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Elementary: Area

Students in grades 3-5 investigate relationships among shapes, studying, for example, the relative areas of a rectangle and a nonrectangular parallelogram with equal bases and heights, or exploring the area of a triangle by visualizing its relation to a corresponding rectangle or other parallelogram. Measurement and geometry also are closely related, as when geometric properties are used to relate the areas of figures of different shapes.

The Elementary Problem of the Week offers a number of interesting problems that allow students to practice their skills in exploring how to find the area of a shape. These problems, listed below, address the NCTM Geometry Standard for Grades 3-5 expectation that students will be able to analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

For background information elsewhere on our site, explore the Elementary Geometry area of the Ask Dr. Math archives. To find relevant sites on the Web, browse and search Euclidean Plane Geometry 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.

Access to these problems requires a Membership.

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

Cubic Changes - Lisa Lavelle
active problem Math Fundamentals, difficulty level 4. Determine how the volume and surface area of a cube change when the edge length is changed. ... more>>

Frugal Flooring - Marita Paynter
active problem Math Fundamentals, difficulty level 2. Help Graeme determine how many tiles he needs to decorate his new bedroom and whether or not he can afford them. ... more>>

The Great Flood - Jon Basden
active problem Elementary, difficulty level 3. How much "flood" water did Mr. Basden clean up with his shop vac? ... more>>

How Does Your Garden Grow? - Team 7 Red Math Students -- Highland Middle School
active problem Elementary, difficulty level 4. Help the HMS students find out how many ways they can arrange their schoolyard garden. ... more>>

Jellybean Rectangles - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Have fun figuring out strategy in the Jellybean Rectangle game. ... more>>

Lawn-Mowing Chore - Judy Ann Brown
active problem Math Fundamentals, difficulty level 4. Find the area of the yard that Josh, Sam, and Mark must mow. ... more>>

Lost in Space - Lisa Lavelle
active problem Math Fundamentals, difficulty level 4. Figure out how big an error the engineers made when they mixed up their units. ... more>>

More Mowing Madness - George Miller and Lisa Lavelle
active problem Math Fundamentals, difficulty level 4. Where should Matt and Georgette change places to evenly split their "Matt-mowing" work? ... more>>

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

Pushing Pennies - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Estimate the number of pennies that you can fit on a sheet of paper, then evaluate your estimate. ... more>>

Puzzling Puzzle Pieces - Lisa Lavelle
active problem Math Fundamentals, difficulty level 2. Explore the ways 108 puzzle pieces can be arranged. ... more>>

Rabbit's Run - Lisa Lavelle
active problem Math Fundamentals, difficulty level 1. Help Regina develop options for building her rabbit's run. ... more>>

Sprinkler Spray - Lisa Lavelle
active problem Math Fundamentals, difficulty level 4. Compare the radii of three sprinklers in Lily's garden. ... more>>

Stained Glass Window - Jackson First Year Algebra Class
active problem Elementary, difficulty level 5. Find the size of a stained glass window for my front door. ... more>>

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