Standard #: MA.6.G.4.2 (Archived Standard)


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Find the perimeters and areas of composite two-dimensional figures, including non-rectangular figures (such as semicircles) using various strategies.


Remarks


Example: Students see that the formula for the area of a circle is plausible by decomposing a circle into a number of wedges and rearranging them into shapes that approximates a parallelogram.

 

Example: Students might trace their foot on a piece of grid paper and use the full squares and the partial squares to estimate the area of the bottom of their foot.



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 , GR item(s)
    Also assesses MA.6.A.3.4 Solve problems given a formula.

    Clarification :
    Students will find the perimeters and areas of composite two-dimensional figures made from convex and concave polygons, circles, and semicircles.
    Content Limits :
    Students may find missing dimensions in order to find the perimeter or area of composite or decomposed two-dimensional figures, given some of the dimensions of a figure. 

    Students will work with composite two-dimensional figures, which may be composed of shapes within other shapes. 

    Polygons used in composite two-dimensional figures may be convex or concave. 

    The figures used within another figure are limited to triangles, quadrilaterals, circles, and semicircles. 

    Composite two-dimensional figures may be created from up to three different simple polygons. 

    Dimensions of polygons may be whole numbers; fractions with denominators of 2, 4, or 10; or decimal values, which may include 0.25, 0.75, or tenths. 

    Composite shapes should not be represented on grids. 

    Items will not include the vocabulary of inscribed or circumscribed, but these concepts may be represented graphically.

    Stimulus Attributes :
    Items should be set in a real-world or mathematical context.

    Items that are set in real-world context may use length and width as dimensions as well as base and height as dimensions.

    Graphics should be used in all of these items.


Sample Test Items (2)

Test Item # Question Difficulty Type
Sample Item 1 Dana plans to paint the front face of her doghouse, as shown by the shaded region below. The face is rectangular in shape, with 2 congruent rectangular doorways cut out.

Doghouse Diagram

Dana needs to calculate the area of the shaded region to be painted so she can purchase the correct amount of paint. What is the area of the shaded region of her doghouse that needs to be painted?

N/A MC: Multiple Choice
Sample Item 2 Mr. Lindbrook wants to purchase molding to place around the edges of the ceiling in his family room. The shape and dimensions of his family room are shown below.

Dimensions Diagram

Mr. Lindbrook needs to know the perimeter of the family room in order to know how much molding to purchase. What is the perimeter, in feet, of Mr. Lindbrook’s family room?

 N/A GR: Gridded-Response


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