Series Collaborating to Develop Mathematical Ideas: Reflecting on Teaching & Learning About Ratios
Math.6.RP.A.2
| Common core State Standards
- Math: Math
- 6: Grade 6
- RP: Ratios & Proportional Relationships
- A: Understand ratio concepts and use ratio reasoning to solve problems
-
2:
Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 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 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.
Math.6.RP.A.3
| Common core State Standards
- Math: Math
- 6: Grade 6
- RP: Ratios & Proportional Relationships
- A: Understand ratio concepts and use ratio reasoning to solve problems
-
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.
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.
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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?
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.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Math.7.RP.A.2
Common core State Standards
- Math: Math
- 7: Grade 7
- RP: Ratios & Proportional Relationships
- A: Analyze proportional relationships and use them to solve real-world and mathematical problems
-
2:
Recognize and represent proportional relationships between quantities.
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a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
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d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
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Discussion and Supporting Materials
Thought starters
- How did the lesson change depending on each classroom context?
- What do the teachers learn from looking at student work?
- How do the teachers support each other and push each other's thinking?
School Details
Enumclaw Middle School550 Semanski Street
Enumclaw WA 98022
Population: 498
Data Provided By:
Teachers
Crystal Morey
Jana Dean
Wendy L. Hughes
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English Language Arts
10 Comments
Des Duthie Mar 5, 2018 2:35am
Crystal Morey Nov 4, 2015 10:56pm
Catharine Burki Sep 7, 2015 12:46pm
Crystal Morey Sep 7, 2015 11:09am
Bonnie Anglin Sep 6, 2015 7:16pm