Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.

Unit Overview

This is the first time that students have formally studied ratio and proportion. The study of ratios and proportional reasoning extends students’ work in measurement and multiplication and division in elementary grades. Ratios and proportional reasoning are the foundation for further study in mathematics, science and are useful in everyday life. Students will be working with ratios, rates, unit rates and percents to solve situations in daily life.

Teacher Notes:

Ratios are used in geometry and in algebra when students study similar figures.
The term ratio is used when units are the same and the term rate is used when units are different in the ratio. The CCSS uses ratio to encompass both situations.
The goal in sixth grade is to study ratios while leaving proportional studies for grade seven.

Enduring Understandings:

At the completion of the unit on ratio concepts, the student will understand that:

A ratio is a multiplicative comparison of two quantities.
A unit rate is a special ratio with a denominator of one that compares different types of measures.

Focus Standards (Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework document):

6.RP.A.3 When students work toward meeting this standard, they use a range of reasoning and representations to analyze proportional relationships.

Possible Student Outcomes:

The student will be able to:

Write ratios given critical information.
Use tables, graphs, tape diagrams and double number line diagrams to represent equivalent ratios.
Use ratios, rates and percent in a wide variety of contexts.

Evidence of Student Learning:

Fluency Expectations and Examples of Culminating Standards:

PARCC has no fluency expectations related to ratio and proportion.

Common Misconceptions:

Students may

confuse mathematical terms such as ratio, rate, unit rate and percent.
not understand how to set up a table or graph.
not understand the difference between an additive relationship and a multiplicative relationship.

Interdisciplinary Connections:

Interdisciplinary connections fall into a number of related categories:

Literacy standards within the Maryland Common Core State Curriculum

Science, Technology, Engineering, and Mathematics standards

Instructional connections to mathematics that will be established by local school systems, and will reflect their specific grade-level coursework in other content areas, such as English language arts, reading, science, social studies, world languages, physical education, and fine arts, among others.

Sample Assessment Items: The items included in this component will be aligned to the standards in the unit and will include:

Items purchased from vendors

PARCC prototype items

PARCC public release items

Maryland Public release items

Interventions/Enrichments/PD: (Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)

Vocabulary/Terminology/Concepts: This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.

Part I – Focus Cluster
Represent and Interpret Data

Ratios and Proportional Relationships: Understand Ratio Concepts and Use Ratio Reasoning to Solve Problems

ratio: Ratio is a comparison of two quantities or measures. Ratios can be expressed in the form , a to b, or a:b. Ratios can be expressed as comparisons of:
1. part to a whole, one part of a whole to another part of the same whole. Part-to-whole would be the ratio of boys to the whole class. measures of two different types which is called a rate.
2. part-to-part would be the ratio of boys to girls in a class. Measures of two different types are called a rate. Rate would be the ratio of miles per gallon to miles per hour.

unit rate: A ratio where the denominator is 1 unit. Example: If 15 buses can seat 675 people, one bus can seat 45 people.

tape diagrams: Tape diagrams are linear models used to represent data and help students organize their thinking. Example: Casey read 7 more books than Jamie. If Casey has read 16 books, how many books did Jamie read?

percent: is another name for hundredths; per hundred; ratio between a number and 100.
- Example: .75 = = 75%

Part II – Part II – Instructional Connections outside the Focus Cluster

dependent variable: In a function of two variables, one variable is dependent and the other is independent. In the equation y = + 4, y is the dependent variable. Its value depends on the value of x. If the value of x = 2, then the value of y is y = 3×2 + 4 or y = 10.
independent variable: In a function of two variables, one variable is dependent and the other independent. In the equation y = + 4, x is the independent variable. The value of y depends on the value of x. If the value of x is 1, then the value of y is y = 3×1 + 4 or y = 7.

Additional Resources:

http://commoncoretools.files.wordpress.com/2012/06/ccss_progression_g
_k6_2012_06_27.pdf

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Last Updated 3/9/2020 2:08 PM