Show what you know about rates

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Objective

SWBAT: • Show what they know about rates.

Big Idea

What do students understand? What gaps do they have in their understanding? Students review and take the quiz.

Lesson Author

Andrea Palmer

Somerville, MA

Grade Level

Sixth grade

Subjects

Math

Number Sense and Operations

proportions

Fractions

Standards

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. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 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).

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.3b

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? (Combine and relabel).

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. (Combine and Relabel)

MP1

Make sense of problems and persevere in solving them.

MP3

Construct viable arguments and critique the reasoning of others.

Do Now

5 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to think about the difference between a ratio and a rate. I want students to understand that a ratio is a way to show a relationship between two amounts. A rate is special type of ratio that shows a relationship between two measurements.

Quiz Review

10 minutes

Before students take their quiz, they work with a partner on this problem. I want students to be able to use math reasoning to show that the student who runs 8 miles per hour is faster. Some students may turn both rates into miles per hour. Other students change both rates into minutes per mile.

As students work, I walk around and monitor student progress. With a few minutes left, I ask students to show and explain their work under the document camera. I have a few students who used different strategies come up and show and explain their work under the document camera. I ask the class for questions and comments on the student work. Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Quiz

35 minutes

Quiz Reflection

For this quiz I used a couple of different resources. My school has a membership for www.testwiz.net. This website has a very extensive item bank of Common Core questions. I search by standard and make modifications as necessary. Also, my school has subscription for the assessment bank for the College Preparatory Mathematics curriculum. The bank has a wide variety of rigorous multiple choice and open-response questions. See www.cpm.org for more details.

I give students the Quiz. Students engage with MP1: Make sense of problems and persevere in solving them. If students do not finish in the allotted time, they set up a time (preferably that day) to come in and complete it. I use this data to inform my instruction. If students struggle with a concept, I will spiral it into do nows and homework assignments. I may also add a few problems on that topic to the next quiz.

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