Topic: Ratios and Proportional Relationships |
Common Core Mathematics 6-8 |
| Cluster Understand ratio concepts and use ratio reasoning to solve
problems. |
| | Grade 6 |
| | | 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 ‚ 0, and use rate language in the context of a ratio relationship.
For example, gThis 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.h gWe paid $75 for 15
hamburgers, which is a rate of $5 per hamburger.h[1Expectations for unit rates in this grade are limited to non-complex fractions]. |
| | | 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 wholenumber
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. |
| Cluster Analyze proportional relationships and use them to solve real-world
and mathematical problems. |
| | Grade 7 |
| | | 7.RP.1. | Compute unit rates associated with ratios of fractions, including ratios
of lengths, areas and other quantities measured in like or different
units. For example, if a person walks 1/2 mile in each 1/4 hour, compute
the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2
miles per hour. |
| | | 7.RP.2. | Recognize and represent proportional relationships between
quantities. |
| | | 7.RP.2.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. |
| | | 7.RP.2.b. | Identify the constant of proportionality (unit rate) in tables,
graphs, equations, diagrams, and verbal descriptions of
proportional relationships. |
| | | 7.RP.2.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. |
| | | 7.RP.2.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. |
| | | 7.RP.3. | Use proportional relationships to solve multistep ratio and percent
problems. Examples: simple interest, tax, markups and markdowns,
gratuities and commissions, fees, percent increase and decrease, percent
error. |