Lesson OverviewStudents calculate the constant of proportionality for a proportional relationship based on a table of values and use it to write a formula that represents the proportional relationship.Key ConceptsIf two quantities are proportional to one another, the relationship between them can be defined by a formula of the form y = kx, where k is the constant ratio of y-values to corresponding x-values. The same relationship can also be defined by the formula x=(1k)y , where 1k is now the constant ratio of x-values to y-values.Goals and Learning ObjectivesDefine the constant of proportionality.Calculate the constant of proportionality from a table of values.Write a formula using the constant of proportionality.

Students explore the idea that not all straight lines are proportional by comparing a graph representing a stack of books with a graph representing a stack of cups. They recognize that all proportional relationships are represented as a straight line that passes through the origin.Key ConceptsNot all graphs of straight lines represent proportional relationships.There are three ways to tell whether a relationship between two varying quantities is proportional:The graph of the relationship between the quantities is a straight line that passes through the point (0, 0).You can express one quantity in terms of the other using a formula of the form y = kx.The ratios between the varying quantities are constant.Goals and Learning ObjectivesUnderstand when a graph of a straight line is and when it is not a proportional relationship.Recognize that a proportional relationship is shown on a graph as a straight line that passes through the origin (0, 0).Make a table of values to represent two quantities that vary.Graph a table of values representing two quantities that vary.Describe what each variable and number in a formula represents.

Students continue to explore the three relationships from the previous lessons: Comparing Dimensions, Driving to the Amusement Park, and Temperatures at the Amusement Park. They graph the three situations and realize that the two proportional relationships form a straight line, but the time and temperature relationship does not.Key ConceptsA table of values that represent equivalent ratios can be graphed in the coordinate plane. The graph represents a proportional relationship in the form of a straight line that passes through the origin (0, 0). The unit rate is the slope of the line.Goals and Learning ObjectivesRepresent relationships shown in a table of values as a graph.Recognize that a proportional relationship is shown on a graph as a straight line that passes through the origin (0, 0).

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.

This video explains how to use graphs, including how to set up a graph, the use of variables, and how to interpret the data. Disclaimer: Host website is responsible for accessibility compliance. Educator is responsible for accommodations.

The purpose of this lesson is to teach students about the three dimensional Cartesian coordinate system. It is important for structural engineers to be confident graphing in 3D in order to be able to describe locations in space to fellow engineers.

* This unit is an adaptation of the Everyday Mathematics (EM) Kindergarten Curriculum, 4th Edition, published by McGraw Hill Education.  The source material is copyrighted and all rights are reserved.  With this in mind, only the adaptations will be explored in this document.  To access the Everyday Mathematics curriculum and some online components, your school or district must purchase them from McGraw Hill.

The Everyday Mathematics curriculum does not teach concepts in the historical unit-by-unit format.  Rather, key concepts are introduced and revisited in several units throughout the year.  The focus on returning to concept strands is referred to as "spiralling."  The spiral strand targeted in this unit is focussed on data collection and representation.  Students will learn how to represent data on (and read data from) charts and graphs.

Students have mastered solving equations and looking at solutions graphically. This unit is an extension and will have students investigate how to find to two equations. This unit will utilize investigate and exploration,  with some direct instruction, to solidify the process and procedures to finding and identifying solutions to systems.

This lesson is from Tools4NCTeachers.In this lesson, students build pattern block animals inspired by literature, describe and graph the shapes used, and interpret the data by asking and answering questions to develop the concepts of geometry and graphing. Remix this lesson to include extension ideas or samples of student work.

In this lesson, students will graph translations (slides) and reflections (flips) on a coordinate plane. The lesson is introduced by having students move across the room to demonstrate translations and reflections.

CK-12 Foundation's Trigonometry FlexBook is an introduction to trigonometry for the high school student. Topics include: Trigonometric Identities & Equations, Circular Functions, and Polar Equations & Complex Numbers.

CK-12's Texas Instruments Trigonometry Student Edition Flexbook is a helpful companion to a trigonometry course, providing students with more ways to understand basic trigonometric concepts through supplementary exercises and explanations.

CK-12's Texas Instruments Trigonometry Teacher's Edition Flexbook is a helpful companion to a trigonometry course, providing students with more ways to understand basic trigonometric concepts through supplementary exercises and explanations.

CK-12 Trigonometry Teacher's Edition provides tips and common errors for teaching CK-12 Trigonometry Student Edition. The solution and assessment guides are available upon request.

In this activity, a student challenges a partner to recreate his quadrilateral or other shape on a geoboard by calling out the ordered pairs of the quadrilateral's vertices.