Students deepen their understanding of ratios to investigate proportional relationships, in order to solve multi-step, real-world ratio problems using new strategies that rely on proportional reasoning.
In Unit 1, seventh grade students deepen their understanding of ratios to investigate and analyze proportional relationships. They begin the unit by looking at how proportional relationships are represented in tables, equations, and graphs. As they analyze each representation, students continue to internalize what proportionality means, and how concepts like the constant of proportionality are visible in different ways. Students then spend time comparing examples of proportional and non-proportional associations, and studying how all the representations are connected to one another. Finally, in this unit, students will solve multi-step, real-world ratio and rate problems using efficient strategies and representations that rely on proportional reasoning (MP.4). These new strategies and representations, such as setting up and solving a proportion, are added to students’ growing list of approaches to solve problems. Throughout the unit, students will engage with MP.2 and MP.6. Translating between equations, graphs, tables, and written explanations requires students to reason both abstractly and quantitatively, and to pay precise attention to units, calculations, and forms of communication throughout their work.
In sixth grade, students were introduced to the concept of ratios and rates. They learned several strategies to represent ratios and to solve problems, including using concrete drawings, double number lines, tables, tape diagrams, and graphs. They defined and found unit rates and applied this to measurement conversion problems. Seventh grade students will draw on these conceptual understandings to fully understand proportional relationships.
Beyond this unit, in Unit 5, seventh grade students will re-engage with proportional reasoning, solving percent problems and investigating how proportional reasoning applies to scale drawings. In eighth grade, students connect unit rate to slope, and they compare proportional relationships across different representations. They expand their understanding of non-proportional relationships to study linear functions in the form of $$y=mx+b$$, and compare these to non-linear functions, such as $$y=6x^2$$.
Pacing: 22 instructional days (18 lessons, 3 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 7th Grade Scope and Sequence Recommended Adjustments.
This assessment accompanies Unit 1 and should be given on the suggested assessment day or after completing the unit.
?
Setting up and solving a proportion |
Example: A group of 4 students buy movie tickets for $24. At this rate, how much would 20 students pay for the movie? $$\frac{4\space \mathrm{students}}{$24} = \frac{20\space \mathrm{students}}{$x}$$ $$4x=24(20)$$ $$x=$120$$ |
?
?
equivalent ratio
ratio
unit rate
part to part ratio
part to whole ratio
commission
rate
dependent variable
constant of proportionality
proportion
independent variable
proportional relationship
?
7.RP.A.1
7.RP.A.2
Solve ratio and rate problems using double number lines, tables, and unit rate.
7.RP.A.2
7.RP.A.2.B
Represent proportional relationships in tables, and define the constant of proportionality.
7.RP.A.2.A
7.RP.A.2.B
Determine the constant of proportionality in tables, and use it to find missing values.
7.RP.A.2.B
7.RP.A.2.C
Write equations for proportional relationships presented in tables.
7.RP.A.2
7.RP.A.2.C
Write equations for proportional relationships from word problems.
7.RP.A.2
7.RP.A.2.A
7.RP.A.2.D
Represent proportional relationships in graphs.
7.RP.A.2
7.RP.A.2.D
Interpret proportional relationships represented in graphs.
7.RP.A.2.A
Compare proportional and non-proportional relationships.
7.RP.A.2.A
Determine if relationships are proportional or non-proportional.
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 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).
7.RP.A.2
7.RP.A.2.A
7.RP.A.2.B
7.RP.A.2.C
7.RP.A.2.D
Use different strategies to represent and recognize proportional relationships.
7.RP.A.1
Find the unit rate of ratios involving fractions.
7.RP.A.1
7.RP.A.3
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.
7.RP.A.1
7.RP.A.3
Solve ratio and rate problems by setting up a proportion, including part-part-whole problems.
7.RP.A.3
Solve multi-step ratio and rate problems using proportional reasoning, including fractional price increase and decrease, commissions, and fees.
7.RP.A.1
7.RP.A.2
7.RP.A.3
Use proportional reasoning to solve real-world, multi-step problems.
Key: Major Cluster Supporting Cluster Additional Cluster
?
?
?