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Geometry and Measurement
Supporting Idea 4 : Geometry and MeasurementArchived
Cluster Standards

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

  • MA.6.G.4.1 : 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.
  • MA.6.G.4.2 : Find the perimeters and areas of composite two-dimensional figures, including non-rectangular figures (such as semicircles) using various strategies.
  • MA.6.G.4.3 : Determine a missing dimension of a plane figure or prism given its area or volume and some of the dimensions, or determine the area or volume given the dimensions.
Cluster Information
Number:
MA.6.G.4
Title:
Geometry and Measurement
Type:
Supporting Idea
Subject:
X-Mathematics (former standards - 2008) - Archived
Grade:
6
Body of Knowledge
Geometry
Cluster Access Points

This cluster includes the following Access Points.

  • MA.6.G.4.In.a : Compare the distance around the outside of circles (circumference) and areas using physical or visual models.
  • MA.6.G.4.In.b : Measure the distance around all sides (perimeter) of polygons, such as squares, triangles, rectangles, and hexagons and compare the areas using physical or visual models.
  • MA.6.G.4.In.c : Measure capacity using cups, pints, quarts, and gallons.
  • MA.6.G.4.Su.a : Identify the distance around the outside of circles (circumference) and compare areas of circles using physical models.
  • MA.6.G.4.Su.b : Measure the lengths of sides of rectangles and triangles and compare the areas of rectangular and square shapes using physical models.
  • MA.6.G.4.Su.c : Measure capacity using cups.
  • MA.6.G.4.Pa.a : Recognize the outside (circumference) and inside (area) of a circle.
  • MA.6.G.4.Pa.b : Recognize the outside (perimeter) and inside (area) of rectangles and triangles.
Cluster Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Lesson Plans
  • 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
  • Story of Pi: This video dynamically shows how Pi works, and how it is used.
Virtual Manipulative
  • 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)