# Lesson Transformed: Grade 8 Mathematics This is the fifth in the series, Lesson Transformed, in which traditional lessons are transformed into engaging experiences for students which exemplify the premises of the Visioning Document.

Lesson #5

Topic: Simultaneous Linear Equations

Content Area: Mathematics

Objective: The students will be able to graph two linear equations in the form y = mx + b and find the point of intersection.

Warm Up: Students will complete Warm Up: Graphing Linear Equations (y = mx + b).  Materials needed: colored pencils or pens (black, red, green, blue).

Notes and Examples: The teacher will explain the process of identifying the slope and y-intercept from a given equation in slope-intercept form as well as graphing the lines and identifying the point of intersection.  Students will follow along and take notes on their handout.

Independent Practice: Solving Systems of Equations by Graphing

#### Transformed Lesson

Objective: The students will create evidence of understanding of how identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations.

Warm Up: Students will complete Warm Up: Graphing Linear Equations (y = mx + b).  Materials needed: colored pencils or pens (black, red, green, blue).  Then, they will check the accuracy of their graphs by utilizing Desmos (graph the same 4 lines with the appropriate colors and compare).

*Note: By utilizing Desmos, students are able to check for understanding.  This also provides the teacher with a formative assessment of the students’ graphing skills.  If the students struggle with the warm up, the teacher can re-teach here as necessary.

Investigation: Do Hybrid Cars Pay for Themselves?  In this learning experience, students are posed with this situation: Your family wants to buy a new Toyota Camry LE and is considering buying the hybrid version if the money saved on gas will be enough to pay the extra cost for the hybrid.  They are challenged to determine:

• How many years will it take from saved gas money to pay for the extra cost for a hybrid?
• Could you ever save enough money on gas (compared to your current car) to pay the entire car payment?

*Note: This real-life math example supports students’ understanding of the meaning of slope and y-intercept as well as the connection of the situation to the relevance of the point of intersection.

Exploration: Systems of Linear Equations: Discoveries – Using this Desmos teacher activity, students will be guided to think about what it means to be a solution to an equation and to a system of equations (simultaneous equations).

Exit Ticket: Teacher should cut apart the Equations in Slope-Intercept Form document below and provide one equation per student.  Students should find a partner and work together to graph their lines on a single coordinate plane (paper-pencil).  After identifying and labeling the point of intersection and verifying the point simultaneously satisfies both equations, take a picture of the graph with the camera feature on their digital device and post to a class Lino Board.