Math / 7th Grade / Unit 5: Percent and Scaling
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.
Math
Unit 5
7th Grade
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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)
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The following assessments accompany Unit 5.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Pre-Unit Student Self-Assessment
Have students complete the Mid-Unit Assessment.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Post-Unit Assessment
Post-Unit Assessment Answer Key
Post-Unit Student Self-Assessment
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Suggestions for how to prepare to teach this unit
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
280 students attend a carnival, representing 80% of the school.
$$\frac{280}{x}=\frac{80}{100}$$
$$x=350$$
$$280=0.80x$$
$$x=280/0.80$$
The central mathematical concepts that students will come to understand in this unit
The materials, representations, and tools teachers and students will need for this unit
To see all the materials needed for this course, view our 7th Grade Course Material Overview.
Terms and notation that students learn or use in the unit
commission
corresponding
discount
markup/markdown
measurement error
percent increase/percent decrease
percent error
scale factor
scale
scale image/drawing
simple interest
tax
tip
To see all the vocabulary for Unit 5, view our 7th Grade Vocabulary Glossary.
Topic A: Percent, Part, and Whole
Define percent and convert between fractions, decimals, and percentages. Solve percent problems mentally with benchmark percentages.
7.RP.A.3
Find percent of a number when given percent and the whole.
7.NS.A.3 7.RP.A.3
Find the whole given a part and percent.
Find the percent given a part and the whole.
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Topic B: Percent Increase and Decrease
Find a new amount given the original and a percent increase or decrease.
7.EE.A.2 7.RP.A.3
Find the original amount given a new amount after a given percent increase or decrease.
Find the percent of increase or decrease given the original and new amounts.
Solve percent problems fluently, including percent increase and decrease.
Topic C: Percent Applications
Solve percent applications involving discount, tax, and tip.
7.EE.B.3 7.RP.A.3
Solve percent applications involving simple interest, commissions, and other fees.
Solve percent applications involving measurement and percent error.
Topic D: Scale Drawings
Define and identify scale images.
7.G.A.1
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.
Use scales in maps to find actual distances between locations.
Use scales in floor plans to find actual measurements and dimensions.
Compute actual areas from scale drawings.
Draw scale drawings at different scales.
Create a scale floor plan (optional).
Key
Major Cluster
Supporting Cluster
Additional Cluster
The content standards covered in this unit
7.EE.A.2 — Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."
7.EE.B.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
7.G.A.1 — Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
7.NS.A.3 — Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
Standards covered in previous units or grades that are important background for the current unit
6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
5.NF.B.5 — Interpret multiplication as scaling (resizing), by:
5.NF.B.5.A — Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.B.5.B — Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
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.
6.RP.A.3.C — Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
Standards in future grades or units that connect to the content in this unit
8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.A.4 — Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 4
Equations and Inequalities
Unit 6
Geometry