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.

For an in-depth discussion of the overarching, “big picture” perspective on student learning of content related to this unit, see:

The Common Core Standards Writing Team (10 September 2011). Progressions for the Common Core State Standards in Mathematics (draft), accessed at:
http://commoncoretools.files.wordpress.com/2011/09/ccss_progression_rp_67_2011
_11_121.pdf

Vertical Alignment: Vertical curriculum alignment provides two pieces of information: (1) a description of prior learning that should support the learning of the concepts in this unit, and (2) a description of how the concepts studied in this unit will support the learning of additional mathematics.

Key Advances from Previous Grades:

Between grade 5 and grade 6, students grow in their ability to analyze ratios, rates, unit rates and percents.
In grade 5 students apply their skills with multiplication and division of fractions to contribute to their study of ratios and unit rates.

Additional Mathematics: Students will use ratios, rates, unit rates and percent skills:

in grade 7 when working with proportional relationships and probability.
in geometry and in algebra when studying similar figures and slopes of lines.

Possible Organization of Unit Standards: This table identifies additional grade-level standards within a given cluster that support the over-arching unit standards from within the same cluster. The table also provides instructional connections to grade-level standards from outside the cluster.

Overarching Unit Standards	Supporting Standards within the Domain	Instructional Connections outside the Cluster
6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.	N/A	N/A
6.RP.A.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship.	N/A	N/A
6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.	6.RP.A.3a: 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. Use tables to compare ratios. 6.RP.A.3b: Solve unit rate problems including those involving unit pricing and constant speed. 6.RP.A.3c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent. 6.RP.A.3c: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.	6.NS.C.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.EE.C.9: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

Connections to the Standards for Mathematical Practice: This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. These proficiencies correspond to those developed through the Literacy Standards. The statements provided offer a few examples of connections between the Standards for Mathematical Practice and the Content Standards of this unit. The list is not exhaustive and will hopefully prompt further reflection and discussion.

In this unit, educators should consider implementing learning experiences which provide opportunities for students to:

1. Make sense of problems and persevere in solving them.

Analyze a problem and depict a good way to solve the problem.
Consider the best way to solve a problem.
Interpret the meaning of an answer to a given problem.

2. Reason abstractly and quantitatively

Consider the ideas that ratios can be represented in more than one way.
Realize the connection between the question and answer.

3. Construct Viable Arguments and critique the reasoning of others.

Justify the process of working with a ratio to answer a question.
Justify an argument using a table, graph, tape diagram or double line graph.

4. Model with Mathematics

Draw a diagram that represents ratio.
Analyze an authentic problem and use a nonverbal representation of the problem.
Use appropriate manipulatives.

5. Use appropriate tools strategically

Use virtual media and visual models to explore ratio and rate problems.

6. Attend to precision

Demonstrate an understanding of the mathematical processes required to solve a problem by communicating all of the steps in solving the problem.
Label appropriately.
Use the correct mathematics vocabulary when discussing problems.

7. Look for and make use of structure.

Look at a table or graph and recognize the relationship that is represented.
Compare, reflect and discuss multiple solution methods.

8. Look for and express regularity in reasoning

Pay special attention to details and continually evaluate the reasonableness of their answers.
Use of mathematical principles in solving problems.

Content Standards with Essential Skills and Knowledge Statements and Clarifications: The Content Standards and Essential Skills and Knowledge statements shown in this section come directly from the Maryland State Common Core Curriculum Frameworks. Clarifications were added as needed. Educators should be cautioned against perceiving this as a checklist. All information added is intended to help the reader gain a better understanding of the standards.

Standards	Essential Skills and Knowledge	Clarification
6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”	Knowledge of ratio as a comparison of any two quantities Knowledge of a ratio is not always a comparison of part-to-whole; Can be part-to-part or whole-to-whole	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 a part to a whole, one part of a whole to another part of the same whole, or measures of two different types which is called a rate. Example: Part-to-whole would be the ratio of boys to the whole class. Part-to-part would be the ratio of boys to girls. Rate would be the ratio of miles per gallon to miles per hour.
6.RP.A.2: Understand the concept of a unit rate associated with a ratio a:b with b ? 0 (b not equal to zero), and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)	Knowledge that a unit rate emphasizes finding an equivalent ratio with a denominator of 1.	unit rate: A ratio where the denominator is 1 unit. Example: If 15 buses can seat 675 people, one bus can seat 45 people.
6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 6.RP.A.3. a: 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. Use tables to compare ratios. 6.RP.A.3. b: Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? 6.RP.A.3. c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means times the quantity); solve problems involving finding the whole given a part and the percent. 6.RP.A.3. d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.	Knowledge of multiplicative recursive patterns Ability to use multiplicative relationships to extend an initial ratio to equivalent ratios; When working backward, use the inverse operation (division). Ability to recognize a linear relationship appears when the pairs are plotted on the coordinate plane Ability to use division to determine unit rate Ability to introduce percent as a special rate where a part is compared to a whole and the whole always has a value of 100 Ability to solve problems using equivalent ratios. (NOTE: Proportions are not introduced until Grade 7.) This is developing proportional reasoning without formal proportions. Ability to expand ratio reasoning to units of measurement	*ratio:* Ratio is a comparison of two quantities or measures. Ratios can be expressed in the form (a/b), 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. 675/15 = 45/1 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 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 = 75/100 = 75%

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Last Updated 3/9/2020 2:08 PM