# Standard: 8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

# 7.RP.2 Recognize and represent proportional relationships between quantities.

a. Decide whether two quantities are in a proportional relationship, e.g. by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

# Assessment rubric

 Mastery Level Description Evidence 4 Extended Thinking 3 Mastery I can use similar triangles to explain why the slope (m) is the same between any two points on a non-vertical line.I can create the equation y=mx for a line through the origin.I can create the equation y=mx+b for a line that passes through the y axis at b [b represents the ordered pair (0,b)].I can graph proportional relationships.I can determine and describe the unit rate as the slope of the graph.I can compare two different proportional relationships using different models such as graphs, equations, or tables. Draw similar triangles on a non-vertical line to show that the slope of the line is constant.Explain the difference between a zero slope and an undefined slope.Create an equation for y=mx.Create an equation for y=mx+b.Understand the difference between the slope of a non-vertical and vertical line.Graph the proportional relationships using tables, or equations.Find the slope given a set of information (i.e. graphs, tables, or equations.Read the graph to determine how to label the slope.Compare the unit rate of proportional relationships. 2 Foundational I can use proportional relationships to solve real world problems.I can use estimation to determine if the answer makes sense.I can recognize and represent proportional relationships.I can graph proportional relationships.I can identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions.I can graph an equivalent ratio.I can observe that the graph of a proportional relationship represents a straight line through the origin.I can represent proportional relationships as equations.I can explain the points (0,0) and (1,r) mean where r is the unit rate on a coordinate graph. Analyze the solution to determine whether or not the answer is reasonable.Use estimation  and  strategies for analyzing proportional relationships to determine whether or not the answer is reasonable.Explain the method used to solve the proportional relationship problem.Use proportional relationships to solve multistep ratio and percent problems.Label answers appropriately.Test using equivalent ratios to determine whether a relationship is proportional. 1 Emerging I can solve real-life problems using ratios and rates.I can make a table to compare ratios and plot the results on a coordinate plane.I can calculate unit rate problems involving unit pricing and speed.I can find a percent of a quantity as a rate per 100.I can change measurements from one unit to another by using ratios. Make a table to compare ratios and plot the results on a coordinate plane.Calculate unit rate problems involving unit pricing and speedCalculate percents and solve problems involving whole, part, and percent.Convert measurement units by using ratios.

# Text and video

CK-12 Understanding Percent (text)

CK-12 Graphing Functions (text)

CK-12 The Percent Equation (text)

CK-12 Percent of Change (text)

CK-12 Applications Using Percent (text)

CK-12 Percents and Fractions (text)

CK-12 Percents and Proportions (text)

CK-12 Percents and Decimals (text)

CK-12 Solving Proportions Using Cross Products (text)

Engage NY 6th Grade Module 1 - Topic D (Percent)

Engage NY 7th Grade Module 1 - Topic A (Proportional Relationships)

Engage NY 7th Grade Module 1 - Topic B (Unit Rates and Constant of Proportionality)

Engage NY 7th Grade Module 1 - Topic C (Ratios and Rates Involving Fractions)

Engage NY 7th Grade Module 1 - Topic D (Ratios of Scale Drawings)

OpenEd eSpark Learning Proportional Graphs Framing (video)

LearnZillion Videos for 6.RP.3

Learnzillion Videos for 7.RP.2

LearnZillion Videos for 7.RP.3

LearnZillion Videos for 8.EE.5

LearnZillion Videos for 8.EE.6

# Interactive & simulations

Geogebra Similar Triangles Show Slope

# Practice/PDF/worksheets

Gooru Slope Exploration

Illuminations Counting for Slope

# Group and collaborative activities

Inside Mathematics Problem of the Month - Movin’ and Groovin’

Inside Mathematics Problem of the Month - First Rate

Inside Mathematics Problem of the Month - Measuring Mammals

# Assessments

Howard County - 6.RP.A.1 Assessment Items

Howard County - 6.RP.A.3a Assessment Items

Howard County - 6.RP.A.3b Assessment Items

Howard County - 6.RP.A.3c Assessment Items

Howard County - 6.RP.A.3d Assessment Items

Howard County - 7.RP.A.1 Assessment Items

Howard County - 7.RP.A.2a Assessment Items

Howard County - 7.RP.A.2b Assessment Items

Howard County - 7.RP.A.2c Assessment Items

Howard County - 7.RP.A.2d Assessment Items

Howard County - 7.RP.A.3 Assessment Items

Howard County - 8.EE.B.5 Assessment Items

Howard County - 8.EE.B.6 Assessment Items

# Resources not free but applicable to the content/standard

IXL.com - 6th Grade Ratios and Rates (R.1 - R.12)

IXL.com - 6th Grade Percents (S.1 - S.8)

IXL.com - 7th Grade Ratios, Rates, Proportions (J.1 - J.14)

IXL.com - 7th Grade Proportional Relationships (K.1 - K.8)

IXL.com - 7th Grade Percents (L.1 - L.10)

IXL.com - 7th Grade Consumer Math (M.1 - M.12)

Flower Power (MangaHigh) - Converting Between Fractions, Decimals, and Percents

Flower Power Lite (MangaHigh) - Converting Between Fractions and Decimals