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M.S. Problems
Middle School
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Middle School: Ratio & Proportion
In grades 68, 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 68 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 middleschool sites, go to
the bottom of the page, set the searcher for middle school (68), and
press the Search button.
Access to these problems requires a Membership.

Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
... more>>

The Big Picture!
 Judy Ann Brown

PreAlgebra, difficulty level 3. A picture is enlarged to four times its area.
... more>>

Boxes of Stationery
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery?
... more>>

Buying Cola
 Leon Roland & class

PreAlgebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy?
... more>>

Citius, Altius, Fortius
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Would recordholding speed skaters and runners break the speed limit in a residential zone?
... more>>

Downhill All the Way
 Judy Ann Brown

PreAlgebra, 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

PreAlgebra, difficulty level 3. Think about and explain the relationship between three differentsized gears.
... more>>

He Ate It All!
 Mr. Marthinsen's Geometry Class

PreAlgebra, 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

PreAlgebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden.
... more>>

Luscious Lemonade
 Judy Ann Brown

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

PreAlgebra, 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

PreAlgebra, 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

PreAlgebra, 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

PreAlgebra, 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

PreAlgebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream.
... more>>
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