Objective
Make connections between the four representations of proportional relationships (Part 1).
Common Core Standards
Core Standards
The core standards covered in this lesson
7.RP.A.2— Recognize and represent proportional relationships between quantities.
Ratios and Proportional Relationships
7.RP.A.2— Recognize and represent proportional relationships between quantities.
7.RP.A.2.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.
Ratios and Proportional Relationships
7.RP.A.2.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.
7.RP.A.2.B— Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Ratios and Proportional Relationships
7.RP.A.2.B— Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
7.RP.A.2.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.
Ratios and Proportional Relationships
7.RP.A.2.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.
7.RP.A.2.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.
Ratios and Proportional Relationships
7.RP.A.2.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.
Foundational Standards
The foundational standards covered in this lesson
6.RP.A.3
Ratios and Proportional Relationships
6.RP.A.3— Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Identify the constant of proportionality in graphs, equations, and tables.
- Represent and analyze proportional relationships in graphs, equations, and tables.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
Lessons 10 and 11 pull together all the representations of proportional relationships – written description, table, graph, and equation – that students have been studying since the beginning of the unit. As needed, review any one representation that students may be stuck on, but continue to engage them in looking at multiple representations at a time in order to strengthen the connections between them.
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Anchor Problems
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Problem 1
A scientist plants a seed in a laboratory and tracks the growth of the plant. The height of the plant in centimeters is proportional to the number of days since it was planted.
a.Explain what point B represents in context of the situation.
b.At what rate is the plant growing? Indicate this as a point on the graph.
c.Write an equation that represents the relationship between days and height.
d.If the plant continues to grow at this rate, how tall will it be after 12 days?
e.If the plant continues to grow at this rate, when will it be 6 cm tall?
Guiding Questions
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Problem 2
Match each table to its equation.
i.$${y = {1 \over 2}x}$$
ii.$${y = {2 \over 3}x}$$
iii.$${y = 2x}$$
iv.$${y=3x}$$
Guiding Questions
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Problem 3
The cost you pay for limes is proportional to the number of limes you buy. Four different stores sell limes for different amounts, as shown in the graphs, table, and equation below. Which store should you go to if you want to pay the least amount for limes? Explain your answer.
Guiding Questions
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Problem Set
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Fishtank Plus Content
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
The width of a small book measures 6 inches, or approximately 15 centimeters. You know that the relationship between inches and centimeters is proportional, but you can’t remember the conversion rate between them.
Let $$y$$represent the number of centimeters and$$x$$represent the number of inches. Represent the relationship in the coordinate plane below, and then write an equation that approximates the relationship between inches and centimeters.
Student Response
An example response to the Target Task at the level of detail expected of the students.
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Additional Practice
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
- MARS Summative Assessment Tasks for Middle School Buses
- SERP Poster Problems Drag Racer Dragonfly
- EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 8—Example 2, Exit Ticket, Problem Set 5-6
- MARS Formative Assessment Lessons for Grade 7 Representing: Road Race
Lesson 9
Lesson 11
