• MA.5.GR.2 Geometric Reasoning

    Find the perimeter and area of rectangles with fractional or decimal side lengths. 



    Find the perimeter and area of a rectangle with fractional or decimal side lengths using visual models and formulas.
    Benchmark Clarifications:
    Clarification 1: Instruction includes finding the area of a rectangle with fractional side lengths by tiling it with squares having unit fraction side lengths and showing that the area is the same as would be found by multiplying the side lengths.
    Clarification 2: Responses include the appropriate units in word form.


    Purpose and Instructional Strategies
    The purpose of this benchmark is for students to understand how to work with fractional and decimal sums and products when calculating perimeter and area. This benchmark connects to previous work where students found areas and perimeters with whole number side lengths in Grade 4 (MA.4.GR.2.1) and prepares for future work of finding area and perimeter on a coordinate plane in Grade 6 (MA.6.GR.1.3).

     During instruction, teachers should encourage students to use models or drawings to assist them with finding the perimeter and area of a rectangle and have them explain how they used the model or drawing to arrive at the solution getting them to understand that multiplying fractional side lengths to find the area is the same as tiling a rectangle with unit squares of the appropriate unit fraction side lengths (MTR.5.1).

     This benchmark provides a natural real-world context and also a visual model for the multiplication of fractions and decimals. When finding the area, teachers can begin with students modeling multiplication with whole numbers and progress into the fractional and decimal parts, such as area models using rectangles or squares, fraction strips/bars and sets of counters. For example, ask questions such as, “What does 2 × 3 mean?” Then, follow with questions for multiplication with fractions, such as, “What does 3/4 x 1/3 mean?” “What does 3/4 × 7 mean?” (7 sets of 3/4) and What does 7 × 3/4 mean?” (3/4 of a set of 7) (MTR.2.1, MTR.3.1, MTR.5.1).

    Common Misconceptions or Errors

     Students may believe that multiplication always results in a larger number. Working with area provides them with concrete situations where this is not true. For example a city block that is 1/10 mile by 1/10 mile has an area of 1/100 of a square mile.

     Students have difficulty connecting visual models to the symbolic representation using equations. Use concrete visuals to represent problems.

    Instructional Tasks
    Instructional Task 1
    Margaret draws a rectangle with a length of 5.2 inches. The width of her rectangle is one-half its length.
    Part A. Draw Margaret’s rectangle and show its dimensions.
    Part B. What is the perimeter of her rectangle in inches?
    Part C. What is the area of her rectangle in square inches?

    Instructional Items
    Instructional Item 1
    What is the area of the square below? 






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