Area Explorer

What is Area Explorer?

This activity allows the user to test his or her skill at calculating the area of a random shape. The user is given a random figure and allowed to enter a value for the area. The applet then informs the user whether or not the answer is correct. The user may continue trying until the answer is correct.

Information about the Units of Area and Perimeter

Area, the space within a shape, is usually expressed with units. Area is given in square units such as 16 meters 2 or 9 feet 2 .

There are two systems of units that are commonly used: standard and metric. Most of America uses the standard system while many other countries use the metric system. Converting standard units to metric units is done by multiplying by a proportionality constant.

Here are the tables of proportionality constants for the units of area.

Metric to Standard Standard to Metric
1 m 2 = 10.464 2 1 ft 2 = 0.093 m 2
1 km 2 = 0.386 mi 2 1 mi 2 = 2.590 km 2
1 km 2 = 247.105 acre 1 acre = 0.0040 km 2
1 cm 2 = 0.155 in 2 1 in 2 = 6.452 cm 2

Metric to Metric Standard to Standard
1 m 2 = 0.000001 km 2 1 ft 2 = 144 in 2
1 km 2 = 1000000 m 2 1 mi 2 = 640 acres
1 cm 2 = 0.0001 m 2 1 acre = 43560 ft 2
1 m 2 = 10000 cm 2 1 in 2 = 9 ft 2

So, if we were to convert 75 feet 2 into meters 2 , it would look like this:

How Do I Use This Activity?

This activity allows users to test their skill at calculating the area of a random shape.

Controls and Output

  • The applet displays a random shape for you to calculate the area. Enter the area of the current shape into the What is the shape's area? text field and click the check answer button.
  • A message will appear beside the text field letting the user know whether or not the answer is correct.
  • To get a new shape, click the Draw New Shape button.
  • To draw only rectangles, be sure the Only Draw Rectangular Shapes box is checked.
  • There are a couple of ways to change the perimeter of the figure. Either use the Adjust Perimeter scroll bar or type in a number in the text box and then click the Draw New Shape button. The maximum perimeter allowed is 50.

  • The Compare Area and Perimeters button allows you to keep track of your previous correct answers in order to compare the corresponding areas to a given perimeter or vice versa. Clicking this button brings up a new window:

    You can sort the data in the comparison box by either the area or perimeter from least to greatest. To sort by area, make sure the area check box is selected and to sort by perimeter, make sure the perimeter check box is selected and then click the sort button.

    In order to return to the activity, simply click back in the main window (though if you are using Internet Explorer on OSX for Mac you will need to click on the title bar of the main window to return to the activity). To clear the data and keep the window open, click the clear button.

  • The button draws a red rectangular box around the figure on the grid. This can serve as a hint in determining the figure's perimeter. Note that once the button is clicked it toggles to read .

Scoring

  • This activity will automatically record how successful you are at answering the questions. To view the score, press the Show Score button at the bottom of the activity and a pop-up window will appear with the scoreboard. To close this pop-up window press the Close button or click back on the main window.
  • To pause the scoring, press the Active button at the bottom of the screen and it will change to a Paused button. To resume scoring, press the Paused button.
  • To reset the scoreboard, open the scoreboard using the Show Score button and then press the Reset button.

Because this activity randomly generates questions, a feature called Seed Random has been implemented that allows multiple users using different computers to work on the same problem. See Seed Random Help for instructions on using this feature.

Description

This applet allows users to practice calculating the area of random shapes. This activity would work well in mixed ability groups of two or three for about twenty-five minutes if you use the exploration questions and ten to fifteen minutes otherwise.

Place in Mathematics Curriculum

This activity can be used to:

  • illustrate the notion of area
  • develop students' visualization skills
  • practice students' skills at calculating area
  • illustrate that shapes of the same perimeter have different areas

Standards Addressed

Grade 3

  • Geometry

    • The student demonstrates an understanding of geometric relationships.

Grade 4

  • Geometry

    • The student demonstrates an understanding of geometric relationships.

Grade 5

  • Geometry

    • The student demonstrates an understanding of geometric relationships.

Grade 6

  • Geometry

    • The student demonstrates an understanding of geometric relationships.
    • The student solves problems (including real-world situations) using perimeter, area, or volume.
    • The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 7

  • Geometry

    • The student demonstrates an understanding of geometric relationships.
    • The student solves problems (including real-world situations).
    • The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 8

  • Geometry

    • The student demonstrates an understanding of geometric relationships.
    • The student solves problems (including real-world situations).
    • The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 9

  • Geometry

    • The student solves problems (including real-world situations).

Grade 10

  • Geometry

    • The student solves problems (including real-world situations).

Grade 4

  • Measurement and Geometry

    • 1.0 Students understand perimeter and area

Grade 5

  • Measurement and Geometry

    • 1.0 Students understand and compute the volumes and areas of simple objects

Grade 7

  • Measurement and Geometry

    • 2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale

Third Grade

  • Geometry

    • Reason with shapes and their attributes.

  • Measurement and Data

    • Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
    • Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Sixth Grade

  • Geometry

    • Solve real-world and mathematical problems involving area, surface area, and volume.

Seventh Grade

  • Geometry

    • Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Number and Quantity

  • Quantities

    • Reason quantitatively and use units to solve problems.

Grades 3-5

  • Measurement

    • Apply appropriate techniques, tools, and formulas to determine measurements

Grades 6-8

  • Measurement

    • Apply appropriate techniques, tools, and formulas to determine measurements

Grades 9-12

  • Geometry

    • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

  • Measurement

    • Apply appropriate techniques, tools, and formulas to determine measurements

Grade 4

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 2: The learner will understand and use perimeter and area.

Grade 6

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 2: The learner will select and use appropriate tools to measure two- and three-dimensional figures.

Geometry

  • Geometry and Measurement

    • Competency Goal 2: The learner will use geometric and algebraic properties of figures to solve problems and write proofs.

Technical Mathematics I

  • Geometry and Measurement

    • Competency Goal 2: The learner will measure and apply geometric concepts to solve problems.

Technical Mathematics II

  • Geometry and Measurement

    • Competency Goal 1: The learner will use properties of geometric figures to solve problems.

Integrated Mathematics

  • Geometry and Measurement

    • Competency Goal 2: The learner will use properties of geometric figures to solve problems.

Integrated Mathematics III

  • Geometry and Measurement

    • Competency Goal 2: The learner will use properties of geometric figures to solve problems.

6th Grade

  • Measurement

    • The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine
    • The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine unit rates; and the use of scale to determine distance.

5th Grade

  • Measurement

    • The student will demonstrate through the mathematical processes an understanding of the units and systems of measurement and the application of tools and formulas to determine measurements.

4th Grade

  • Measurement

    • Standard 4-5: The student will demonstrate through the mathematical processes an understanding of elapsed time; conversions within the U.S. Customary System; and accurate, efficient, and generalizable methods of determining area.

8th Grade

  • Measurement

    • The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and
    • The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and volume; and the use of conversions within and between the U.S. Customary System and the metric system.

5th Grade

  • Measurement

    • The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.

4th Grade

  • Measurement

    • The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.

Grade 4

  • Measurement

    • 11. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass.

Grade 5

  • Measurement

    • 10. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems.

7th Grade

  • Measurement

    • 7.7 The student, given appropriate dimensions, will
    • 7.7a The student, given appropriate dimensions, will estimate and find the area of polygons by subdividing them into rectangles and right triangles

5th Grade

  • Measurement

    • 5.10 The student will differentiate between perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation.
    • 5.11d The student will choose an appropriate measuring device and unit of measure to solve problems involving measurement of area - square units
    • 5.11d The student will choose an appropriate measuring device and unit of measure to solve problems involving measurement of area — square units

Textbooks Aligned

Grade Six

  • Covering and Surrounding

    • Investigation Four: Constant Perimeter, Changing Area

Book 3

  • Module 1 - Amazing Feats, Facts and Fictions

    • Section 6: Solving Equations
    • Section 6: Simplifying Expressions
    • Section 6: Area, Perimeter

6th

  • Module 5 - Creating Things

    • Section 5: Area
    • Extended Exploration - Add a Square

Be Prepared to

  • define and describe the concept of area
  • walk the class through finding the pattern for area of the object using the information on the chart for question one of the exploration questions