This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

Unit 3: Unit Rates and Percentages
Lesson 2: Anchoring Units of Measurement

This lesson is optional. Students have worked with standard units of length since grade 2, and standard units of volume and mass since grade 3. This lesson is designed to anchor students’ perception of standard units of length, volume, weight, and mass with a collection of familiar objects that they can refer to in later lessons in preparation for using ratio reasoning to convert measurement units.

The main task of this lesson is a card-sorting activity in which students match common objects with their closest unit of length, volume, mass, or weight to establish anchor quantities for each unit of measurement. Since this lesson reinforces standards from previous grade levels instead of introducing grade 6 standards, if you believe that your students already have a firm grasp of these units of measurement, you may choose to skip this lesson.

Unit 3: Unit Rates and Percentages
Lesson 13: Benchmark Percentages

The goal of this lesson is to help students understand the connection between benchmark percentages and common fractions (MP7). In these materials, we have identified 10%, 25%, 50%, and 75% as primary benchmark percentages and multiples of 10% as secondary benchmark percentages.

It is common to say that 25% = 1/4 or 10% = 1/10 . In these materials we avoid this usage and say rather that 25% of a quantity is 1/4 of that quantity, or that 10% of a quantity is 1/10 of that quantity.

This lesson builds on understanding of equivalent fractions, multiplying fractions, and dividing by unit fractions from grades 4 and 5.

Unit 3: Unit Rates and Percentages
Lesson 1: The Burj Khalifa

In the previous unit, students began to develop an understanding of ratios and familiarity with ratio and rate language. They represented equivalent ratios using discrete diagrams, double number lines, and tables. They learned that a:b is equivalent to every other ratio sa:sb, where s is a positive number. They learned that “at this rate” or “at the same rate” signals a situation that is characterized by equivalent ratios.

In this unit, students find the two values a/b and b/a that are associated with the ratio a:b, and interpret these values as rates per 1. For example, if a person walks 13 meters in 10 seconds, that means they walked 13/10 meters per 1 second and 10/13 seconds per 1 meter.

To kick off this work, in this lesson, students tackle a meaty problem that rewards finding and making sense of a rate per 1 (MP1). Note there is no need to use or define the term “rate per 1” with students in this lesson. All of the work and discussion takes place within a context, so students will be expected to understand and talk about, for example, the minutes per window or the meters climbed per minute, but they will not be expected to use or understand the more general term “rate per 1.”

This task was developed by high school and postsecondary mathematics and agriculture sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This task was developed by high school and postsecondary mathematics and agriculture sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This task was developed by high school and postsecondary mathematics and agriculture sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This task was developed by high school and postsecondary mathematics and agriculture sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This task was developed by high school and postsecondary mathematics and agriculture sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.