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1.OA Doubles?
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
5.OA Sidewalk Patterns
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
A-CED Cash Box
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The given solutions for this task involve the creation and solving of ...

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.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/18/2013
A-CED Regular Tessellations of the plane
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This task examines the ways in which the plane can be covered ...

This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

Subject:
Mathematics
Algebra
Geometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/21/2013
A-CED Uranium 238
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
A-REI, A-SSE, N-CN  Vertex of a parabola with complex roots
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
A-REI, A-SSE, N-CN  Vertex of a parabola with complex roots
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
A-REI, A-SSE, N-CN  Vertex of a parabola with complex roots
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
A-REI An Extraneous Solution
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
A-REI Basketball
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This task provides a simple but interesting and realistic context in which ...

This task provides a simple but interesting and realistic context in which students are led to set up a rational equation (and a rational inequality) in one variable, and then solve that equation/inequality for an unknown variable.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
12/15/2012
A-REI Canoe Trip
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
A-REI Ideal Gas Law
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
A-REI Solving Two Equations in Two Unknowns
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
A-REI  Who wins the Race?
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This is a task from the Illustrative Mathematics website that is one ...

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.

Subject:
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Date Added:
10/10/2017
Abstract Algebra
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Algebra is the language of modern mathematics. This course introduces students to ...

Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields.

Subject:
Algebra
Material Type:
Lecture
Provider:
Harvard University
Provider Set:
Harvard Extension School
Author:
Benedict Gross
Date Added:
01/22/2018
Abstract Algebra II
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This course is a continuation of Abstract Algebra I: the student will ...

This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232)

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
10/13/2017
Accurately Weighing Pennies I
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This problem involves solving a system of algebraic equations from a context: ...

This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/15/2012
Accurately Weighing Pennies II
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This task is a somewhat more complicated version of "Accurately weighing pennies ...

This task is a somewhat more complicated version of "Accurately weighing pennies I'' as a third equation is needed in order to solve part (a) explicitly. Instead, students have to combine the algebraic techniques with some additional problem-solving (numerical reasoning, informed guess-and-check, etc.)

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/15/2012
Addition Fact Strategies - Counting On (+1/+2)
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This lesson is intended to help students begin to transition away from ...

This lesson is intended to help students begin to transition away from a one-to-one correspondence. Students at this point should be able to use concrete ojects to identify values.Goal: Students will be able to use a number line to "Count On from Greater" 

Subject:
Algebra
Numbers and Operations
Material Type:
Lesson Plan
Author:
Samuel Shackleford
Date Added:
04/02/2018
Advanced Algebra II: Activities and Homework
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No Strings Attached
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This is the main text of Kenny Felder's course in Advanced Algebra ...

This is the main text of Kenny Felder's course in Advanced Algebra II. It consists of a series of worksheets, some intended to be used in class as group activities, and some intended to be used as homework assignments. This text is designed for use with the "Advanced Algebra II: Conceptual Explanations" and the "Advanced Algebra II: Teacher's Guide" collections to make up the entire course.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Provider:
Rice University
Provider Set:
Connexions
Author:
Kenny Felder
Date Added:
10/13/2017
Advanced Algebra II: Teacher's Guide
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No Strings Attached
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This is the Teacher's Guide for Kenny Felder's course in Advanced Algebra ...

This is the Teacher's Guide for Kenny Felder's course in Advanced Algebra II. This guide is *not* an answer key for the homework problems: rather, it is a day-by-day guide to help the teacher understand how the author envisions the materials being used. This text is designed for use with the "Advanced Algebra II: Conceptual Explanations" and the "Advanced Algebra II: Homework and Activities" collections (coming soon) to make up the entire course.

Subject:
Algebra
Material Type:
Full Course
Teaching/Learning Strategy
Provider:
Rice University
Provider Set:
Connexions
Author:
Kenny Felder
Date Added:
10/13/2017
Advanced Partial Differential Equations with Applications, Fall 2009
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" The focus of the course is the concepts and techniques for ...

" The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc."

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Rosales, Rodolfo R.
Date Added:
01/01/2009
Algebra
Conditions of Use:
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This course discusses how to use algebra for a variety of everyday ...

This course discusses how to use algebra for a variety of everyday tasks, such as calculate change without specifying how much money is to be spent on a purchase, analyzing relationships by graphing, and describing real-world situations in business, accounting, and science.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
10/13/2017
Algebra2Go - Prealgebra
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Prepare yourself to take an Algebra course with the Algebra2go䋢 prealgebra resources ...

Prepare yourself to take an Algebra course with the Algebra2go䋢 prealgebra resources page. Whether you are attending Saddleback College's prealgebra class (math 351), taking a prealgebra class at another school, or need to refresh your math skills for a business or science class, Professor Perez and his favorite student Charlie have the tools that can help you. We have five primary types of study materials: class notes, video worksheets, video lectures, practice problems, and practice quizzes. For some topics we have some additional tools to assist you.

Subject:
Algebra
Material Type:
Full Course
Homework/Assignment
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
10/13/2017
Algebra2go:  Decimals
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Part of the course for community college students featuring Professor Perez and ...

Part of the course for community college students featuring Professor Perez and his student Charlie, teaching about decimal concepts and operations.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lecture
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
10/13/2017
Algebra2go- PreAlgebra - Intro to Subtraction
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This course is for community college students featuring Professor Perez and his ...

This course is for community college students featuring Professor Perez and his student Charlie. This lesson demonstrates subtraction, including when the answer is negative, on the number line.

Subject:
Algebra
Material Type:
Assessment
Full Course
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
10/13/2017
Algebra2go: Pre-algebra Conversions
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No Strings Attached
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This is part of the course for community college students featuring Professor ...

This is part of the course for community college students featuring Professor Perez and his student Charlie, teaching how to make conversions between different kinds of units.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Lecture
Unit of Study
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Date Added:
10/13/2017
Algebra I
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This course is oriented toward US high school students. Its structure and ...

This course is oriented toward US high school students. Its structure and materials are aligned to the US Common Core Standards. Foci include: graphing, equations and inequalities.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
10/13/2017
Algebra II Module 1: Polynomial, Rational, and Radical Relationships
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Students connect polynomial arithmetic to computations with whole numbers and integers. Students ...

Students connect polynomial arithmetic to computations with whole numbers and integers.  Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.  This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions.  Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra.  Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
05/14/2013
Algebra II Module 2
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Module 2 builds on students’ previous work with units and with functions ...

Module 2 builds on students’ previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
08/15/2014
Algebra II Module 3: Exponential and Logarithmic Functions
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In this module, students synthesize and generalize what they have learned about ...

In this module, students synthesize and generalize what they have learned about a variety of function families.  They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4).  They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions.  They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3).  Students identify appropriate types of functions to model a situation.  They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit.  The description of modeling as, “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions,” is at the heart of this module.  In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
09/16/2014
Algebra II Module 4: Inferences and Conclusions from Data
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Students build a formal understanding of probability, considering complex events such as ...

Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability.  The idea of using a smooth curve to model a data distribution is introduced along with using tables and techonolgy to find areas under a normal curve.  Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.  Data is used from random samples to estimate a population mean or proportion.  Students calculate margin of error and interpret it in context.  Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
03/24/2016
Algebra II, Spring 2011
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This undergraduate level course follows Algebra I. Topics include group representations, rings, ...

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Artin, Michael
Date Added:
01/01/2011
Algebra I Module 3:  Linear and Exponential Functions
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In earlier grades, students define, evaluate, and compare functions and use them ...

In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
09/17/2013
Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions
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In earlier modules, students analyze the process of solving equations and developing ...

In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.

Subject:
Algebra
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
09/17/2013
Algebraic Combinatorics, Spring 2009
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" This is an introductory course in algebraic combinatorics. No prior knowledge ...

" This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected."

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Musiker, Gregg
Date Added:
01/01/2009
Algebraic Equations, Inequalities, and Properties
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This lesson is about trying to get students to make connections between ...

This lesson is about trying to get students to make connections between ideas about equations, inequalities, and expressions. The lesson is designed to give students opportunities to use mathematical vocabulary for a purpose to describe, discuss, and work with these symbol strings.The idea is for students to start gathering global information by looking at the whole number string rather than thinking only about individual procedures or steps. Hopefully students will begin to see the symbol strings as mathematical objects with their own unique set of attributes. (7th Grade Math)

Subject:
Algebra
Numbers and Operations
Material Type:
Activity/Lab
Lecture
Lesson Plan
Teaching/Learning Strategy
Provider:
Noyce Foundation
Provider Set:
Inside Mathematics
Author:
Disston, Jacob
Date Added:
10/10/2017
Algebraic Geometry, Spring 2009
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" This course provides an introduction to the language of schemes, properties ...

" This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry."

Subject:
Algebra
Geometry
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Kedlaya, Kiran
Date Added:
01/01/2009
Algebraic Techniques and Semidefinite Optimization, Spring 2006
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This research-oriented course will focus on algebraic and computational techniques for optimization ...

This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Parrilo, Pablo
Date Added:
01/01/2006
Algebraic Topology II, Spring 2006
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In this second term of Algebraic Topology, the topics covered include fibrations, ...

In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Behrens, Mark
Date Added:
01/01/2006
All About Multiplication
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This unit consists of four lessons in which students explore several meanings ...

This unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Grace M. Burton
Date Added:
11/05/2000
All about Linear Programming
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Students learn about linear programming (also called linear optimization) to solve engineering ...

Students learn about linear programming (also called linear optimization) to solve engineering design problems. As they work through a word problem as a class, they learn about the ideas of constraints, feasibility and optimization related to graphing linear equalities. Then they apply this information to solve two practice engineering design problems related to optimizing materials and cost by graphing inequalities, determining coordinates and equations from their graphs, and solving their equations. It is suggested that students conduct the associated activity, Optimizing Pencils in a Tray, before this lesson, although either order is acceptable.

Subject:
Mathematics
Algebra
Geometry
Material Type:
Lesson
Provider:
TeachEngineering
Provider Set:
TeachEngineering NGSS Aligned Resources
Author:
Andi Vicksman
CU Teach Engineering (a STEM licensure pathway), Engineering Plus Degree Program, University of Colorado Boulder
Maia Vadeen
Malinda Zarske
Nathan Coyle
Russell Anderson
Ryan Sullivan
Date Added:
10/13/2017
Animal Populations
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In this task students have to interpret expressions involving two variables in ...

In this task students have to interpret expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Applications of Linear Functions
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This final lesson in the unit culminates with the Go Public phase ...

This final lesson in the unit culminates with the Go Public phase of the legacy cycle. In the associated activities, students use linear models to depict Hooke's law as well as Ohm's law. To conclude the lesson, students apply they have learned throughout the unit to answer the grand challenge question in a writing assignment.

Subject:
Technology and Engineering
Mathematics
Algebra
Material Type:
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Aubrey McKelvey
TeachEngineering.org
VU Bioengineering RET Program, School of Engineering,
Date Added:
09/18/2014
Applied Geometric Algebra, Spring 2009
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Laszlo Tisza was Professor of Physics Emeritus at MIT, where he began ...

Laszlo Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976. Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems. The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface below. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

Subject:
Algebra
Physics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Tisza, L
Date Added:
01/01/2009
The Art of Approximation in Science and Engineering: How to Whip Out Answers Quickly
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The purpose of this learning video is to show students how to ...

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

Subject:
Technology and Engineering
Algebra
Numbers and Operations
Physics
Material Type:
Lecture
Provider:
MIT Learning International Networks Consortium
Provider Set:
M.I.T. Blossoms
Author:
Stephen M. Hou
Date Added:
10/10/2017
As People Get Older, They Get Taller
Conditions of Use:
Read the Fine Print
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This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data ...

This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data analysis concepts and the major theme of analyzing change. In the first lesson, students measure the heights of classmates and older students and construct a table of height and age data to compare them. The second lesson's instructional goal is to understand how change in one variable, age, can relate to change in a second variable, height. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.

Subject:
Mathematics
Algebra
Functions
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
Elana Joram and Christina Hartman
Date Added:
11/05/2008
Barbie Bungee (linear functions)
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The consideration of cord length is very important in a bungee jump‰ŰÓtoo ...

The consideration of cord length is very important in a bungee jump‰ŰÓtoo short, and the jumper doesn't get much of a thrill; too long, and ouch! In this lesson, students model a bungee jump using a Barbieĺ¨ doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions.

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Author:
NCTM Illuminations
Samuel E. Zordak
Thinkfinity/Verizon Foundation
Date Added:
02/12/2009
Beginning Algebra
Conditions of Use:
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This course is also intended to provide the student with a strong ...

This course is also intended to provide the student with a strong foundation for intermediate algebra and beyond. Upon successful completion of this course, you will be able to: simplify and solve linear equations and expressions including problems with absolute values and applications; solve linear inequalities; find equations of lines; and solve application problems; add, subtract, multiply, and divide various types of polynomials; factor polynomials, and simplify square roots; evaluate, simplify, multiply, divide, add, and subtract rational expressions, and solve basic applications of rational expressions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 001)

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Date Added:
10/13/2017
Beginning and Intermediate Algebra
Conditions of Use:
No Strings Attached
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This course covers a range of algebraic topics: Setting up and solving ...

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.

Subject:
Algebra
Material Type:
Full Course
Textbook
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Author:
Tyler Wallace
Date Added:
10/13/2017
Bernardo and Sylvia Play a Game
Conditions of Use:
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This task presents a simple but mathematically interesting game whose solution is ...

This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.

Subject:
Mathematics
Algebra
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
10/21/2013
Block Pounds
Conditions of Use:
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In this Illuminations lesson plan students explore the use of variables as ...

In this Illuminations lesson plan students explore the use of variables as they solve for the weights of objects using information presented in pictures. Learners model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols. A student activity sheet is available and downloadable (pdf).

Subject:
Mathematics
Algebra
Material Type:
Interactive
Lesson Plan
Provider:
National Council of Teachers of Mathematics
Provider Set:
Illuminations
Date Added:
11/05/2009
Braking Distance
Conditions of Use:
Remix and Share
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This task provides an exploration of a quadratic equation by descriptive, numerical, ...

This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

Subject:
Mathematics
Algebra
Functions
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
Building and Solving Equations 1
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This lesson unit is intended to help teachers assess how well students ...

This lesson unit is intended to help teachers assess how well students are able to create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.

Subject:
Algebra
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP)
Mathematics Assessment Project (MAP)
Date Added:
11/01/2017