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.
Topic B defines sets of all ratios that are equivalent ratios as ratio relationships. Students represent ratio relationships by using ratio tables, double number lines, and points in the coordinate plane. They use these models and the addition and multiplication patterns in the ratio relationship to solve for unknown quantities.
6.NS.8: Interpret, model, and use ratios to show the relative sizes of two quantities. Describe how a ratio shows the relationship between two quantities. Use the following notations: a/b, a to b, a:b.
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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1) Represent equivalent ratios by using ratio tables and double number lines.
2) Use representations of ratio relationships to solve problems.
Lesson at a Glance
This lesson establishes two new tools to represent sets of equivalent ratios: a ratio table and a double number line. Students use these tools when they work in pairs to find unknown quantities such as the amount of sugar in different amounts of soda. Students create and improve their representations of sets of equivalent ratios to help them solve a sequence of problems. This lesson introduces the term ratio relationship.
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1) Plot points in the coordinate plane that each represent a ratio.
2) Identify characteristics of graphs, tables, and double number lines representing ratio relationships.
Lesson at a Glance
In this digital lesson, students explore different representations of a ratio relationship. In the context of choosing a pet, students construct the familiar ratio table and double number line to examine the relationships between the total costs to feed different pets and the number of days of feeding them. By plotting the pairs of numbers in the coordinate plane, students discover that the set of ordered pairs that represent a ratio relationship lie on a line. Students then informally compare the total costs of food for different pets by looking at representations of the ratio relationships between the total cost to feed a pet and the number of days of feeding them. 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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Use addition patterns in tables and graphs of equivalent ratios to describe ratio relationships and find unknown quantities.
Lesson at a Glance
In this lesson, students first recognize addition patterns in a ratio table. Through a class discussion, they connect these addition patterns to the horizontal and vertical increases between points on the corresponding graph. Students compare tables that have addition patterns and identify which table represents a ratio relationship and why. Working in pairs, students use addition patterns in tables and graphs to find unknown quantities in real-world situations.
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1) Use graphs and tables to explore multiplication patterns in ratio relationships.
2) Use multiplication to complete ratio tables.
Lesson at a Glance
Students begin this lesson by examining addition and multiplication patterns in the graph of a ratio relationship. They work in pairs to solve problems that encourage the use of multiplication patterns. Students make connections between multiplication patterns in ratio tables, graphs, and double number lines. They then use multiplication strategies to solve for unknown quantities in ratio relationships.
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Write and use equivalent ratios when one of the numbers in the ratio is 1.
Lesson at a Glance
In this lesson, students use ratio tables to write a ratio A:B in the form A/B : 1 and 1 : B/A . Students explain the meaning of A/B and B/A in context. Through teacher-led discussion, students explore multiplication patterns between the two numbers in a ratio. In a problem-solving stations activity, students apply the multiplication strategies they learn in the lesson.
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Solve multi-step ratio problems by reasoning about equivalent ratios.
Lesson at a Glance
This lesson introduces the concept of a changing ratio through a pictorial scenario. Students begin the lesson by solving problems involving multiple ratios. Through a teacher-led example, students explore how to use tape diagrams to model changing ratios. A stations activity allows students to work through problems with changing ratios at varied difficulty levels.
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