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: Sketch graphs of $f(x) = \cos{x}$ and $g(x) = \sin{x}$. Find a translation of the plane which maps the graph of $f(x)$ to itself. Find a reflection of ...

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: Below is a picture of an angle $\theta$ in the $x$-$y$ plane with the unit circle sketched in purple: Explain why $\sin{(-\theta)} = -\sin{\theta}$ and...

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: Use the unit circle and indicated triangle below to find the exact value of the sine and cosine of the special angle $\pi/4.$...

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 aspects of the task and its potential use.

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 this task, you will show how all of the sum and difference angle formulas can be derived from a single formula when combined with relations you have...

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: The points on the graphs and the unit circle below were chosen so that there is a relationship between them. Explain the relationship between the coord...

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 the triangle pictured above show that \left(\frac{|AB|}{|AC|}\right)^2 + \left(\frac{|BC|}{|AC|}\right)^2 = 1 Deduce that $\sin^2{\theta} + \cos^2{\...

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: Below is a picture of a right triangle with $a$ the measure of angle $A$: Joyce knows that the sine of $a$ is the length of the side opposite $A$ divid...

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of different equations.

In this seminar you will learn how to factor monomials using prime factorization. You will apply prior knowledge about factoring integers. You will use the techniques learned in this seminar to factor polynomials with multiple terms as you move forward. When factoring monomials using this method, you will identify what product of prime numbers and variables will create the expression. This seminar will also begin finding the greatest common factor among multiple monomials, which is a skill that will be used moving forward on polynomials with multiple terms.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomialsCC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms.

In this seminar you will learn how to factor polynomials by looking for a common factor. You will apply the concepts of factoring integers, as well as factoring monomials and looking for the greatest common factor among terms. The techniques learned in this seminar will allow you to factor polynomials with multiple terms, and find solutions using factoring.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomialsCC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms

In this seminar you will learn how to factor quadratic equations. You will apply the concepts of factoring integers, factoring monomials, and looking for the greatest common factor among terms. The techniques learned in this seminar will allow you to use factoring to find solutions to quadratics and help with graphing.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomialsCC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms.CC.2.2.HS.C.5Construct and compare linear, quadratic, and exponential models to solve problems

The Factoring module is separated into two parts -- factoring numbers and factoring algebraic expressions.  Each part has subtopics. Each subtopic has a video lecture and a practice assignment.  The video lecture page includes guided notes in pdf form and videos that follow the guided notes.  Each video lecture page also includes supplemental YouTube videos which are optional for students and may be used if further instruction is needed.  The practice assignment is a set of exercises in Derivita that correspond to the skills covered in the video lecture.This work, by Magdalene (Maxie) Inigo, is licensed under a Creative Commons Attribution 4.0 International License.Links to an external site.CC-BY

For trinomials where the leading coefficient is not 1, factoring can be a labor intensive and difficult process. The "ac" method makes factoring more manageable.

This unit integrates a series of lessons on justice system based on given statistical facts. The essential question of the unit is: How can complex text and statistical numbers assist in illustrating the truth of our justice system? In Illustrating the truth through powerful colorful graphs that accentuate the statistics hidden in the text and illustrate facts in a dynamic form.

The aim of this video lesson is to introduce the concept of factorials, and to show students that everyday events in their lives have so much to do with factorials - even if they do not realize it! During this video, students will learn about the large number of ways to arrange people and objects using the mathematical concept of factorials. This video lesson will begin with a story of a family vacation to Pulau Pinang, an island located 330 km from the city of Kuala Lumpur in Malaysia. In this video, lessons about using factorials are demonstrated through several challenges this family encounters during their vacation. A prerequisite for this lesson is knowledge of the multiplication rule of counting. During the classroom activities, students are asked to carry out collaborative learning challenges in groups of 6. These activities require students to arrange cards to show different factorial arrangements that can be made. The materials needed for this activity are very simple. We only need to provide a few pieces of blank or colored paper for each student. The lesson will take about 40 – 50 minutes to complete.

This resource is a chart of definitions and examples of terms used to describe the features of a graph.

Students apply the vocabulary and concepts from the Activity 9: Feedback Loop Introduction to assess and create earth science feedback loops with the LOOPY online modeling program. (Optional) The students then engage in a discussion of the limitations of the LOOPY program to create feedback loop diagrams.

Students are introduced to feedback loop vocabulary and experiment with different relationships between reservoirs in simple feedback loops using LOOPY, a free, online modeling program.