Explore Algebraic Expressions in this free video unit. It is comprised of 6 lessons with 4-7 short videos in each lesson. Featuring the reasoning of Grade 9 students, the unit explores how to generalize arithmetic to algebra and relate algebraic symbols to their meaning in context. The videos provide a foundation for the Common Core State Standards about equivalent forms of functional relationships. Showing these videos is great for helping students develop meaning for algebraic expressions beyond symbol manuipulation. 

Explore Binomials in this free video unit. It is comprised of 6 lessons with 7-8 short videos in each lesson. Featuring the reasoning of Grade 10 students, the unit moves beyond the procedure of FOIL by exploring the “why” behind multiplication of binomials. The videos provide a foundation for the Common Core State Standards about performing operations on polynomials. Showing these videos can help students become more comfortable operating binomials by grounding the operations in real-world contexts. 

Explore Exponentials in this free video unit. It is comprised of 7 lessons with 4-7 short videos in each lesson. Featuring the reasoning of Grade 8 students, the unit explores generalizing and graphing exponential functions through the use of a dynamic applet. Show these videos to help students visualize exponential growth in a real-world context and make sense of fractional exponents. 

Explore Parabolas in this free video unit as a part of Project MathTalk. It is comprised of 10 lessons with 5-7 short videos in each lesson. Featuring the reasoning of Grade 10 students, the unit explores how to make sense of the geometric definition of a parabola. The videos provide a foundation for the Common Core State Standard: “Derive the equation of a parabola given a focus and directrix.” Showing these videos are great for classrooms that want to make connections between Geometry and Algebra. 

Explore Proportions in this free video unit. It is comprised of 7 lessons with 4-6 short videos in each lesson. Featuring the reasoning of Grade 6 students, the unit explores how to form and iterate ratios through the use of a dynamic applet. The videos provide a foundation for the Common Core State Standards about using ratios and rates to solve math problems. Showing these videos are helpful for teachers who want to move students from reasoning additively to forming multiplicative comparisons. 

Explore Trigonometry in this free video unit. It is comprised of 8 lessons with 4-6 short videos in each lesson. Featuring the reasoning of Grade 11 students, the unit explores explores the concepts of angle measure and the sine function. The videos provide a foundation for the Common Core State Standard covering trigonometric concepts. Show these videos to help students build intuition for difficult trigonometric ideas, like moving fluidly between angles and radians and using trigonometric functions to model real world data. 

This curriculum guide offers a list of Open Educational Resources (OER) that are arranged in a logical sequence for introducing polynomials with visual models, particularly using arrays and area models.

Prepared with pre-algebra or algebra 1 classes in mind, this module leads students through the process of graphing data and finding a line of best fit while exploring the characteristics of linear equations in algebraic and graphic formats. Then, these topics are connected to real-world experiences in which people use linear functions. During the module, students use these scientific concepts to solve the following hypothetical challenge: You are a new researcher in a lab, and your boss has just given you your first task to analyze a set of data. It being your first assignment, you ask an undergraduate student working in your lab to help you figure it out. She responds that you must determine what the data represents and then find an equation that models the data. You believe that you will be able to determine what the data represents on your own, but you ask for further help modeling the data. In response, she says she is not completely sure how to do it, but gives a list of equations that may fit the data. This module is built around the legacy cycle, a format that incorporates educational research feindings on how people best learn.

This set of problems for Linear Algebra in the open-source WeBWorK mathematics platform was created under a Round Eleven Mini-Grant for Ancillary Materials Creation. The problems were created for an implementation of the CC-BY Lyrix open textbook A First Course in Linear Algebra. Also included as an additional file are the selected and modified Lyryx Class Notes for the textbook.

Topics covered include:

Linear Independence
Linear Transformations
Matrix of a Transformation
Isomorphisms
Eigenvalues and Eigenvectors
Diagonalization
Orthogonality

The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.

This seminar will allow you to identify the domain and range of a relation, and then use the relationships that exist in order to determine whether or not the relation is a function. You will define functions, and you will learn how to identify and use functional notation. You will gain an understanding of the concept of a functional relationship which will allow you in the future to study specific functions in depth.StandardsCC.2.2.HS.C.1 - Use the concept and notation of functions to interpret and apply them in terms of their context.

The purpose of this task is to give students practice writing a constraint equation for a given context. Instruction accompanying this task should introduce the notion of a constraint equation as an equation governing the possible values of the variables in question.

This task looks at zeroes and factorization of a general polynomial. It is related to a very deep theorem in mathematics, the Fundamental Theorem of Algebra, which says that a polynomial of degree d always has exactly d roots, provided complex numbers are allowed as roots and provided roots are counted with the proper "multiplicity.''

The intention of this task is to provide extra depth to the standard A-APR.2 it is principally designed for instructional purposes only. The students may use graphing technology: the focus, however, should be on what happens to the function g when x=0 and the calculator may or may not be of help here (depending on how sophisticated it is!).

For a polynomial function p, a real number r is a root of p if and only if p(x) is evenly divisible by x_r. This fact leads to one of the important properties of polynomial functions: a polynomial of degree d can have at most d roots. This is the first of a sequence of problems aiming at showing this fact.

This task continues ``Zeroes and factorization of a quadratic polynomial I.'' The argument here generalizes, as shown in ``Zeroes and factorization of a general polynomial'' to show that a polynomial of degree d can have at most d roots. This task is intended for instructional purposes to help students see more clearly the link between factorization of polynomials and zeroes of polynomial functions.

In this activity, learners use basic measurements of the Earth and pieces of rock and iron to estimate the mass of the Earth. Learners will calculate mass, volume, and density, convert units, and employ the water displacement method. To calculate an even more accurate estimate of the mass of the Earth, this resource includes optional instructions on how to measure the iron core mass.