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.
In this topic, students compare ratio relationships in context by using ratios to answer questions such as Which lemonade should have a stronger lemon flavor? Students use a variety of strategies to compare ratio relationships, including making direct comparisons by using a ratio table, by creating equivalent ratios, and by calculating the value of the ratio.
6.NS.9: Understand the concept of a unit rate and use terms related to rate in the context of a ratio relationship.
6.NS.10: Use reasoning involving rates and ratios to model real-world and other mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).
6.AF.9: 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.
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Compare ratio relationships by using graphs, tables, and double number lines.
Lesson at a Glance
In this digital lesson, students explore what it means for two sets of equivalent ratios to belong to the same ratio relationship. Students model ratio relationships by using graphs, tables, and double number lines, and they observe notable features when two different ratio relationships are represented on the same model. By using these observations, students decide on their preferred representation for comparing ratio relationships. Throughout the lesson, students are supported in their work with dynamic mathematical feedback. 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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Compare ratio relationships by using ratio tables.
Lesson at a Glance
In this lesson, students begin their comparisons of real-world ratio relationships by using a variety of visual tools, including pictorial representations and graphs. Next, students transition to making direct comparisons by using ratio tables. Students interpret and explain the real-world meaning of the comparisons.
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Compare ratio relationships by creating equivalent ratios.
Lesson at a Glance
In this lesson, students encounter ratio tables that do not allow for direct comparison. In pairs, they explore how to identify common factors and multiples to find ratios that allow for direct comparison. Students conclude by participating in a Take a Stand routine, where they examine ratio tables that share no common factors or multiples. Students use familiar tools and strategies to compare the ratio relationships and justify their reasoning.
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Compare ratio relationships by using the value of the ratio.
Lesson at a Glance
Students build on the prior lesson by working with a partner to create equivalent ratios in which one quantity is 1 unit. They learn that this method uses the value of the ratio to compare. Students practice finding the value of the ratio with teacher guidance and then they work independently by using the value of the ratio to compare ratio relationships given as verbal descriptions. This lesson introduces the term value of the ratio.
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Lesson at a Glance
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