Ratios as Fractions and Rates

It is at the middle school level that students move from understanding fractions to working with ratios and setting up proportions. You will find here problem-solving activities that you can use to introduce the concept of ratio as a rate that can be expressed as a fraction—miles per hour, drops per minute, for example. And you will find real-world problems that can be set up as proportions. Each activity was selected with student appeal in mind.

---

All About Ratios http://math.rice.edu/~lanius/proportions/index.html

Designed to introduce the concept of ratio at the most basic level, this activity could open the idea to younger middle school students. Each multiple-choice problem shows sets of colorful elements and asks students to choose the one that matches the given ratio. The activity is from the collection titled Mathematics Lessons that are Fun! Fun! Fun! MSP full record

Which Tastes Juicier? http://www.figurethis.org/challenges/c25/challenge.htm

Students are challenged to decide which of four cans of grape juice concentrate requiring different amounts of water would have the strongest grape juice taste. A hint suggests forming ratios that are fractions to compare quantities. Two solutions are given, each fully illustrated with tables. Students are then offered further mixture-related questions. MSP full record

Tern Turn: Are We There Yet? http://www.figurethis.org/challenges/c18/challenge.htm

If you know an arctic tern's rate of flight and hours per day in flight, can you calculate how many days would be required to fly the 18,000-mile roundtrip from the Arctic Circle to Antarctica? A hint suggests that students first calculate how many miles the tern flies in one day. Similar questions follow, offering more opportunities to practice distance-rate-time problems. MSP full record

Drip Drops: How Much Water Do You Waste? http://www.figurethis.org/challenges/c56/challenge.htm

A leaky faucet is dripping at the rate of one drop every two seconds. Students are asked to decide if the water lost in one week would fill a drinking glass, a sink, or a bathtub. The only hint is that a teaspoon holds about 20 drops. The full solution demonstrates how to convert the drops to gallons using an equation or a table. Students then consider, "How much water is lost in one year by a single leaky faucet? By two million leaky faucets?" MSP full record

How Far Can You Go on a Tank of Gas? http://www.figurethis.org/challenges/c24/challenge.htm

Which car will go the farthest on a single tank of gas? Students are given the mileage and gasoline tank capacity of three models of automobiles and are encouraged to begin the problem by calculating how far each car could go in the city and on the highway. In follow-up problems, students compare the fuel efficiency of different sports cars and calculate how often a commuter would need to refuel. MSP full record

Capture Recapture: How Many Fish in a Pond? http://www.figurethis.org/challenges/c52/challenge.htm

A real application of the ideas of proportion! To estimate the number of fish in a pond, scientists tag a number of them and return them to the pond. The next day, they catch fish from the pond and count the number of tagged fish recaptured. From this, they can set up a proportion to make their estimation. Hints on getting started are given, if needed, and the solution explains the setup of the proportion. MSP full record

Neighborhood Math http://www.pbs.org/teachersource/mathline/concepts/neighborhoodmath.shtm

This site contains four activities in a neighborhood setting: Math at the Mall, Math in the Park or City, Wheel Figure This Out, and Gearing Up. Students calculate the amount of floor space occupied by various stores, find the height of objects, and take a mathematical look at bicycles. The third and fourth activities involve both geometry and ratios. Answers and explanations of the four activities are included.MSP full record

Understanding Rational Numbers and Proportions http://illuminations.nctm.org/LessonDetail.aspx?id=L284

To work well with ratios, learners need a solid basis in the idea of rational number. This complete lesson includes three well-developed activities that investigate fractions, proportion, and unit rates—all through real-world problems students encounter at a bakery.

---

 Back to top

Copyright June 2006 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.