"This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems."

The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level (e.g, 6.EE.5). By asking students to reason about solutions without explicily solving them, we get at the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally very simple; the point of the task is not to test technique in solving equations, but to encourage students to reason about them.

This task illustrates the process of rearranging the terms of an expression to reveal different aspects about the quantity it represents, precisely the language being used in standard A-SSE.B.3.

The Illustrative Mathematics Project provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.

Students are asked to consider the expression that arises in physics as the combined resistance of two resistors in parallel. However, the context is not explicitly considered here. The task is good general preparation for problems more specifically aligned to either A-SSE.1 or A-SSE.2.

The purpose of this task is to help students see manipulation of expressions as an activity undertaken for a purpose.

This blended unit introduces students to linear inequalities and systems of inequalities. Students will algebraically and graphically verify solutions to linear inequalities and systems of linear inequalities.  Instruction and practice will be provided via Khan Academy.  As a capstone project, students will use linear programming to develop a diet plan for a celebrity; the diet plan requires students to research nutritional data and costs for two food products, while using linear programming to find the diet plan that satisfies the celebrity's daily nutritional needs at the lowest cost.

Selection of material from the following topics: calculus of variations (the first variation and the second variation); integral equations (Volterra equations; Fredholm equations, the Hilbert-Schmidt theorem); the Hilbert Problem and singular integral equations of Cauchy type; Wiener-Hopf Method and partial differential equations; Wiener-Hopf Method and integral equations; group theory.

Students will study polynomials and factoring; roots; radical and rational expressions and equations; functions and their graphs; quadratic equations, complex numbers and parabolas. Applications in these areas will be covered. Use of graphing utilities will also be explored.

This is a unit that formalizes the definition of functions. Students will connect the idea of mathematical relationships to the concept of functions. With a mix of direct instruction, guided notes with procedural practice, and individual practice, this unit will ground students in the concept and provide a deep understanding of its usefulness.

This lesson is an introduction to learning to graph linear equations written in Slope-Intercept Form. It was written for the Beginning Algebra 1 student.

This animation from KET's distance learning physics course demonstrates the mathematical formula for a scientific law as it applies to light.

The purpose of this task is to give students practice in reading, analyzing, and constructing algebraic expressions, attending to the relationship between the form of an expression and the context from which it arises. The context here is intentionally thin; the point is not to provide a practical application to kitchen floors, but to give a framework that imbues the expressions with an external meaning.

This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing.

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.

In this unit, students will learn how to use inverse operations to solve equations/inequalities containing variables, write equations/inequalities to represent real life situations, and simplify equations/inequalities before solving.

This activity is a culmnating assessment of students' abilities to describe a linear function in words, in an equation, in a table, in a graph, identify a solution, and explain the solution.
Remix of: AEA Template for Building Lessons

Students use latex tubes and bicycle pumps to conduct experiments to gather data about the relationship between latex strength and air pressure. Then they use this data to extrapolate latex strength to the size of latex tubing that would be needed in modern passenger sedans to serve as hybrid vehicle accelerators, thus answering the engineering design challenge question posed in the first lesson of this unit. Students input data into Excel spreadsheets and generate best fit lines by the selection of two data points from their experimental research data. They discuss the y-intercept and slope as it pertains to the mathematical model they generated. Students use the slope of the line to interpret the data collected. Then they extrapolate with this information to predict the latex dimensions that would be required for a full-size hydraulic accumulator installed in a passenger vehicle.

This task asks students to consider the linear and quadratic functions appearing on a coordinate plane.

Students measure the relative intensity of a magnetic field as a function of distance. They place a permanent magnet selected distances from a compass, measure the deflection, and use the gathered data to compute the relative magnetic field strength. Based on their findings, students create mathematical models and use the models to calculate the field strength at the edge of the magnet. They use the periodic table to predict magnetism. Finally, students create posters to communicate the details their findings. This activity guides students to think more deeply about magnetism and the modeling of fields while practicing data collection and analysis. An equations handout and two grading rubrics are provided.