Real World Systems of Linear Equations

This guide provides a program overview, background knowledge needed for understanding, vocabulary, discussion questions and activities, tips for using a calculator, as well as print and Internet resources to supplement the teaching of targeted algebra concepts.

Weblink address (URL):

Standards & Objectives

Academic standards

CCSS.Math.Content.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by...
CCSS.Math.Content.8.EE.C.7: Solve linear equations in one variable.
CCSS.Math.Content.8.EE.C.8: Analyze and solve pairs of simultaneous linear equations.
CLE 3102.3.7: Construct and solve systems of linear equations and inequalities in two variables by various methods.
GLE 0506.4.1: Use basic formulas and visualization to find the area of geometric figures.
GLE 0706.3.7: Use mathematical models involving linear equations to analyze real-world phenomena.
GLE 0706.3.8: Use a variety of strategies to efficiently solve linear equations and inequalities.
GLE 0806.3.2: Represent, analyze, and solve problems involving linear equations and inequalities in one and two variables.
GLE 0806.3.3: Solve systems of linear equations in two variables.
SPI 0706.3.6: Solve linear equations with rational coefficients symbolically or graphically.
SPI 0706.3.7: Translate between verbal and symbolic representations of real-world phenomena involving linear equations.
SPI 0706.3.8: Solve contextual problems involving two-step linear equations.
SPI 0706.3.9: Solve linear inequalities in one variable with rational coefficients symbolically or graphically.
SPI 0806.3.1: Find solutions to systems of two linear equations in two variables.
SPI 0806.3.2: Solve the linear equation f(x) = g(x).
SPI 0806.3.6: Analyze the graph of a linear function to find solutions and intercepts.
TSS.Math.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by...
TSS.Math.8.EE.C.7: Solve linear equations in one variable.
TSS.Math.8.EE.C.8: Analyze and solve systems of two linear equations.

Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.

Learning objectives:

Before studying the content discussed in the video, students should already be able to:
Identify the parts of the Cartesian coordinate system.

Plot points in the coordinate plane.
Perform calculations with integers.
Substitute values into an algebraic equation.

Lesson Variations

Blooms taxonomy level:

Understanding

Extension suggestions:

Discuss with students the various ways to write a linear equation: point slope form, slope-intercept form, and standard form.Write several linear equations on the board and have students rewrite the equations in the various linear equation forms, comparing and contrasting the different forms and indicating when it would be advantageous to use each form.
Slope refers to the steepness of a line or object. Have students investigate the slopes of various objects, like a flight of stairs, a handicapped access ramp or even a mountain, by measuring the rise and the run and calculating the slope.

References

Contributors:

Greg Matney

Originator:

Ayers Institute for Learning & Innovation