Ratios, Rates, Unit Rates, and Proportions
7th Grade Curriculum: Common Core State Standards
Analyze proportional relationships and use them to solve real-world and mathematical problems.
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.
Recognize and represent proportional relationships between quantities.
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.
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
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.
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.
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.
Georgia Unit Student Edition for this Unit:
• What is Unit Rate? ...........................................................................8
• Analyze and Applying Unit Rate........................................................10
• Orange Fizz Experiment ..................................................................13
• Proportion and Non-Proportion (FAL) ...............................................18
• Creating A Scale Map..................................................................……20
• Which Is The Better Deal?.................................................................23
• Developing a Sense of Scale (FAL).....................................................25
• Patterns & Percents .........................................................................27
• 25% Scale (Short Cycle Task) ..........................................................31
• Ice Cream (Short Cycle Task)............................................................33
• Increasing and Decreasing Quantities (FAL) .......................................35
• Nate & Natalie’s Walk.......................................................................37
• Buses (Short Cycle Task)..................................................................38
Click Here to Open the Unit to Access the Different Tasks:
CCGPS_Math_7_7thGrade_Unit3SE.pdf
Here is some helpful information for parents on what students are learning in this unit:
Notes on Proportional Relationships:
http://rpdp.net/adm/uploads/math/resource_2287.pdf
Want some Extra Practice? Here are some worksheets along with answer keys:
Proportions and Percents:
Converting between percents, fractions, and decimals
Percent problems, straightforward
Finding percent change
Markup, discount, and tax (easy, hard)
Proportions
Proportion word problems
Similar figures
Similar figure word problems
Simple and compound interest
Try out this webquest to see if you can find the best deal (unit rate):
https://sites.google.com/site/unitratewebquest/home
Here are some great instructional videos to help:
Unit Rates-Better Buy:
http://learnzillion.com/lessons/868-find-the-best-deal-by-comparing-unit-rates
Determining the Unit Rate from a Proportional Relationships (this is a good one):
AND...Here are some really funny instructional videos to help:
Identifying Rates:
http://mathsnacks.com/ratey.php
Ratios and Proportions:
http://mathsnacks.com/baddate.php
Ratios and Differences:
http://mathsnacks.com/atlanteandodgeball.php
Proportional Relationships-Graphing:
http://mathsnacks.com/overruled.php
Extra Practice Questions for the test: