## Wednesday, January 6, 2016

### 8th Grade Math - Unit 3: Systems of Equations

I decided to change how I paced and taught my Systems of Equations Unit. This year in my Linear Relationships in Situations Unit I set up the foundation for using slope-intercept form in situations.  I taught the students how to represent situations with an equation, on a graph and with a table.  I taught the students how to interpret and explain the equation (y = mx +b) as it applied to the situation.  And I taught the students that the best method for solving problems using slope-intercept form was algebraically with the equation.  This foundation helped the students to be successful in solving Systems of Equations in Situations.

Solving Systems of Equations by Graphing - (2 Weeks)
I started the unit by having students solve systems of equations graphically and understand that the solution was the point of intersection.

Interactive Math Notebook Guided Notes - Solving Systems Graphically

iMath Lesson - ClassFlow: Solving Systems of Equations Graphically

Here is the link to my ClassFlow Systems of Equations LessonFeel Free to Use.
#__Solving Systems of Equations by Graphing__#

The next part of the concept was Solving Systems of Equations in Real World Situations. I started by having the students interpret the situation into two equations. I then had the students build a double table and complete each table using the equation for each situation.  I had the students also represent the situation graphically by graphing both situations and looking for the point of intersection. I had them find the solution in the table and on the graph and then interpret the solution in context of the situation.

Interactive Math Notebook Guided Notes - Solving Systems in Situations

iMath Lesson - Showbie: Systems in the Real World Task

Here is the link to my Showbie "Paperless" Task. Feel Free to Use. :o)
Systems of Equations in Situations: Mathland Bike Task

iMath Lesson - Socrative: Systems in the Real World Task  (self-paced)

Here is my Socrative Code. Feel Free to Use. :o)
Systems of Equations in Real World Situations:  SOC-18498671

After the students had an understanding of writing, solving and interpreting systems of equations using multiple representations, I taught the students how to solve algebraically (setting the equations equal).  The students realized that using the equations when solving was the most effective method for systems of equations in situations.

Interactive Math Notebook Guided Notes - Solving Systems Algebraically

iMath Lesson - Socrative: Systems in Situations: Solving Algebraically (self-paced)

Here is my Socrative Code. Feel Free to Use. :o)
Systems of Equations: Solving Algebraically (Setting =)  SOC-18607281

Solving Systems Using Substitution - (2 days)
This is the first year that I taught the substitution method to my Math 8 students.  It has always been the most difficult method for the students so I always focused on the elimination method.  I only planned on spending a couple of days on solving by substitution.

My goal for teaching the substitution method was to introduce them to the method and then move on to elimination, because that was the preferred method.  I knew that the elimination method would be easy to the students after trying the substitution method.  I was really surprised that my students did not fear this method and actually embraced it.  :o)

Interactive Math Notebook Guided Notes - Solving Systems Using Substitution

iMath Lesson - Classkick: Solving Systems Using Substitution
I introduced my students to the Classkick app.  It was a hit.  They loved it because they could raise a virtual hand and I could help them in real time from my iPad.  I liked it because I could see all of the students working in real time on my iPad and leave feed back.

Here is the link to a zip file with the slides I made for my classkick lesson.
Feel Free to Use. :o)Classkick Substitution Zip File

Socrative: Solving Systems Using Substitution "Team Task"

Here is my Socrative Code. Feel Free to Use. :o)
Solving Systems by Substitution "Team Task":  SOC-18657394

Solving Systems Using Elimination - (3 Weeks)
I split the elimination method into 4 categories, and let the students know each time which category were were moving to. "Easy". set up for elimination. "Hard", multiply by a -1, "Harder", multiply one of the equations by a value to set up for elimination. "Hardest". multiply both equations by values to set up for elimination.

I spent a few days on "Easy", to make sure that the students had a foundation for solving a system when it is set up for elimination, because they must be able to do this for all of the other categories. I then spent a few days on "Hard", and then a few days on "Harder".   I did not give the notes for all of the categories at one time.  I only gave the section of the notes that was the focus.

Interactive Math Notebook Guided Notes - Solving Systems Using Elimination

iMath Lesson - Socrative: Solving Systems Using Elimination (self-paced)

Here is my Socrative Code. Feel Free to Use. :o)
Solving Systems by Elimination (Easy):  SOC-18740133

iMath Lesson - Showbie: Solving Systems Using Elimination Review

Here is the link to my Showbie "Paperless" Review. Feel Free to Use. :o)
Systems of Equations Using Elimination Guided Practice Review

iMath Lesson - Classkick: Solving Systems Using Elimination

Here is the link to a zip file with the slides I made for my classkick lesson.
Feel Free to Use.  Classkick Elimination Zip File

Socrative: Solving Systems Using Elimination "Team Task"

Here is my Socrative Code. Feel Free to Use. :o)
Solving Systems by Elimination "Team Task":  SOC-18831208

For the next part of the unit I moved the students to word problems and solving by elimination.  The first day was an introduction using pictures to set up the equations.  This really set a foundation for setting up the equations from word problems.

iMath Lesson - Showbie: Solving Systems Word Problems Introduction

Here is the link to my Showbie "Paperless" Practice. Feel Free to Use. :o)
System of Equations Writing Equations From Pictures Intro

I then introduced the students to word problems and showed them how to interpret and set up the equations, and then solve using elimination.

Interactive Math Notebook Guided Notes - Solving Systems Elimination Word Problems

iMath Lesson - Socrative: Solving Systems Word Problems Poster Task
This was by far one of my Socrative lessons that I created. The students loved making the review posters and it really helped solidify the concept of elimination word problems.  :o)

Here is my Socrative Code. Feel Free to Use. :o)
Systems of Equations by Elimination Poster Task:  SOC-18913896

I then introduced them to the long awaited "Hardest" method and then had them apply this method in complex word problems. The key to their success was the collaborative team practice problems and discussions.

Interactive Math Notebook Guided Notes - Solving Systems Elimination (Hardest)

iMath Lesson - Socrative: Solving Systems Elimination (Self-Paced)

Here is my Socrative Code. Feel Free to Use. :o)
Systems of Equations by Elimination (Hardest):  SOC-19793108

Socrative: Complex Elimination Word Problems "Team Task"

Here is my Socrative Code. Feel Free to Use. :o)
Systems of Equations by Elimination (Hardest) WP:  SOC-19041322

Solutions to Systems of Equations (2 Days)
The last part of the unit was focused on the types of solutions; one solution, no solution, or infinite many solutions. I gave them a foundation of what the solutions mean on a graph and then focused on determining the type of solution given a systems of equations that was set up for elimination.  This part of the concept was really easy for my students because they have a really good understanding of solutions to equations in one variable from the linear equations unit.

Interactive Math Notebook Guided Notes - Solutions to Systems of Equations

The students spent a couple of days on a cumulative review "Team Task" and ended the unit with a test on the entire unit of systems of equations.

Unit Reflection
All of the changes and tweaks I made to this unit this year were spot on.  The unit flowed and the students were able to make the connections throughout the entire unit.  The students were super successful and surpassed my expectations for this unit.

I would like to spend more time on solutions to systems of equations if possible. and another thing I would change is giving mini quizzes throughout the unit instead of a long comprehensive test at the end.

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