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Ratio and Proportion
These problems require students to understand and use ratios and proportions to represent quantitative relationships. They may require developing, analyzing, and explaining methods such as scaling and finding equivalent ratios to solve problems involving proportions.

Some of these problems are also in the following subcategories:

Related Resources
Interactive resources from our Math Tools project:
   Math 7: Ratio and Proportion
The closest match in our Ask Dr. Math archives:
   Middle School: Ratio and Proportion
NCTM Standards:
   Number and Operations Standard for Grades 6-8

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>>

Bartering for Bananas - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 4. How many bananas can Byron get with five fish? ... more>>

Bella's Bagel Bakery - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 1. How much more area is covered with cream cheese on the large bagel than on the small bagel? ... more>>

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

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

Building on Water - Judy Ann Brown
teacher support active problem Pre-algebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building. ... more>>

Buying Cola - Leon Roland & class
teacher support 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
teacher support active problem Pre-algebra, difficulty level 2. Would record-holding speed skaters and runners break the speed limit in a residential zone? ... more>>

Designing Doorways for Rich and Riz - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 2. Find the height for a doorway for Riz that gives him a proportional amount of room as Rich has in the pictured doorway. ... more>>

Downhill All the Way - Judy Ann Brown
teacher support 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>>

Election Day in Prealgpoweria - Steve Risberg, Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 3. How many votes does each candidate in Prealgpoweria receive and how many eligible voters are there? ... more>>

Garden Grove - Steve Risberg & Stephen Weimar
teacher support active problem Pre-algebra, difficulty level 3. Determine the amount of dirt and the amount of peat moss needed to have the correct ratio of dirt to peat moss for the garden. ... more>>

The Gates - Suzanne and Richard Alejandre
teacher support active problem Pre-algebra, difficulty level 3. How much time did Suzanne spend walking on "The Gates" pathway? ... 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>>

Golfing Luck? - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 2. Work with probability on the practice hole of the golf course. ... more>>

He Ate It All! - Mr. Marthinsen's Geometry Class
teacher support 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
teacher support active problem Pre-algebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden. ... more>>

I'm a Groundhog? - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 2. Using Suzanne's height, Phil's height, and Suzanne's shadow length, find Phil's shadow length. ... more>>

Join Us for a Quarter-pound Burger - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 2. Work with fractions and percents to help plan this cookout. ... more>>

Lee's Lawn Chair - Lee & Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 3. Using the measurements given in the problem, determine the scale factor used to create the larger chair. ... more>>

Lightning Strikes - Judy Ann Brown
teacher support active problem midpow, difficulty level 1. It takes five seconds for the sound of thunder to travel one mile. How far away is the lightning if thirty-two seconds pass between the flash of the lightning bolt and the sound of the thunder? ... more>>

Luscious Lemonade - Judy Ann Brown
teacher support 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>>

Membership Boom! - Judy Ann Brown
teacher support active problem Pre-algebra, difficulty level 3. Find the number of students involved in the Math Club, and the number of students in the school. ... more>>

Milk Madness - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 4. Help Georgina find out how much milk is left using the number pattern she describes. ... more>>

The Most Appealing Nose Contest - Judy Ann Brown
teacher support 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>>

New Home for Fibonacci and Fractal - Judy Ann Brown
teacher support active problem Pre-algebra, difficulty level 2. Determine how long it will take Jimal and Leslie to fill the new 15-gallon aquarium. ... more>>

The Nutty Squirrel - Alice Miller
teacher support 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
teacher support 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>>

The Oracle's Oration - Annie Fetter
teacher support active problem Pre-algebra, difficulty level 3. Explain how payment should be distributed based on the number of rolls two people shared with the group of three. ... more>>

Ostrich Llama Count - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 2. Given the combined number of heads and legs of ostriches and llamas, help Raul and Esteban figure out how many ostriches and how many llamas there are. ... more>>

Peeling Potatoes - Terry Trotter
teacher support active problem Pre-algebra, difficulty level 2. How many potatoes did Annie and Steve have to peel? ... more>>

Pi Day Treats - Judy Ann Brown
teacher support active problem Pre-algebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration. ... more>>

A Pound of Valentine's Chocolates - Suzanne Alejandre, Claire Mead
teacher support active problem Pre-algebra, difficulty level 2. How long should a one pound box of chocolates last if Isolde eats it alone? ... more>>

Saturday Bike Ride - Judy Ann Brown
teacher support active problem Pre-algebra, difficulty level 2. Now that spring has arrived, Ali and Maya decide to dust off their bikes and go for a Saturday ride. Help find what time they will meet. ... more>>

Seesaw - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 3. How did the four friends balance on the seesaw? ... more>>

Sizing Up Sequoias - Suzanne Alejandre
teacher support active problem Pre-algebra, difficulty level 2. Compared to a given seed weight, find out how much an average mature sequoia weighs. ... more>>

A Snowy Driveway - Claire Mead
teacher support active problem Pre-algebra, difficulty level 3. Usually Bertha and Gertrude shovel snow together. How long would it take Bertha to shovel the same amount alone? ... 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>>

Timber! - Steve Risberg
teacher support active problem Pre-algebra, difficulty level 3. A tree breaks three-eighths of the way up the trunk, and the tip hits the ground 40 feet from the base of the trunk. How tall was the tree? ... more>>

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

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