In module 1, students are introduced to ratio reasoning. They use tape diagrams, double number lines, tables, and graphs to model and compare ratio relationships, determine equivalent ratios, and solve real-world problems. Then, students develop an understanding of rates associated with ratio relationships. They calculate unit rates and use them to solve problems involving speed, unit pricing, measurement conversions, and other real-world applications. At the end of the module, students understand a percent as a fraction with a denominator of 100, and they apply their ratio and rate reasoning to solve for the unknown percent, part, or whole in real-world problems.
This topic introduces percents. Students understand percent as a fraction with a denominator of 100, and they apply their ratio and rate reasoning from previous topics to solve percent problems. Students use double number lines, mental math, and other computational strategies to solve for the unknown percent, part, or whole.
6.NS.5: Know commonly used fractions (halves, thirds, fourths, fifths, eighths, tenths) and their decimal and percent equivalents. Convert between any two representations (fractions, decimals, percents) of positive rational numbers without the use of a calculator.
5.NS.6: Understand, interpret, and model percents as part of a hundred (e.g., by using pictures, diagrams, and other visual models).
7.C.6: Use proportional relationships to solve ratio and percent problems with multiple operations (e.g., simple interest, tax, markups, markdowns, gratuities, conversions within and across measurement systems, and percent increase and decrease).
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1) Relate percents to a part-to-whole relationship where the whole is 100.
2) Model percents and write percents in fraction and decimal forms.
Lesson at a Glance
In this digital lesson, students discover the meaning of a percent in the context of charging a cell phone battery. Students continue to use this context to explore percents and express percents in equivalent fraction and decimal forms. Finally, students match denominations of money to percents and explore percents greater than 100%. Throughout the lesson, students are supported in their work with dynamic mathematical feedback. The term percent is introduced in this lesson. Use the digital platform to prepare for and facilitate this lesson. Students will also interact with lesson content and activities via the digital platform.
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Calculate a percent when given a part and the whole.
Discover that if multiple parts make a whole, then the percents representing the parts should total 100%.
Lesson at a Glance
This lesson begins with a guided example that explores how to use a tape diagram to determine unknown percents. Through observation and discussion, students extend their understanding from the prior lesson, where they worked with percents on a 10 × 10 grid, to using tape diagrams to find unknown percents when the whole is not 100. In pairs, students discuss the connections between percents and equivalent ratios. Students then explore how to use double number lines to calculate percents, focusing on percents greater than 100%. The lesson concludes with a discussion about the strategies and tools students have used so far to determine unknown percents. Students also consider which strategies and tools are the most helpful in different situations.
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Calculate a part when given the whole and a percent.
Lesson at a Glance
In this lesson, students first calculate percents by using double number lines. They develop fluency with mental calculations of benchmark percentages through a teacher-led Whiteboard Exchange. To calculate more challenging percentages that are not benchmark percentages, students explain and apply a variety of strategies. In a Would You Rather? game, students choose a method to determine the percent of a quantity.
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Calculate the whole when given a part and a percent.
Lesson at a Glance
In this lesson, students solve percent problems by finding the whole when given a part and a percent. Before they begin to solve a problem, students ask themselves questions about what information is given in the problem and what the problem asks them to find. Students work in pairs, using double number lines and tape diagrams to make sense of multi-step percent problems, choose strategies, and persevere in solving.
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Solve multi-step percent problems.
Lesson at a Glance
In this lesson, students apply their understanding of percents to solve two multi-step percent problems. In the first problem, students work in pairs to calculate the greatest and least possible parts when given three different whole amounts and percents. Students notice patterns in their calculations and explore how to most efficiently organize their thinking. In the second problem, students work in groups to create a cafeteria menu from different food items. They calculate the percent of the total number of calories that come from different nutrients and adapt their solution to meet a variety of requirements.
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Lesson at a Glance
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