Curriculum / Math / 7th Grade / Unit 1: Proportional Relationships / Lesson 7
Proportional Relationships
Lesson 7 of 18
Criteria for Success
Tips for teachers, anchor problems, problem set, target task, additional practice.
Interpret proportional relationships represented in graphs.
Common Core Standards
Core standards.
The core standards covered in this lesson
Ratios and Proportional Relationships
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
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.A — Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Identify the constant of proportionality in a graph by finding the value of $$y/x$$ from coordinate point $$(x,y)$$ .
- Identify the constant of proportionality or unit rate as the value $$r$$ , when $$x$$ is $$1$$ , represented by the coordinate point $$(1,r)$$ .
- Explain the meaning of $$(0, 0)$$ in context of the situation.
Suggestions for teachers to help them teach this lesson
Students reason abstractly as they represent proportional situations using tables and graphs, and interpret the information to identify the constant of proportionality and write an equation. Given a graph of a proportional relationship, students re-contextualize information represented in coordinate points to explain what $$ (0, 0)$$ and $$ (0, r)$$ mean in context of the problem (MP.2).
Lesson Materials
- Graph Paper (1 per student)
- Ruler (2-3 sheets per student)
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
In a video game, for every 3 coins you collect, you earn 4 points.
a. Create a table of values to represent the relationship.
b. Graph the relationship.
c. Determine the equation that represents the relationship.
Guiding Questions
Three toy cars race down a straight path. The distance each car traveled, in meters, over time, measured in seconds, is shown in the graph below.
a. At what speed is each car traveling? Where can you see each speed in the graph?
b. Explain the significance of the coordinate point $$(1, r)$$ . What do you think the “ $$r$$ ” represents?
The graph below shows the number of gallons of gasoline used by a car over a given number of miles.
a. Explain what each point A, B, and C means in the context of the situation.
b. Plot the point that represents the unit rate. Explain how you determined your answer, and what it means in context of the situation.
c. Does this car get more or less miles per gallon of gasoline than a car that gets 30 miles per gallon?
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
A souvenir shop sells magnets, 2 for $3. The graph below shows the proportional relationship.
Which statements below are true? For each false statement, correct it so that the statement reads true.
Student Response
An example response to the Target Task at the level of detail expected of the students.
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.
- Illustrative Mathematics Robot Races
- Illustrative Mathematics Buying Coffee
- RDA Performance Task Bank Grade 7 Mathematics Sample TE Item
- RDA Performance Task Bank Grade 7 Mathematics Sample SR Item
- EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 10 — Problem Set
Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs
Solve ratio and rate problems using double number lines, tables, and unit rate.
7.RP.A.1 7.RP.A.2
Represent proportional relationships in tables, and define the constant of proportionality.
7.RP.A.2 7.RP.A.2.B
Determine the constant of proportionality in tables, and use it to find missing values.
7.RP.A.2.A 7.RP.A.2.B
Write equations for proportional relationships presented in tables.
7.RP.A.2.B 7.RP.A.2.C
Write equations for proportional relationships from word problems.
7.RP.A.2 7.RP.A.2.C
Represent proportional relationships in graphs.
7.RP.A.2 7.RP.A.2.A 7.RP.A.2.D
7.RP.A.2 7.RP.A.2.D
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Topic B: Non-Proportional Relationships
Compare proportional and non-proportional relationships.
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.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D
Make connections between the four representations of proportional relationships (Part 2).
Use different strategies to represent and recognize proportional relationships.
Topic D: Solving Ratio & Rate Problems with Fractions
Find the unit rate of ratios involving fractions.
Find the unit rate and use it to solve problems.
7.RP.A.1 7.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.
Use proportional reasoning to solve real-world, multi-step problems.
7.RP.A.1 7.RP.A.2 7.RP.A.3
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Jake Disston begins the period by challenging his students to work at their tables to group the cards they have in front of them, creating as many different groupings as they can, and devising language to describe each group.
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JESSE RAGENT: It is clear early on that there is lots of background knowledge that the students bring to the task. In the first few minutes I hear lots of relevant vocabulary "... just x, just y, slope, positive, negative, 0, undefined, intercept..." And yet, as the first student reports, it becomes clear that while there is some understanding of the information, there still remains plenty of misunderstanding and confusion. his clip reminds me of the need to honor all responses in class discussion. Jake is able to elegantly bring the incorrect notion of Dylan's "linear" grouping of the quadratics into proper focus and clarity in a way that did not denigrate the student at all. Additionally, I am reminded of how I should provide opportunities like this that enable me as a teacher to see how students will bring prior knowledge to a novel task. Only then will I know how deep (or shaky) their learning is.
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Lesson 7 Homework Practice Words, Equations, Tables, and Graphs 1. Each copy of a book costs $18 and shipping ... The graph shows the number of laps walked over 80 minutes. a. Make a table showing the input, minutes, and ... Explain. c. State the domain and range of the relation. Copy and complete each table. Then state the domain and range of ...
Lesson 7 Homework Practice . Words, Equations, Tables, and Graphs . Copy and complete each table. Then write an equation to represent the relationship. 1. Each copy of a book costs $18 and shipping is $9 per order. (Let b = number of books, Let c = total cost) ... The graph shows the number of laps walked over 80 minutes. a.
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7.RP.A.2 — Recognize and represent proportional relationships between quantities. 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.
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FiMC. Instructors: Jake Disston/Jesse Ragent. 1. Generalizing on Multiple Representations on Functions. 2. Goal of the Lesson. • Help students move from learning and doing procedures to looking for generalizations about types of graphs and their equations. • Making connections between graphs and equations, moving from specifics to general.
Mathematics Success - Grade 7 T127 LESSON 7: Representing Proportional Relationships with Equations Step 7: Have students write an equation for Question 7 and fill in the blanks using the information from Step 6. IP, CP, WG: Have students work with a partner to complete the problems with the pictorial representations on S60. Remind them
Only then will I know how deep (or shaky) their learning is. Clip Transcript. Jake Disston begins the period by challenging his students to work at their tables to group the cards they have in front of them, creating as many different groupings as they can, and devising language to describe each group.
Standardized Test Practice Vocabulary Review Lesson Resources ... Common Core State Standards Supplement, SE Hotmath Homework Help Multilingual eGlossary Math Review Math Tools Study to Go Online Calculators. Mathematics. Home > Chapter 1 > Lesson 5. Oklahoma Pre-Algebra. Chapter 1, Lesson 5: Words, Equations, Tables, and Graphs. Extra Examples ...
This product contains 9 pages (18 problems) for students to write equations from tables and graphs at a 6th grade level. Most of the problems are of the form y=kx or y=x+b with a few challenging questions at the end with 2 steps in the form y=mx+b. The problems start easier and get progressively more difficult, including fractional slopes and y intercepts with decimals.
Description. Math Teachers ~ you're in for a TREAT ...one of my BEST sellers! GREAT practice over Equations-Tables-and-Graphs! For each problem, students write the equation, fill in the table and graph the results. Worksheet is 2 pages plus Answer KEY is 2 pages. You'll love this and use it year after year!
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Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Personal Tutor Self-Check Quizzes. Common Core State Standards Supplement, SE Hotmath Homework Help Multilingual eGlossary Math Review Math Tools Study to Go Online Calculators. Mathematics. Home > Chapter 1 > Lesson 5. Pre-Algebra. Chapter 1, Lesson 5: Words ...