ALEX Learning Activity

  

Stained Glass Systems

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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  This learning activity provided by:  
Author: DeLaura Downs
System:Jefferson County
School:Jefferson County Board Of Education
  General Activity Information  
Activity ID: 2273
Title:
Stained Glass Systems
Digital Tool/Resource:
Stained Glass Systems Student Sheet
Web Address – URL:
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.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
12. Solve systems of two linear equations in two variables by graphing and substitution.

a. Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.

b. Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the x-value that will generate the given y-value for both equations.
  • Recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y-intercepts) have no solutions, and lines that are the same (same slope, same y-intercept) will have infinitely many solutions.
  • Use substitution to solve a system, given two linear equations in slope-intercept form or one equation in standard form and one in slope-intercept form.
  • Make sense of their solutions by making connections between algebraic and graphical solutions and the context of the system of linear equations.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.12.1: Define variables.
M.8.12.2: Recall how to estimate.
M.8.12.3: Recall how to solve linear equations.
M.8.12.4: Demonstrate how to graph solutions to linear equations.
M.8.12.5: Recall how to graph ordered pairs on a Cartesian plane.
M.8.12.6: Recall that linear equations can have one solution (intersecting), no solution (parallel lines), or infinitely many solutions (graph is simultaneous).
M.8.12.7: Define simultaneous.
M.8.12.8: Recall how to solve linear equations.
M.8.12.9: Recall properties of operations for addition and multiplication.
M.8.12.10: Discover that the intersection of two lines on a coordinate plane is the solution to both equations.
M.8.12.11: Define point of intersection.
M.8.12.12: Recall how to solve linear equations.
M.8.12.13: Demonstrate how to graph on the Cartesian plane.
M.8.12.14: Identify ordered pairs.
M.8.12.15: Recall how to solve linear equations in two variables by using substitution.
M.8.12.16: Create a word problem from given information.
M.8.12.17: Recall how to solve linear equations.
M.8.12.18: Explain how to write an equation to solve real-world mathematical problems.

Prior Knowledge Skills:
  • Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
  • Demonstrate an understanding of an extended coordinate plane.
  • Draw a four-quadrant coordinate plane.
  • Draw and extend vertical and horizontal number lines.
  • Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
  • Recall how to graph points in all four quadrants of the coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.12 Solve two-step linear equations where coefficients are less than 10 and answers are integers.
Learning Objectives:

I can solve systems of linear equations by graphing.

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

 
  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

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.
Advanced 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.
Variation Tips (optional):

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

Students can give characteristics of polygons found and justify reasoning.

 
Notes or Recommendations (optional):

I use this as a class activity after students have graphed linear equations and following an introduction to graphing a system of linear equations.
  Keywords and Search Tags  
Keywords and Search Tags: graphing, graphing systems of equations, linear systems, simultaneous pairs of equations, system of equations