Grade 6: Ratios, Rates, and Percents

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COMMON CORE STANDARDS

Content Standards

Ratios and Proportional Relationships

6.RP.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.”

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ¹ 0, 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 ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

6.RP.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.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.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.3(c) 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.3(d) Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

 

Standards for Mathematical Practice

 SMP.1 Make sense of problems and persevere in solving them. (Students must understand the problem

context in order to translate them into ratios/rates.)

SMP.2  Reason abstractly and quantitatively. (Students must understand the relationship between two quantities in order to express them mathematically.)

SMP.3 Construct viable arguments and critique the reasoning of others. This supports ELA 6.W.1: Write arguments to support claims with clear reasons and relevant evidence. (This will be reinforced in class discussion and in the written requirements of the CEPA.)

SMP.4 Model with mathematics. (Students can model a real-life situation using ratios and rates.)

SMP.7 Look for and make use of structure. (The structure of a ratio is unique and can be used across a wide variety of problem-solving situations.)

 

Supporting Standards

Reading Standards for Literacy in Science and Technical Subjects

RST.6-8.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6 – 8 texts and topics.

Writing Standards for Literacy in History/Social Studies, Science and Technical Subjects

WHST.6-8.2(a) Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.

WHST.6-8.2(b) Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples.

WHST.6-8.2(c) Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts.

WHST.6-8.2(d) Use precise language and domain-specific vocabulary to inform about or explain the topic.

WHST.6-8.2(e) Establish and maintain a formal style and objective tone.

WHST.6-8.2(f) Provide a concluding statement or section that follows from and supports the information or explanation presented.

WHST.6-8.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

 

DESCRIPTION OF UNIT

This Grade 6 unit titled “Ratios, Rates, and Percentsfrom the Massachusetts Department of Elementary and Secondary Education is intended to be completed in four to five weeks of mathematics instruction. The focus of the unit is to have students develop an understanding of ratios and rates. Students learn that ratios compare the same types of measures and represent part:whole and part:part relationships. They also learn that ratios that compare different types of measures are called rates.  Students apply these concepts to a variety of real world and mathematical situations, including problems involving measurement conversions and percents. In the authentic culminating performance task, every student assumes the role of a school cafeteria chef to create a pizza recipe and plan ingredients to make pizza for 12, 60, and 240 students. They then compute unit prices for the ingredients, prepare a budget, and calculate the cost to feed varying numbers of people. Using ratio/rate language, each student writes a proposal to persuade a cafeteria manager to use their recipe.

CAUTIONS

Connecticut teachers should be aware that teacher notes and preparation materials will require familiarity to be used effectively. Prior knowledge is required for student success in all lessons, making it important to consider the variability of learners and make adaptations as necessary prior to instruction.

 

RATIONALE FOR SELECTION

This exemplary unit includes clear and sufficient guidance to support teaching and learning of the targeted standards, including when appropriate, the use of technology and media. It addresses instructional expectations and is easy to understand and use. The Standards for Mathematical Practice that are central to the lesson are identified, handled in a grade-appropriate way, and are well connected to the content being addressed. The unit plan provides opportunities for students to independently apply mathematical concepts in real-world situations and solve challenging problems with persistence. It gradually removes supports, requiring students to independently demonstrate their mathematical understanding.  Unit materials include varied modes of curriculum-embedded assessments that are designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted CCSS. A rubric for evaluating student work on the assessment tasks is included.