This lesson is intended to help the educator assess what areas and how well the students understand the varying algebraic forms of linear equations. Specifically, this lesson will help identify and help students who have are having difficulties with:

• Comprehending and understanding the meaning of algebraic expressions.

• Simplifying equations that are made up of two separate variables.

Materials Needed:

• Each individual student will need a copy of the Linear Equations handout, notes, and readily available pen/pencil, eraser, and calculator.

• Each student will also need to take out their personal mathematics notebook for the power notes section of the lesson.

• Solving Linear Equations with two variables by substitution and elimination worksheet.

• A projector typed device to work notes

• Laptops to take their quick quiz on Quiz Hub.

Student Grouping:

• The students will begin the instructional period working in groups of three on a series of problems presented on the board. After they compete the work, the educator will review the work and create a set of different problems to help students improve their understanding.

• After reviewing the new notes and doing interactive examples, students will work independently on problem sets given through the Linear Equations handout.

• A class discussion will follow the completion of the notes.

• Following this, the students will split apart again and do their own Power Notes in their notebooks.


The method utilized in this lesson are more formative based and student-centered rather than teacher-centered. This selection of these methods is due to wanting the students to articulate and determine what information is going to be needed for the greatest opportunity of content comprehension. The formative approach gives an altering look to the lesson and how it is presented to the students. When they are given more control of what goes on in their education, they are more likely to stay focused on task. With that and in this lesson however, there is a switch of teaching methods from student-centered to teacher-centered. The instructional period near the beginning of the lesson will help bring direct focus to the information being presented and help articulate what focus areas need to be covered again based of the questions being asked following the instruction. The teacher should have complete control during this point of the class period and help centralize the education to the criteria presented. Also, the teacher should be able to directly tailor to the specific needs of the students in the class. Through the use of technology based literacy options such as Kahoot!, the students can experience the content in different formats which should help them achieve greater comprehension.


Opening: A series of problem sets will be presented on the white boards around the classroom that the group of three students will complete on a separate sheet of paper for their “warm-up” period. After completing the set problems, the students will turn in the work to the teacher to allow the teacher to assess what areas the specific students need to work on before beginning the lesson of the day. After completion, a Quiz Hub activity will be introduced to the class to further hone in necessary skills needed for comprehending this material being presented. While this activity is being done, the educator will stop and go over problems as the students are working them out to show common mistakes that are made. Depending on class size and time frame, a 15-20 minute window should be allowed for the students to complete work and actively participate in the Quiz Hub. It is important to note that more time should be added if the problem sets presented on the board are causing the students problems, and likewise for the activity as well. This is the formative approach to teaching that should allow for qualitative assessment opportunities to be made instead of grading them based off work presented.

Main Lesson: The main lesson is focused around introducing the concepts behind linear equations with two variables. This is an interactive portion of the lesson where the teacher is taking control of the classroom space and presenting information in a high technological method with the usage of visual aids and interactive presentations. With this part, the students should be filling out the printed off note sections that were given to them at the beginning of the lesson and they should be filling in all areas of information and asking questions if uncertain about content being presented. Inside this main lesson, solving linear equations algebraically will be done to show all the different areas encompassed with this content. A great emphasis will be put on ensuring that the students understand how the correlation between solving the equations algebraically represent the needed components to answer both equations and make them true statements. After allowing them to visually see work being done and working on it, this is when you will hand the other worksheet to them that has examples on how to solve these equations utilizing the substitution and elimination method. These worksheets show very direct methods that may need to be covered in extended class periods due to possible confusion popping up. However, from past experience in the class and from previous classes, this work being done should be a refresher and should not be newly introduced material. This portion of the lesson will take up the greatest majority of the lesson, encompassing upwards of 20-35 minutes of your class time depending on the level and understanding of the students in the classroom. If the comprehension of the material is not going well, more time may be needed to teach the lesson and ensure that understanding is met.

Closing: Depending on time allowance in the class, after completing the main portion of the lesson, the students will work on their Power Notes in their class notebook. The Power Notes section of this content area breaks down equations presented in the class time and offers a more critically thought out approach to answering the problem sets. Each student must utilize the Power Note method with three different problems, engraining the method and the terminology to ensure comprehension is met. After finishing their individual Power Notes, they will be given to time to discuss their notes with other classmates. This is a time for them to collaborate on different parts of their assignment and base understanding and feed off their knowledge of the material. This area is a student-centered teaching moment that allows the teacher to walk around and collectively check on the work being presented and steer students in the right direction if assistance is needed. Also, allowing the students to work together will help transition into the homework portion of this assignment and bring a full conclusion into the lesson of the day. Also, during this time, questions can be asked in a more private manner to allow for more direct responses, and 10-15 minutes should be enough time for this closing portion.


The utilization of the “Fist-to-Five” technique gives students the opportunity to express their knowledge level without speaking out and feeling embarrassed about not understanding the content. On the scale, a fist means I do not understand and a five would be I get it all. This small evaluation period will help the teacher assess the needs of the students with their physical cue and make planning for the next lesson much easier. If the evaluation period happens during the next day, students will be given similar problems presented to them from the lesson the day before and they will have to work and submit work for grading to show understanding. This type of evaluation gives immediate results to which students understand and do not understand the content. Also, informative evaluation will be happening based on questions being presented throughout the lesson and can be utilized if more content based practices are needed. This evaluation period should only take about two to five minutes to complete.

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