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 topic D, students develop an understanding of the 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 rate applications.
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.
6.GM.1: Convert between measurement systems (English to metric and metric to English) given conversion factors, and use these conversions in solving real-world problems.
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1) Find distance and time corresponding to a given speed.
2) Identify real-world examples of rates and interpret their meanings in context.
Lesson at a Glance
In this lesson, students use their intuition to reason about the speeds various animals travel. Students then apply prior knowledge of speed to think about which animals would win races. Through this context, students explore the relationship between distance and time to understand the concept of a rate (speed). Given a rate, pairs of students apply ratio reasoning to answer questions about distance and time different animals travel, as well as other real-world contexts. This lesson introduces the term rate.
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1) Identify rates and unit rates.
2) Calculate one quantity when given another quantity and a constant rate.
Lesson at a Glance
In this lesson, students apply and extend their understanding of rates. They reason about an opening question that asks how long it would take one of the world’s fastest sports cars to travel the same distance that a bicycle travels in 12 hours. Students find unit rates for different rates and use the unit rates in calculations and in comparisons. Working in pairs, students analyze multiple representations of ratio relationships, such as ratio tables, double number lines, and graphs, to make sense of rate problems and ultimately answer the opening question. This lesson introduces the term unit rate.
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Compare rates with like units of measurement by using unit rate.
Lesson at a Glance
In this digital lesson, students tap to the beat of two songs and record the number of beats in a given number of seconds. Students find the number of beats per minute and then use this rate to identify the unit rate. Students use unit rates to determine which song has a faster tempo. Students enter these rates into an animation of drums beating, which gives them a visualization of each rate and allows them to check their answers. 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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Convert units of measurement by applying rate reasoning.
Lesson at a Glance
Students begin this lesson by applying their understanding of rates and unit rate to perform familiar unit conversions. Students work independently and in pairs to perform unit conversions within the same measurement system and in different measurement systems. In pairs, students solve multi-step word problems requiring unit conversions. Students conclude this lesson with a discussion on how rates can help when converting units of measurement and how this applies to solving real-world problems.
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1) Apply rate reasoning to solve real-world ratio problems involving speed, unit pricing, and unit conversions.
2) Find an unknown quantity when given a rate and a known quantity.
Lesson at a Glance
In this lesson, students work in groups to complete differentiated practice problems that are organized as stations. In groups, students apply their understanding of rates and unit rates to solve a variety of real-world problems, including calculating speeds, comparing the price per unit of items, and converting between units. Students also apply rate reasoning to solve multi-step problems involving more than one rate in a situation.
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Solve problems involving multiple constant rates.
Lesson at a Glance
Student first work in pairs and later in small groups to explore the time it takes to get from Earth to the moon. Students perform multiple unit conversions in which they must convert both the first and second quantities of a rate to different units of measurement. Then students choose a method of travel to the moon and use the problem-solving routine Read–Represent–Solve–Summarize to model and solve problems involving multiple rates and unit conversions.
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Lesson at a Glance
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