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Elementary: Ratio, Proportion

While the detailed use of ratio and proportion in representing quantitative relationships is often deferred until middle school, the groundwork can be laid in grades 3-5 as students learn about fractions, decimals, and percents, and study relations among numbers through problems involving ratios (e.g., Cat Walk, where you'll find three dog steps for every four cat steps) or rates (Speeders, Beware!, with a speed limit of 35 mph).

Elementary Problems of the Week in which ratio and/or proportion play an important part are listed below. They may address the NCTM Grades 3-5 Number and Operations Standard or the Reasoning and Proof Standard.

To find relevant sites on the Web, browse and search Ratio/Proportion in our Internet Mathematics Library; to find elementary sites, go to the bottom of the page, set the searcher for late elementary level (3-5), and press the Search button. Some of the Middle School Ratio and Proportion answers in the Dr. Math archives may also interest students in grades 3-5.

Access to these problems requires a Membership.

Across Wisconsin - Jo Wenzler
active problem Math Fundamentals, difficulty level 2. Determine how long it will take this athletic math teacher to bike across Wisconsin (requires a little map reading). Initially a two-week problem. ... more>>

At the Movies - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Explore the changes in movie and theater prices. ... more>>

The Big Balloon Blowup - Leon Roland & class
active problem Math Fundamentals, difficulty level 3. Help Ulrike and Lars determine the number of balloons in each bag. ... more>>

Cat Walk - Math Olympiad Problem (revised)
active problem Elementary, difficulty level 2. Using the ratio of dog steps to cat steps and the length of a dog step, calculate the number of feet a cat walks in 24 steps. ... more>>

Chime Time - Lisa Lavelle (adapted)
active problem Elementary, difficulty level 3. Determine how long it takes a clock to chime. ... more>>

Circles Around - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Use this exploration problem to discover the relation between circumference and diameter. ... more>>

Growing Pains - Lisa Lavelle
active problem Elementary, difficulty level 4. Predict the height and weight of a child after ten years. ... more>>

How Much Was That Ticket? - Lisa Lavelle - idea suggested by Jody Newman
active problem Elementary, difficulty level 4. Determine how much I spent at the movie theater. ... more>>

How Safe Is Your Bike? - Chief Brian Craig and Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Compare the bicycle theft rates in three different cities. ... more>>

Is There Really a Discount? - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Determine which friend is correct about the final price on a sales item. ... more>>

Jumping Rope - Leon Roland & class
active problem Math Fundamentals, difficulty level 2. Just how long was the rope with which we started? ... more>>

McPrincipal's Night at McDee's - Antonietta D.
active problem Elementary, difficulty level 4. Just how much did the teachers from Mathematics Elementary School sell (and earn) in their charity drive? ... more>>

A Million in Time - Lisa Lavelle
active problem Math Fundamentals, difficulty level 2. "Human beings can expect to live a million..." Use your conversion skills to determine which unit of time best completes this statement. ... more>>

Movie Line Madness - Lisa Lavelle
active problem Math Fundamentals, difficulty level 4. Determine what time it will be when Odysseus and Penelope finish taking care of their movie customers. ... more>>

Neighborhood Watch - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Find out how many trips will be made around the neighborhood in this watch program. ... more>>

The New Rug - Lisa Lavelle
Elementary, difficulty level 3. Find the number of squares needed to cover the Reading area. ... more>>

Railroad Crossing - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Determine how far apart Division Junction and Logarithm Square are, based on the time Emily and Edward Engineer cross paths. ... more>>

Raisin Nut Cookies - Marsha May
active problem Math Fundamentals, difficulty level 4. Sarah needs to convert her cookie recipe for her cousin. ... more>>

Sacagawea Cheerios - Stephen Maurer
active problem Math Fundamentals, difficulty level 3. Determine how many Sacagawea coins the government will give away during this Cheerios promotion. ... more>>

Saline Solutions - Lisa Lavelle
active problem Elementary, difficulty level 3. Measure the ingredients needed to mix the saline solutions. ... more>>

Something Fishy - Basden's 8th Hour MathDogs
active problem Math Fundamentals, difficulty level 3. Find the maximum number of goldfish and koi for the schoolyard garden pond. ... more>>

Speeders, Beware! - Stephen Maurer (and Chief Brian Craig)
active problem Elementary, difficulty level 4. Evaluate the method the Swarthmore Borough Police Department uses for catching speeders. ... more>>

Splish Splash - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Determine the ratio of my volume to T.J.'s volume. ... more>>

Timber!!! - Lisa and Judy Gardner
active problem Math Fundamentals, difficulty level 3. Determine the lengths of two pieces of a damaged redwood tree. ... more>>

Video Viewing - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Just how much television will Frank and Lisa watch? ... more>>

Volunteering at the Food Bank - Abby Martin
active problem Math Fundamentals, difficulty level 2. Calculate the number of volunteer hours needed to keep a food bank in operation. ... more>>

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