This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions. The task lends itself to an extended discussion comparing the differences that students have found and relating them back to the equation and the graph of the two functions.

In this lesson, eighth grade students will collect data. They will use this data to analyze the relationship between the height of an individual and the length of his/her foot. Students will use a line of fit to make predictions for people of different heights.

In this lesson, students relate constant speed and proportional relationships to linear functions using information from a table. Students know that distance traveled is a function of the time spent traveling and that the total cost of an item is a function of how many items are purchased.

In this lesson, students know that a function allows us to make predictions about the distance an object moves in any time interval. Students calculate average speed of a moving object over specific time intervals. Students know that constant rate cannot be assumed for every situation and use proportions to analyze the reasoning involved.

This general math site offers reference material on a host of math topics, plus a math message board and links to relevant material online. The tables cover a range of math skills, from basic fraction-decimal conversion to the more advanced calculus and discrete math. The information is presented in notation form, with diagrams, graphs, and tables. The site is available in English, Spanish, and French. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/

Adapted from mathematicsvisionproject.com’s Material Overview:
The Mathematics Vision Project (MVP) was created as a resource for teachers to implement the Common Core State Standards (CCSS) using a task-based approach that leads to skill and efficiency in mathematics by first developing understanding. The MVP approach develops the Standards of Mathematical Practice through experiential learning. Students engage in mathematical problem solving, guided by skilled teachers, in order to achieve mathematical proficiency: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. The MVP authors created a curriculum where students do not learn solely by either “internalizing what a teacher or book says or, on the other hand, solely by inventing mathematics on their own.”
The MVP classroom experience begins by confronting students with an engaging problem and allows them to grapple with solving it. As students’ ideas emerge, take form, and are shared, the teacher deliberately orchestrates the student discussions and explorations toward a focused math goal. Students justify their own thinking while clarifying, describing, comparing, and questioning the thinking of others leading to refined thinking and mathematical fluency. What begin as ideas become concepts that lead to formal, traditional math definitions and properties. Strategies become algorithms that lead to procedures supporting efficiency and consistency. Representations become tools of communication which are formalized as mathematical models. Students learn by doing mathematics.

CK-12 Foundation's Middle School Math Grade 6 Flexbook covers the fundamentals of fractions, decimals, and geometry. Also explored are units of measurement, graphing concepts, and strategies for utilizing the book's content in practical situations.

Provides teaching tips, information on common errors, differentiated instruction, enrichment, and problem solving for teachers to use with the CK-12 Middle School Math - Grade 6, Student Edition.

A work in progress, CK-12's Math 7 explores foundational math concepts that will prepare students for Algebra and more advanced subjects. Material includes decimals, fractions, exponents, integers, percents, inequalities, and some basic geometry.

This lesson unit is intended to help teachers assess how well students are able to: choose appropriate mathematics to solve a non-routine problem; generate useful data by systematically controlling variables; and develop experimental and analytical models of a physical situation.

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

This shows how Newton's method (also known as Newton-Raphson) is used to find a root of a function. You can show/hide various parts of the construction, and edit the particular function being considered.

This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation.

Students follow the steps of the engineering design process while learning more about assistive devices and biomedical engineering applied to basic structural engineering concepts. Their engineering challenge is to design, build and test small-scale portable wheelchair ramp prototypes for fictional clients. They identify suitable materials and demonstrate two methods of representing design solutions (scale drawings and simple models or classroom prototypes). Students test the ramp prototypes using a weighted bucket; successful prototypes meet all the student-generated design requirements, including support of a predetermined weight.

In this lesson, students interpret the rate of change and initial value of a line in context. Students interpret slope as rate of change and relate slope to the steepness of a line and the sign of the slope, indicating that a linear function is increasing if the slope is positive and decreasing if the slope is negative.

In this lesson, students examine and recognize real-world functions, such as the cost of a book, as discrete rates. Students examine and recognize real-world functions, such as the temperature of a pot of cooling soup, as continuous rates.

For this task, students demonstrate how slopes are affected when reflections are made.

This mini-unit is part of a much larger content focus on Linear Functions in an 8th grade Resource Math class. Students will be learning about the basics in functions and their use in Pre-Algebra. This unit allows students to receive direct interaction with teachers to receive content in a managable format, while giving them opportunities to learn and discover some of the content on their own. The mini-unit focus solely on the different representations of functions in their basic form. By the end of the unit, students will be able to identifying and compare and contrast different representations of functions.

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable.

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.