Standard #: MA.6.G.4.1 (Archived Standard)


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Understand the concept of Pi, know common estimates of Pi (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles.


Remarks


Using various circular objects, students determine that the ratio of circumference to diameter approximates the value of Pi.

General Information

Subject Area: X-Mathematics (former standards - 2008)
Grade: 6
Body of Knowledge: Geometry
Idea: Level 2: Basic Application of Skills & Concepts
Supporting Idea: Geometry and Measurement - Geometry and Measurement
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    Item Type(s): This benchmark may be assessed using: MC item(s)
    Also assesses MA.6.A.3.4 Solve problems given a formula.

    Clarification :
    Students will use 22/7 or 3.14 as an approximation for to determine the approximate circumference and area of circles. 

    Students will find the diameter or radius, given the circumference or area of a circle.

    Content Limits :
    Items may include using vocabulary such as radius, diameter, and center.

    Item graphics or options may include the use of visual representations or vocabulary associated with a circle, such as chord, arc, sector, and central angle. These terms will not be directly assessed.
    Stimulus Attributes :
    Items may be set in a real-world or mathematical context.

    Graphics should be used in most of these items, as appropriate.
    Response Attributes :
    Multiple-choice responses should include only correct units (e.g., answers for area questions should all have square units).


Sample Test Items (1)

Test Item # Question Difficulty Type
Sample Item 1 In a regulation wrestling match, wrestlers compete within a circular zone 9 meters in diameter.

Mat Diagram

Which of the following is closest to the area of the circular zone?

 N/A MC: Multiple Choice


Related Resources

Lesson Plans

Name Description
Relationship of Circumference to Diameter ~ Understanding Pi

In this lesson, students will develop an understanding of the meaning of pi and how it relates to the relationship to circumference and diameter. This is a hands-on activity where students measure circular objects and calculate the relationship of the circumference to the diameter.

Don't Be a Square - Measurement

"Students will learn the relationship between the radius and diameter of a circle and the relationship of the diameter and the circumference of a circle. Students will also find the approximate circumference of a circle, given either the diameter or radius." (from MATH Can Take You Places)

Using Pi to Solve Equations

This lesson includes measurement activities that help students understand where the value of pi originated, as well as activities that help students apply the value of pi to real-life scenarios.

Video/Audio/Animation

Name Description
Story of Pi This video dynamically shows how Pi works, and how it is used.

Virtual Manipulative

Name Description
Circle Tool

This applet allows students to investigate the relationships between the area and circumference of a circle and its radius and diameter. There are three sections to the site: Intro, Investigation, and Problems.

  • In the Intro section, students can manipulate the size of a circle and see how the radius, diameter, and circumference are affected. Students can also play movie clip to visually see how these measurements are related.
  • The Investigation section allows students to collect data points by dragging the circle radius to various lengths, and record in a table the data for radius, diameter, circumference and area. Clicking on the x/y button allows students to examine the relationship between any two measures. Clicking on the graph button will take students to a graph of the data. They can plot any of the four measures on the x-axis against any of the four measures on the y-axis.
  • The Problems section contains questions for students to solve and record their answers in the correct unit.

(NCTM's Illuminations)

Student Resources

Virtual Manipulative

Name Description
Circle Tool:

This applet allows students to investigate the relationships between the area and circumference of a circle and its radius and diameter. There are three sections to the site: Intro, Investigation, and Problems.

  • In the Intro section, students can manipulate the size of a circle and see how the radius, diameter, and circumference are affected. Students can also play movie clip to visually see how these measurements are related.
  • The Investigation section allows students to collect data points by dragging the circle radius to various lengths, and record in a table the data for radius, diameter, circumference and area. Clicking on the x/y button allows students to examine the relationship between any two measures. Clicking on the graph button will take students to a graph of the data. They can plot any of the four measures on the x-axis against any of the four measures on the y-axis.
  • The Problems section contains questions for students to solve and record their answers in the correct unit.

(NCTM's Illuminations)



Parent Resources

Video/Audio/Animation

Name Description
Story of Pi: This video dynamically shows how Pi works, and how it is used.


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