The given solutions for this task involve the creation and solving of a system of two equations and two unknowns, with the caveat that the context of the problem implies that we are interested only in non-negative integer solutions. Indeed, in the first solution, we must also restrict our attention to the case that one of the variables is further even.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: In each of the equations below, rewrite the equation, solving for the indicated variable If $F$ denotes a temperature in degrees Fahrenheit and $C$ is ...

A work in progress, CK-12's Algebra I Second Edition is a clear presentation of algebra for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations.

CK-12 Foundation's Basic Algebra FlexBook is an introduction to the algebraic topics of functions, equations, and graphs for middle-school and high-school students.

This course covers a range of algebraic topics:  Setting up and solving linear equations, graphing, finding linear relations, solving systems of equations, working with polynomials, factoring, working with rational and radical expressions, solving rational and radical equations, solving quadratic equations, and working with functions.  More importantly, this course is intended to provide you with a solid foundation for the rest of your math courses.  As such, emphasis will be placed on mathematical reasoning, not just memorizing procedures and formulas. There is enough content in this course to cover both beginning and intermediate college-level algebra.

This lesson begins with a demonstration prompting students to consider how current generates a magnetic field and the direction of the field that is generated. Through formal lecture, students learn Biot-Savart's law in order to calculate, most simply, the magnetic field produced in the center of a circular current carrying loop. For applications, students find it is necessary to integrate the field produced over all small segments in an actual current carrying wire.

Students revisit the mathematics required to find bone mineral density, to which they were introduced in lesson 2 of this unit. They learn the equation to find intensity, Beer's law, and how to use it. Then they complete a sheet of practice problems that use the equation.

Overview of how the Pennsylvania Common Core Standards for Mathematics are driving changes in classrooms and schools, and where resources can be found to support the implementation of those changes.

CK-12 Foundation's Algebra FlexBook is an introduction to algebraic concepts for the high school student. Topics include: Equations & Functions, Real Numbers, Equations of Lines, Solving Systems of Equations & Quadratic Equations.

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.

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.

In this stage students practice using the Design Recipe to write functions which solve for word problems. Towards the end of the lesson students should be ready to begin using the Design Recipe on problems from your own math curriculum.

This film features a cross-disciplinary project which resulted from a collaboration between a mathematics teacher and an art teacher, celebrating the beauty of both fields. Although its sub-title is Making Calculus Delicious, the math featured in the book is primarily geometry and algebra, with students creating artistic interpretations of mathematical concepts and formulas. The translation of mathematics to art promoted fresh conceptual discussion and creative thinking, and inspires consideration of the elegance in mathematics.

As a continuation of the theme of potential and kinetic energy, this lesson introduces the concepts of momentum, elastic and inelastic collisions. Many sports and games, such as baseball and ping-pong, illustrate the ideas of momentum and collisions. Students explore these concepts by bouncing assorted balls on different surfaces and calculating the momentum for each ball.

The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of of a car). Indeed, the given form of the combined fuel economy computation is useful for direct calculation, but if asked for an approximation, is not particularly helpful.

This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one. Two of the equations are of physical significance and are examples of Ohm's Law and Newton's Law of Universal Gravitation.

This lesson unit is intended to help teachers assess how well students are able to: use the Pythagorean theorem to derive the equation of a circle; and translate between the geometric features of circles and their equations.

This is course material published for a secondary Math 1 course. Authors of this work are: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius and updated from the original work in 2013 in partnership with the Utah State Office of Education.

This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, it will help you identify and help students who have difficulty: decomposing complex shapes into simpler ones in order to solve a problem; bringing together several geometric concepts to solve a problem; and finding the relationship between radii of inscribed and circumscribed circles of right triangles.