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Applications of Systems of Equations: An Electronic Circuit
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Educational Use
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Does the real-world application of science depend on mathematics? In this activity, students answer this question as they experience a real-world application of systems of equations. Given a system of linear equations that mathematically models a specific circuit—students start by solving a system of three equations for the currents. After becoming familiar with the parts of a breadboard, groups use a breadboard, resistors and jumper wires to each build the same (physical) electric circuit from the provided circuit diagram. Then they use voltmeters to measure the current flow across each resistor and calculate the current using Ohm’s law. They compare the mathematically derived current values to the measured values, and calculate the percentage difference of their results. This leads students to conclude that real-world applications of science do indeed depend on mathematics! Students make posters to communicate their results and conclusions. A pre/post-activity quiz and student worksheet are provided. Adjustable for math- or science-focused classrooms.

Subject:
Algebra
Applied Science
Engineering
Mathematics
Measurement and Data
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
Activities
Author:
Marianne Livezey
Date Added:
11/01/2017
Are Random Triangles Acute or Obtuse?
Conditional Remix & Share Permitted
CC BY-NC-SA
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This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

Subject:
Geometry
Mathematics
Statistics and Probability
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Gilbert Strange
Date Added:
06/02/2012
Basic Mathematics
Unrestricted Use
CC BY
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This course is a continuation of MAT087, Basic Mathematics. Topics include signed numbers, decimal numbers, exponential notation, scientific notation, solving and graphing linear equations, an introduction to polynomials, and systems of linear equations and their graphs. Geometrical topics include lines and angles, closed curves and convex polygons, triangles and similarities, and symmetry and proportion in nature and art. Students may complete this course during the first three weeks of the semester by passing the MyMathLab modules. Students will then be eligible to take either MAT 099 Intermediate Algebra, MAT 114-Quantitative Reasoning or MAT 120-Intro to Statistics the following semester. This course does not satisfy degree requirements.

Subject:
Mathematics
Material Type:
Full Course
Provider:
Northern Essex Community College
Author:
Jim Sullivan
Date Added:
05/15/2019
Basic Mathematics
Unrestricted Use
CC BY
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Topics include signed numbers, decimal numbers, exponential notation, scientific notation, solving and graphing linear equations, an introduction to polynomials, and systems of linear equations and their graphs. Geometrical topics include lines and angles, closed curves and convex polygons, triangles and similarities, and symmetry and proportion in nature and art. All course content by John McColgan. Content added to OER Commons by Victoria Vidal.

Subject:
Mathematics
Numbers and Operations
Material Type:
Syllabus
Provider:
Roxbury Community College
Date Added:
10/09/2019
Basic Mathematics
Unrestricted Use
CC BY
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This course is a continuation of MAT087, Basic Mathematics. Topics include signed numbers, decimal numbers, exponential notation, scientific notation, solving and graphing linear equations, an introduction to polynomials, and systems of linear equations and their graphs. Geometrical topics include lines and angles, closed curves and convex polygons, triangles and similarities, and symmetry and proportion in nature and art. Students may complete this course during the first three weeks of the semester by passing the MyMathLab modules. Students will then be eligible to take either MAT 099 Intermediate Algebra, MAT 114-Quantitative Reasoning or MAT 120-Intro to Statistics the following semester. This course does not satisfy degree requirements.

Subject:
Mathematics
Material Type:
Full Course
Provider:
Roxbury Community College
Author:
John McColgan
Date Added:
05/15/2019
Building and Solving Equations 1
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.

Subject:
Algebra
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
CTE Health Sciences: Dental Impressions
Conditional Remix & Share Permitted
CC BY-NC-SA
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This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Subject:
Algebra
Applied Science
Business and Communication
Health, Medicine and Nursing
Mathematics
Ratios and Proportions
Material Type:
Activity/Lab
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
07/27/2012
CTE Health Sciences: Spread of Disease
Conditional Remix & Share Permitted
CC BY-NC-SA
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This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Subject:
Algebra
Applied Science
Functions
Health, Medicine and Nursing
Mathematics
Material Type:
Activity/Lab
Lesson Plan
Provider:
National Association of State Directors of Career Technical Education Consortium
Provider Set:
Career Technical Education
Date Added:
07/26/2012
Cell Phone Plans
Unrestricted Use
CC BY
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This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Classifying Solutions to Systems of Equations
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using substitution to complete a table of values for a linear equation; identifying a linear equation from a given table of values; and graphing and solving linear equations.

Subject:
Algebra
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
Date Added:
04/26/2013
Comparing Speeds in Graphs and Equations
Unrestricted Use
CC BY
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This task provides the opportunity for students to reason about graphs, slopes, and rates without having a scale on the axes or an equation to represent the graphs. Students who prefer to work with specific numbers can write in scales on the axes to help them get started.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Coupon versus discount
Unrestricted Use
CC BY
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This task involves solving equations with rational coefficients, and requires students to use the distributive law ("combine like terms"). The equation also provides opportunities for students to observe structure in the equation to find a quicker solution, as in the second solution presented.

Subject:
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Differential Equations: 2nd Order Linear Homogeneous Differential Equations 1
Conditional Remix & Share Permitted
CC BY-NC-SA
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This 10-minute video lesson provides an introduction to 2nd order, linear, homogeneous differential equations with constant coefficients. [Differential Equations playlist: Lesson 13 of 45]

Subject:
Algebra
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Khan, Salman
Date Added:
02/20/2011
Differential Equations: 2nd Order Linear Homogeneous Differential Equations 2
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CC BY-NC-SA
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This 8-minute video lesson continues the discussion from the previous video and shows how to find the general solution. [Differential Equations playlist: Lesson 14 of 45]

Subject:
Algebra
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Khan, Salman
Date Added:
02/20/2011
Differential Equations: 2nd Order Linear Homogeneous Differential Equations 3
Conditional Remix & Share Permitted
CC BY-NC-SA
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This 6-minute video lesson continues the discussion from the previous videos and introduces some initial conditions to solve for the particular solution. [Differential Equations playlist: Lesson 15 of 45]

Subject:
Algebra
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Khan, Salman
Date Added:
02/20/2011
Differential Equations: 2nd Order Linear Homogeneous Differential Equations 4
Conditional Remix & Share Permitted
CC BY-NC-SA
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This 9-minute video lesson continues the discussion from the previous videos and provides another example using initial conditions. [Differential Equations playlist: Lesson 16 of 45]

Subject:
Algebra
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Khan, Salman
Date Added:
02/20/2011