Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 65562
Applying Area and Perimeter
Students are asked to find the dimensions of rectangles by applying the formulas for area and perimeter.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, area, perimeter, formula, length, width
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ApplyingAreaAndPerimeter_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually, in small groups, or in a whole-group setting. If the task is given in a whole-group setting, the teacher should ask each
student to explain his or her thinking and strategy.
1. The teacher provides the student with the Applying Area and Perimeter worksheet and reads aloud each of the following problems while allowing the student ample time
to complete each problem.
A rectangle has a length of 9 inches and a perimeter of 22 inches. What is the width of the rectangle?
A rectangle has an area of 42 square centimeters and a length of 7 centimeters. What is the width of the rectangle?
A plan for a new wing of classrooms includes a rectangular closet with an area of 48 square feet and a perimeter of 32 feet. If the dimensions of the closet are whole
numbers, what are the length and width of the closet?
2. After the student determines the dimensions in the problems, the teacher should prompt the student to explain his or her thinking.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the concepts of area and perimeter.
page 1 of 4 Examples of Student Work at this Level
The student:
Does not know the area and perimeter formulas.
Confuses the area and perimeter formulas.
Multiplies the given numbers to determine missing dimensions.
Adds the given numbers to determine missing dimensions.
Questions Eliciting Thinking
What is the difference between area and perimeter?
How do you find the area of a rectangle? How do you find the perimeter of a rectangle?
Can you draw a diagram to match the description? How can you find the missing dimension?
Can you write an equation to match the description? How can you find the missing value?
What does each given number represent in the problem?
Instructional Implications
Remind the student that perimeter represents the combined lengths of the sides of a figure and is measured in linear units while area is a measure of the amount of surface
inside the figure and is measured in square units. Have the student draw a rectangle and use one color of crayon to outline the sides of a rectangle and another color to
shade the interior of the rectangle. Emphasize that the outline represents the perimeter and the shaded interior represents the area of the region inside the rectangle.
Then have the student write the formulas for area, A = lw and perimeter, P = 2(l +w) and label length (l) and width (w) on their diagram.
Guide the student to draw and label a diagram to represent each description and then construct an equation to model the information given in the problem. Guide the
student to consider each equation and determine a strategy to find the missing length(s).
Give the student additional examples of rectangles with a given area or perimeter and one dimension and ask the student to find the missing dimension of each rectangle.
Have the student use tiles or grid paper to build rectangles with given dimensions. Guide the student to see the difference between area and perimeter. Consider using
MFAS tasks from 3.MD.3.6, 3.MD.3.7, and 3.MD.3.8 to build the student’s conceptual understanding of area and perimeter of rectangles.
Moving Forward
Misconception/Error
The student is unable to correctly apply the formulas for area and perimeter to solve the problem.
Examples of Student Work at this Level
The student understands the formulas for area and perimeter but is unable to use them to find the missing dimensions. The student:
Applies the formulas inconsistently.
Cannot determine the dimensions that give both an area of 48 square feet and a perimeter of 32 feet.
Questions Eliciting Thinking
What numbers can you multiply to get a product of 48? Can you list all of the factors of 48? Which factor pair will make a perimeter of 32?
How do you find the area of a rectangle? How do you find the perimeter of a rectangle?
Can you explain how you got your answer?
Instructional Implications
Review the formulas for finding area and perimeter of a rectangle and how to apply them. Provide examples of one-step problems involving rectangles. For example, given:
Length and width, find the area.
Area and length, find the width.
Length and width, find the perimeter.
Perimeter and either the length or width, find the missing dimension.
When the student is proficient with one-step problems involving area and perimeter of rectangles, reintroduce problems in which both dimensions must be determined for a
given area and perimeter.
Provide the student with additional practice in determining all factors of a number and then applying these in word problems involving area and perimeter.
page 2 of 4 Almost There
Misconception/Error
The student makes an error in computation or labeling the unit.
Examples of Student Work at this Level
The student understands and is able to apply the formulas for finding area and perimeter. The student:
Makes a computational error.
Labels the unit incorrectly or not at all (e.g., square units instead of linear).
Forgets to divide by two when determining the width of the first rectangle saying the width is four.
Questions Eliciting Thinking
Good mathematicians always check their work. Can you add your numbers again to ensure that you have the correct answer?
What does four inches represent in the first problem? Did you find the length of just one side?
When do you use square units? Would you use inches (cm, ft) or square inches (cm, ft) in this problem? Why?
Instructional Implications
Provide the student with feedback on the error made and ask him or her to revise the work.
Provide the student with samples of work containing errors and ask him or her identify the errors and make necessary corrections.
Provide additional practice in determining missing widths or lengths and applying the formulas for area and perimeter of rectangles.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly determines:
1. The width is two inches.
2. The width is six centimeters.
3. The dimensions of the closet are 12 feet by 4 feet.
Questions Eliciting Thinking
What are the lengths of the sides of a square if the perimeter is 42 inches?
How are area and perimeter related? How is perimeter different from area?
How are the units used to measure area and perimeter alike? How are they different?
If the perimeter were measured in feet instead of inches, would the number of units be smaller or larger? Does the same concept work for area?
Instructional Implications
Challenge the student to determine all possible whole number combinations of length and width that result in an area of 60 square feet. Then have the student determine
which combination results in the greatest perimeter.
Provide the student with problems in which it is necessary to determine the cost of building materials such as the cost of tile and carpet given the dimensions of a room.
Ensure that the cost per square unit of materials is given in whole numbers of dollars.
Consider using MFAS What Is the Perimeter of the Lettuce Section? (4.MD.1.3) to assess the student’s understanding of applying the area and perimeter formulas in a real
world context.
Provide additional problems in which the student needs to determine missing lengths as shown in the following image.
page 3 of 4 ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Applying Area and Perimeter worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.4.MD.1.3:
Description
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the
width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a
multiplication equation with an unknown factor.
page 4 of 4