Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 43586
How Many Square Units?
Students determine the area of a right triangle.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, right triangle, area, square unit
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_HowManySquareUnits_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher gives the student the attached How Many Square Units? worksheet and asks the student to determine the area of the triangle.
2. Finally, the teacher asks the student to explain how he or she determined the number of square units of area.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand the relationship between the square units in the diagram and the area of the figure.
Examples of Student Work at this Level
The student counts all the squares shown on the grid (16 square units) and does not understand how to count the area of the right triangle.
The student only counts the full squares in the interior of the triangle (six square units).
Questions Eliciting Thinking
What do you think area means? How is area measured?
Which squares should we count to find the area of the triangle? Can we count to find the area of this shape only?
page 1 of 3 Do you think the area of the right triangle will be more than or less than 16 square units?
Is there any part of the triangle where it becomes difficult to count squares?
Instructional Implications
Consider using the MFAS task Unit Square (3.MD.3.5) which assesses the student’s understanding of area measurement.
Be sure the student has a basic understanding of area measurement. Provide clear instruction for the student on how to determine the area of a figure by counting the
number of unit squares that cover a figure without any gaps or overlaps. Begin with figures that can be covered by whole squares. Then, transition the student to figures
that encompass halves of unit squares such as triangles and trapezoids.
Moving Forward
Misconception/Error
The student understands the relationship between the square units in the diagram and the area of the figure but makes significant errors in counting.
Examples of Student Work at this Level
The student makes a counting error when determining the area, and he or she is unable to correct even with teacher prompting.
The student counts the half squares in the triangle as wholes when finding the area and says the area is 10 square units.
Questions Eliciting Thinking
When you counted these squares, you counted them the same as you counted the whole squares. Do you think that is correct?
What fraction of a square do you think this partial square is (point to one of the half squares along the hypotenuse of the triangle)? If each of these is one-half of a unit
square, how many would you need to put together to form a whole unit square? What would that make the area of the triangle?
Instructional Implications
Ensure that the student understands that a diagonal of a square divides the square into two congruent triangles each with half the area of the original square.
Have the student cut squares in half diagonally and then align the two triangular halves to confirm that they are congruent.
Note: It is important for students to understand that halves that are not congruent can be formed. However, for this task it is critical to understand that a diagonal of a
square divides the square into two congruent right triangles.
Almost There
Misconception/Error
The student makes a mistake when counting the partial squares in the figure.
Examples of Student Work at this Level
The student errs in counting the partial squares but with teacher prompting is able to correct his or her mistake. However, the student still lacks confidence in the final
answer.
Questions Eliciting Thinking
What fraction of a square do you think this partial square is (point to one of the half squares along the hypotenuse of the triangle)? If each of these is one-half of a unit
square, how many would you need to put together to form a whole unit square? What would that make the area of the triangle?
Instructional Implications
Have the student cut squares in half diagonally and then align the two triangular halves to confirm that they are congruent.
Note: It is important for students to understand that halves that are not congruent can be formed. However, for this task it is critical to understand that a diagonal of a
square divides the square into two congruent right triangles.
Provide repeated opportunities for the student to determine the area of different shapes by counting. Ensure that the shapes include halves of unit squares as well as
whole unit squares.
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 counts to find the correct area of the right triangle (eight square units). The student counts the six whole squares first and then combines the two half
page 2 of 3 squares to make a whole square.
The student determines that the area of the larger square that contains the right triangle is 16 square units and then divides 16 by 2 to find the area of the triangle.
Questions Eliciting Thinking
Can you think of another way to determine the area?
If you know the area of the larger square (16 square units), can you use that to help you determine the area of the triangle?
Instructional Implications
Consider using the MFAS task Area of a Right Trapezoid (3.MD.3.6).
Encourage the student to discover and generalize a formula for determining the area of a rectangle. Ask the student to relate the formula to counting the number of unit
squares the rectangle contains and to explain why the formula works.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
How Many Square Units? 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.3.MD.3.6:
Description
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
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