Circle Tool

  • Circle Tool

    Grade: 3rd to 5th, 6th to 8th

    How do the area and circumference of a circle compare to its radius and diameter? This activity allows you to investigate these relationships in the Intro and Investigation sections and then hone your skills in the Problems section.

    Activity

    Instructions

    Modes

    • In the Intro section, explore the relationship of the circumference to the radius and diameter. Play CircleTool IMAGE VideoButtonthe movie clip to visually see how they are related. 
    • In the Investigation section, collect data points by dragging the radius to various lengths, and the click the "Add to Table" button to record the data in the table. By default, the radius, diameter, circumference and area are shown in a table.
      • Clicking on the x/y button allows you to examine the relationship between any two measures. CircleTool IMAGE x/yButton
      • Clicking on the graph button will take you to a graph of the data. You can plot any of the four measures on the x-axis against any of the four measures on the y-axis. CircleTool IMAGE GraphButton
       
    • In the Problems section, determine the answer to each question using the applet, a calculator, or paper and pencil. Don't forget to indicate the proper units!
     

    Exploration

    Can you determine the relationship between…
    • …radius and diameter?
    • …radius and circumference?
    • …diameter and circumference?
    • …radius and area?

    Some relationships can be discovered using the x/y button. Others will require more investigation, but the graph should give you some insight.

    Objectives and Standards

    NCTM Standards and Expectations
    • Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
    • 3-5
    • 6-8
    • Geometry