This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Students are exptected to identify the slope of the line with the unit rate in this real world problem.

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.

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.

Students learn about the role engineers and mathematicians play in developing the perfect bungee cord length by simulating and experimenting with bungee jumping using washers and rubber bands. Working as if they are engineers for a (hypothetical) amusement park, students are challenged to develop a show-stopping bungee jumping ride that is safe. To do this, they must find the maximum length of the bungee cord that permits jumpers (such as brave Washy!) to get as close to the ground as possible without going "splat"! This requires them to learn about force and displacement and run an experiment. Student teams collect and plot displacement data and calculate the slope, linear equation of the line of best fit and spring constant using Hooke's law. Students make hypotheses, interpret scatter plots looking for correlations, and consider possible sources of error. An activity worksheet, pre/post quizzes and a PowerPoint® presentation are included.

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]

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]

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]

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]