In this four part series, we visit the classrooms of two partner teachers who plan all their lessons together but have totally different styles inside the classroom. See the same lesson unfold in each class, the class structures used by each teacher, and the group work formats used by each.

This lesson introduces solar energy and tasks students with solving an algebraic equation to determine the amount of daily sunlight needed to make a solar panel effective.

Step 1 - Inquire: Students work through a practice problem and discuss what they already know about solar energy.

Step 2 - Investigate: Students briefly learn some background information about solar energy and then use algebra to calculate the amount of peak sun hours needed to make a solar panel effective. Students compare their calculated values to real-world data to determine if this amount of sunlight is possible in their area.

Step 3 - Inspire: Students make predictions and discuss if they think their home could be powered by solar panels using the calculations from class as evidence.

Students write expressions for geometric situations. They examine how different equivalent expressions can show different ways of thinking about the same problem.Key ConceptsStudents use their previous knowledge of how to find the perimeter and area of squares and rectangles. They write algebraic expressions for the perimeter and area of geometric figures. They examine how equivalent expressions, used to represent a problem situation, give clues to the approach the writer of the expression used to solve the problem. In the Challenge Problem, they use the distributive property to find the solution.ELL: For ELLs, access prior knowledge by writing the words area and perimeter on the board. Have students create concept maps associated with area and perimeter. Record students' responses on large poster paper that you can display in the room. The goal is to generate a list of words that students can use as a reference.Goals and Learning ObjectivesAccess prior knowledge of how to find the perimeter and area of squares and rectangles.Write algebraic expressions for finding perimeter or area of figures.Identify equivalent expressions.

This 11-minute video lesson shows that orthogonal matrices preserve angles and lengths. [Linear Algebra playlist: Lesson 129 of 143]

In the last stage, students wrote some very simple functions - but more sophisticated functions demand a more thoughtful approach. The Design Recipe is a structured approach to writing functions that includes writing a purpose statement and test cases to ensure that the function works as expected. Once students have mastered the Design Recipe process, they can apply it to any word problem they encounter.

Using the Design Recipe, students will work through a series of word problems about calculating the height of a rocket after a given number of seconds from launch. The functions they write will be used to animate the rocket launch.

This 9-minute video lesson provides definitions of the vector dot product and vector length.

In this lesson we will build on students' understanding variables by making functions that reduce the number of inputs required. These 'fast functions' allow students to practice using the Design Recipe to develop simple functions without the additional overhead of parsing a word problem.

In the past lessons students have defined Variables and written Fast Functions. In this stage, they will continue to explore function writing with ever increasing complexity.

Booleans are the fourth and final data type that students will learn about in this course. In this stage, students will learn about Boolean (true/false) values, and explore how they can be used to evaluate logical questions.

Objective: Students will demonstrate a cursory knowledge of solving basic algebraic equations, as well as an understanding of the methods necessary to evaluate them.  Students will know and understand the steps involved with basic algebra,  so as to prepare them for Algebra in their educational future.          

This Intermediate Algebra textbook was developed with consideration of neuroscience principles about learning. It is organized around the concepts of 'solving' and 'graphing'. The problem sets incorporate distributed and mixed practice to promote long term memory formation for the concepts and procedures involved in each section.

This 16-minute video lesson shows that a projection onto a subspace is a linear transformation. [Linear Algebra playlist: Lesson 110 of 143]

To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and the two ways will always result in the same vector.​​

This sample shell is produced by the California Community Colleges CVC-OEI to support faculty in the use of Open Educational Resources and development of courses aligned to the OEI Course Design Rubric. The shell may be used for online, hybrid, &/or face-to-face classes. The shell is available for all faculty, not just those faculty in the CCC system. The team producing this shell includes Helen Graves, Liezl Madrona, Cyrus Helf, Nicole Woolley & Barbara Illowsky. If you are having challenges importing the shell, here are some steps to take. (1) Create an empty shell in your sandbox. (2) Import the Canvas Commons course into your shell. (3) Adapt the content as you wish. (4) If all else fails, contact your college IT person or Canvas administrator.

Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Complex Variables, Differential Equations, and Linear Algebra is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. Students should have mastered the first two courses in the series (Single Variable Calculus and Multivariable Calculus) before taking this course.
The series was first released in 1972, but equally valuable today for students who are learning these topics for the first time.
About the Instructor
Herb Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the Mathematics As A Second Language website, providing arithmetic and algebra materials to elementary and middle school teachers.
Acknowledgements
Funding for this resource was provided by the Gabriella and Paul Rosenbaum Foundation.
Other Resources by Herb Gross
Calculus Revisited: Single Variable Calculus 
Calculus Revisited: Multivariable Calculus

This site teaches Reasoning with Equations and Inequalities to High Schoolers through a series of 5909 questions and interactive activities aligned to 36 Common Core mathematics skills.

This lab is generally the first lab for this course. It introduces students to desmos.com and helps them become familiar with it.
The lab investigates the visual changes to a line as the slope and y-intercept change.