Curriculum / Math / 7th Grade / Unit 1: Proportional Relationships / Lesson 11
Math
Unit 1
7th Grade
Lesson 11 of 18
Jump To
Lesson Notes
There was an error generating your document. Please refresh the page and try again.
Generating your document. This may take a few seconds.
Are you sure you want to delete this note? This action cannot be undone.
Make connections between the four representations of proportional relationships (Part 2).
The core standards covered in this lesson
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.
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.
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.
The foundational standards covered in this lesson
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
The Problem Set Guidance describes a possible activity to help students make connections between the representations. This is a good opportunity for students to showcase their collective work and look at the work of others, via posters, a gallery walk, or in small groups.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
A proportional relationship is shown in the graph below.
a. Describe a situation that could be represented with this graph.
b. Write an equation for the relationship. Explain what each part of the equation represents.
Upgrade to Fishtank Plus to view Sample Response.
Jonathan and his brother Jeffrey went on a long run to prepare for an upcoming road race. Jonathan ran 18 miles in 4 hours. It took Jeffrey 6 hours to run the same route as his brother. Both brothers ran at a constant speed.
a. Draw a graph to represent the relationship between distance and time for the two brothers. Label each line with the brother’s name.
b. Explain what the graph tells you about the speed of each brother.
c. The road race is a marathon and is 26.2 miles long. If Jonathan and Jeffrey each run at the same constant speed as they did in their preparation run, then how long will it take each brother to finish the road race?
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Patrice makes a spicy salsa by adding red pepper flakes to a chunky tomato mix in proportional amounts. For example, she mixes $$\frac{1}{2}$$ teaspoon of red pepper flakes to 2 cups of tomato mix.
Represent the relationship between red pepper flakes, in teaspoons, to tomato mix, in cups, in two different ways (table, graph, or equation). In your work, define any variables that you use.
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.
Next
Use different strategies to represent and recognize proportional relationships.
Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs
Solve ratio and rate problems using double number lines, tables, and unit rate.
Standards
7.RP.A.17.RP.A.2
Represent proportional relationships in tables, and define the constant of proportionality.
7.RP.A.27.RP.A.2.B
Determine the constant of proportionality in tables, and use it to find missing values.
7.RP.A.2.A7.RP.A.2.B
Write equations for proportional relationships presented in tables.
7.RP.A.2.B7.RP.A.2.C
Write equations for proportional relationships from word problems.
7.RP.A.27.RP.A.2.C
Represent proportional relationships in graphs.
7.RP.A.27.RP.A.2.A7.RP.A.2.D
Interpret proportional relationships represented in graphs.
7.RP.A.27.RP.A.2.D
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Non-Proportional Relationships
Compare proportional and non-proportional relationships.
7.RP.A.2.A
Determine if relationships are proportional or non-proportional.
Topic C: Connecting Everything Together
Make connections between the four representations of proportional relationships (Part 1).
7.RP.A.27.RP.A.2.A7.RP.A.2.B7.RP.A.2.C7.RP.A.2.D
Topic D: Solving Ratio & Rate Problems with Fractions
Find the unit rate of ratios involving fractions.
7.RP.A.1
Find the unit rate and use it to solve problems.
7.RP.A.17.RP.A.3
Solve ratio and rate problems by setting up a proportion.
Solve ratio and rate problems by setting up a proportion, including part-part-whole problems.
Solve multi-step ratio and rate problems using proportional reasoning, including fractional price increase and decrease, commissions, and fees.
7.RP.A.3
Use proportional reasoning to solve real-world, multi-step problems.
7.RP.A.17.RP.A.27.RP.A.3
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
We've got you covered with rigorous, relevant, and adaptable math lesson plans for free