Stained Glass Systems

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

8

Overview

Students are given the scenario of being commissioned to create a stained-glass window for a new architecture firm. This provides a real-world scenario for students to practice graphing systems of equations (simultaneous pairs of linear equations), as well as creating systems of equations when given constraints.

This activity is a result of the ALEX Resource Development Summit.

Phase

During/Explore/Explain

Mathematics (2019) Grade(s): 8

MA19.8.12
Solve systems of two linear equations in two variables by graphing and substitution.

Vocabulary

System of linear equations
Point of intersection
One solution
No solution
Infinitely many solutions
Parallel lines
Slope-intercept form of a linear equation
Standard form of a linear equation

Knowledge

Students know:

The properties of operations and equality and their appropriate application.
Graphing techniques for linear equations (using points, using slope-intercept form, using technology).
Substitution techniques for algebraically finding the solution to a system of linear equations.

Skills

Students are able to:

generate a table from an equation.
Graph linear equations.
Identify the ordered pair for the point of intersection.
Explain the meaning of the point of intersection (or lack of intersection point) in context.
Solve a system algebraically using substitution when both equations are written in slope-intercept form or one is written in standard form and the other in slope-intercept form.

Understanding

Students understand that:

any point on a line when substituted into the equation of the line, makes the equation true and therefore, the intersection point of two lines must make both equations true.
Graphs and equations of linear relationships are different representations of the same relationships, but reveal different information useful in solving problems, and allow different solution strategies leading to the same solutions.

Learning Objectives

I can solve systems of linear equations by graphing.

I can solve systems of linear equations in a real-world context.

Activity Details

The student will be able to graph systems of linear equations and determine a solution by using a real-world scenario of creating a stained glass window using constraints. Students will be given the systems of equations to graph and will then solve them by graphing them on graph paper. Students can either label the solution on the graph, or they can write or type the solution on the direction sheet. This is up to the teacher's discretion. Students will be able to further show their understanding of the solution to a system of equations by creating their own systems that pass through a given point on the coordinate plane. In addition, students will color code polygons that are formed by the intersection of the simultaneous pairs of equations, creating a stained glass image.

The teacher can post digital tool either on Google Classroom or can provide a hard copy to each student.

Assessment Strategies

The teacher will review student work to make sure that students are correctly solving the systems of equations by graphing by checking solutions that are either written on the final product or by checking solutions that are given on the direction sheet.

Variation Tips

Teachers can graph systems and have students give equations for the lines.

Students can give characteristics of polygons found and justify reasoning.

Background / Preparation

You will need to post a copy of the instructions on Google Classroom or share a Google Doc with students.

You could also provide a copy of instructions to each student if technology is not available.

Each student will need graph paper to complete the task, as well as colored pencils or markers to color the identified polygons.

Stained Glass Systems Student Sheet

https://docs.google.com/document/d/12I61eKTuEWCVVzW-jnMrfFMDa1pOEkPfjFnVaG-hQi8…

Approved Date

2019-05-09

Owner (Author)

auburntailgater

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