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 students to ratios and ratio notation. Students use tape diagrams to model ratios and solve problems. They explore different ways to group and compare objects to develop an understanding of equivalent ratios by the end of the topic.
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).
I can...
Use multiplicative reasoning to estimate the solution to a real-world problem.
Lesson at a Glance
This lesson is an open-ended modeling exploration. Students watch a video showing jars of jelly beans and create a class list of questions about the video. Students work in groups and apply multiplicative reasoning to estimate the number of jelly beans in jars. Groups of students present their solution strategies to the class. This lesson is designed as a formative assessment for several mathematical practices. There is an optional extension to challenge students.
I can...
1) Write ratios that relate two quantities as an ordered pair of numbers.
2) Use ratio language to compare two quantities.
Lesson at a Glance
In this lesson, students discuss their reactions to a video, which introduces the need to use new language to compare two quantities. After discussing a few examples, students realize that there are situations in which comparing quantities by using multiplicative comparison language is impractical or does not make sense. Through teacher-led instruction and peer discussion, students learn how to write ratios and how to use ratio language to describe the relationship between two quantities. This lesson introduces the term ratio.
I can...
1) Write multiple ratios to describe the same situation.
2) Represent ratios with tape diagrams.
Lesson at a Glance
In this lesson, students write and compare different ratios to represent people sitting at tables in a restaurant. They write both part-to-part and part-to-whole ratios. Then they group the people in different ways and use ratio language to describe the groupings. Through teacher-led facilitation and partner interaction, students represent ratios with tape diagrams.
I can...
1) Create ratios by making batches of different quantities.
2) Use tape diagrams to determine unknown quantities in ratios.
Lesson at a Glance
In this digital lesson, students use multiple geometric tiles to understand batches of quantities in the same ratio. Students model ratios by using multiple tape diagrams and notice patterns in repeating groups of quantities. Students then use these observations to solve contextual problems. Use the digital platform to prepare for and facilitate this lesson. Students will also interact with lesson content and activities via the digital platform.
I can...
1) Find equivalent ratios by multiplying both numbers in a given ratio by the same nonzero number.
2) Use equivalent ratios to find unknown quantities.
Lesson at a Glance
This lesson formalizes a concept that students experienced in previous lessons: equivalent ratios. Students learn strategies to identify equivalent ratios and represent them by using tape diagrams. Through small group activities, students write equivalent ratios and use them to solve real-world problems. This lesson introduces the term equivalent ratios.