Students expand on and apply their understanding of percentages by studying percent increase and decrease, percent applications such as tax and simple interest, and scaled geometric drawings.
In Unit 5, seventh-grade students use their understanding of ratios and proportions from Unit 1 to solve various real-world applications involving percentages and scale drawings. They begin the unit by studying the relationship between percent, part, and whole using familiar strategies from sixth grade as well as new strategies from this year, such as proportions. Students then investigate how percentages can be used to represent increases and decreases in quantities. They use visual diagrams to model these situations and to understand how 100% plus 20% of a value is the same as 120% of that value (MP.2). Students continue to build fluency with percent problems as they solve real-world problems such as calculating purchase totals while considering discounts and tax. Lastly, students study scale drawings and learn how a scale can be used to create scale copies of large measurements such as maps or floor plans. They apply proportional reasoning and strategically use tools to re-create scale drawings or find actual measures from scale drawings (MP.5). Throughout this unit, students use skills and concepts they already have to make sense of and reason through new problems (MP.1), including continuing to work with a range of rational numbers.
In sixth grade, students learned several strategies to solve ratio and rate problems, including tables, tape diagrams, double number lines, and equations. They also defined percent as a rate per 100 and solved percent problems to find the whole, part, or percent. These standards are foundational to this seventh-grade unit, and the first four lessons in this unit incorporate these concepts and skills.
In eighth grade, students will refine their understanding of scale and scale drawings when they study dilations in their transformations unit. They will define similar figures and use dilations and other transformations to prove that two images are similar or scale drawings of one another.
Pacing: 23 instructional days (19 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 5 and should be given on the suggested assessment day or after completing the unit.
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Table |
Example: 280 students attend a carnival, representing 80% of the school. |
Tape diagram |
Example: 280 students attend a carnival, representing 80% of the school. |
Double number line |
Example: 280 students attend a carnival, representing 80% of the school. |
Proportion | Example: 280 students attend a carnival, representing 80% of the school.
$$\frac{280}{x}=\frac{80}{100}$$ $$x=350$$ |
Percent equation |
Example: 280 students attend a carnival, representing 80% of the school. $$280=0.80x$$ $$x=280/0.80$$ $$x=350$$ |
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commission
percent increase/percent decrease
markup/markdown
discount
tax
scale factor
tip
simple interest
measurement error
percent error
scale
corresponding
scale image/drawing
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7.RP.A.3
Define percent and convert between fractions, decimals, and percentages. Solve percent problems mentally with benchmark percentages.
7.RP.A.3
7.NS.A.3
Find percent of a number when given percent and the whole.
7.RP.A.3
7.NS.A.3
Find the whole given a part and percent.
7.RP.A.3
7.NS.A.3
Find the percent given a part and the whole.
7.RP.A.3
7.EE.A.2
Find a new amount given the original and a percent increase or decrease.
7.RP.A.3
7.EE.A.2
Find the original amount given a new amount after a given percent increase or decrease.
7.RP.A.3
Find the percent of increase or decrease given the original and new amounts.
7.RP.A.3
7.EE.A.2
Solve percent problems fluently, including percent increase and decrease.
7.RP.A.3
Solve percent applications involving discount, tax, and tip.
7.RP.A.3
Solve percent applications involving simple interest, commissions, and other fees.
7.RP.A.3
Solve percent applications involving measurement and percent error.
7.G.A.1
Define and identify scale images.
7.G.A.1
7.RP.A.3
Define and determine scale factor between two scale images. Use scale factor to draw scale images.
7.G.A.1
7.RP.A.3
Use a scale to determine actual measurements.
7.G.A.1
7.RP.A.3
Use scales in maps to find actual distances between locations.
7.G.A.1
7.RP.A.3
Use scales in floor plans to find actual measurements and dimensions.
7.G.A.1
7.RP.A.3
Compute actual areas from scale drawings.
7.G.A.1
7.RP.A.3
Draw scale drawings at different scales.
7.G.A.1
7.RP.A.3
Create a scale floor plan (optional).
Key: Major Cluster Supporting Cluster Additional Cluster
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