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Middle School: Ratio & Proportion

In grades 6-8, students learn to understand and use ratios and proportions to represent quantitative relationships. Students develop, analyze, and explain methods such as scaling and finding equivalent ratios to solve problems involving proportions. Experience with ratios, rates, and percents helps form a solid foundation for an understanding of and facility with proportionality, which, more than setting two ratios equal and solving for a missing term, involves recognizing quantities that are related proportionally and using numbers, tables, graphs, and equations to explore how quantities are related.

Middle School Problems of the Week in which ratio and/or proportion play an important part are listed below. They address the NCTM Number and Operations Standard for Grades 6-8 expectation that students will understand relationships among numbers.

For background information elsewhere on our site, explore Middle School Ratio and Proportion in the Ask Dr. Math archives. To find relevant sites on the Web, browse and search Ratio/Proportion in our Internet Mathematics Library; to find middle-school sites, go to the bottom of the page, set the searcher for middle school (6-8), and press the Search button.

Access to these problems requires a Membership.

Balancing Mobiles - Suzanne Alejandre
teacher support active problem Pre-Algebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile. ... more>>

The Big Picture! - Judy Ann Brown
active problem Pre-Algebra, difficulty level 3. A picture is enlarged to four times its area. ... more>>

Boxes of Stationery - Annie Fetter, Suzanne Alejandre
active problem Pre-Algebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery? ... more>>

Buying Cola - Leon Roland & class
active problem Pre-Algebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy? ... more>>

Citius, Altius, Fortius - Suzanne Alejandre
active problem Pre-Algebra, difficulty level 2. Would record-holding speed skaters and runners break the speed limit in a residential zone? ... more>>

Downhill All the Way - Judy Ann Brown
active problem Pre-Algebra, difficulty level 2. Starting at 10,000 feet above sea level, descending a 6% grade followed by a 4% grade will put a car how many feet above sea level? ... more>>

Gearing Up - Suzanne Alejandre
teacher support active problem Pre-Algebra, difficulty level 3. Think about and explain the relationship between three different-sized gears. ... more>>

He Ate It All! - Mr. Marthinsen's Geometry Class
active problem Pre-Algebra, difficulty level 3. The professor ate an entire pizza in 28 minutes. Figure out the size of the pizza. ... more>>

How Wide Is My Garden? - Judy Ann Brown
active problem Pre-Algebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden. ... more>>

Luscious Lemonade - Judy Ann Brown
active problem Math Fundamentals, difficulty level 3. The label on the lemon concentrate says that I need to mix 2 cups of concentrate with 3 cups of water. How much lemon concentrate should I buy to make 25 gallons of lemonade? ... more>>

The Most Appealing Nose Contest - Judy Ann Brown
active problem Pre-Algebra, difficulty level 3. Use the given information to determine the amount of money raised for the Humane Society by the Student Council. ... more>>

The Nutty Squirrel - Alice Miller
active problem Pre-Algebra, difficulty level 3. How high could a human jump if she could jump with the power of a squirrel? ... more>>

Oceans of Fun - Judy Ann Brown
active problem Pre-Algebra, difficulty level 3. Help the Math Club approximate the portion of the Earth's surface that is covered by the oceans. ... more>>

Tiling Triangles - Suzanne Alejandre
teacher support active problem Pre-Algebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it. ... more>>

Valley Springs Snow Cream - Kelly Crisp
active problem Pre-Algebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream. ... more>>

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