Getting Started |
Misconception/Error The student confuses perimeter and area. |
Examples of Student Work at this Level The student sums the lengths of the sides of the figure instead of finding the area. |
Questions Eliciting Thinking What does perimeter mean? How do we find the perimeter?
What does area mean? How do we find area? |
Instructional Implications 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 rectangle by counting the number of unit squares that cover the rectangle without any gaps or overlaps. Give the student opportunities to draw unit squares on rectangles and count them to find the area. Next, model for the student how to find the area of rectilinear figures by decomposing them into non-overlapping rectangles and summing their areas. Provide more opportunities for the student to find the areas of rectilinear figures, and give feedback and assistance as needed.
Provide direct instruction on the difference between area and perimeter. Provide rectangles with whole number dimensions, and ask the student to find both the area and the perimeter of the rectangles.
Consider using the MFAS task Fenced Dog Run (3.MD.3.6) which assesses the student’s understanding of counting unit squares to determine the area of a figure. |
Moving Forward |
Misconception/Error The student does not view area as being additive. |
Examples of Student Work at this Level The student understands that the length and width of a rectangle can be multiplied to find area but tries to multiply all of the lengths together instead of decomposing the shape into two separate rectangles.
The student understands that finding the area of a rectangle involves multiplication, but he or she selects incorrect numbers to multiply (e.g., 14 x 3 and 9 x 5). |
Questions Eliciting Thinking Can we draw a line to form two rectangles? Where would you draw the line?
What if we find the area of one of these rectangles? What do you think we would do next? |
Instructional Implications Guide the student to decompose rectilinear figures into rectangles, find the area of each rectangle, and sum these areas to find the area of the original figure. Provide additional opportunities for the student to find the areas of rectilinear figures. Ask the student to explain his or her strategy and provide feedback. |
Almost There |
Misconception/Error The student makes minor computational errors when finding the area. |
Examples of Student Work at this Level The student decomposes the figure into two rectangles but makes minor computational errors when multiplying and/or adding the two products. |
Questions Eliciting Thinking Can you explain how you found the area of the figure? Let’s check your work. Can you multiply and then add again? |
Instructional Implications If the student consistently makes errors when multiplying, encourage the student to model the multiplication with an array and skip count to find the product.
When finding the area of a rectilinear figure, encourage the student to review his or her strategy and then check his or her computations.
Provide the student with additional opportunities to find the area of other rectilinear figures. |
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 that the area of the figure is 72 square centimeters and is able to clearly explain his or her strategy. |
Questions Eliciting Thinking Can you find another way to divide the figure into rectangles? Should you get the same area if you divided the figure differently?
Another student added all of the sides. What did he or she do wrong?
What is the difference between area and perimeter? |
Instructional Implications Ask the student to find the area of a rectilinear figure in more than one way. Ask the student to explain why different approaches result in the same area measurement.
Have the student draw (or list the dimensions) of every rectangle, with whole number dimensions, that have an area of 20 square units. Then, ask the student to find the perimeter of each rectangle.
Consider using the MFAS task Using Arrays to Model the Distributive Property (3.MD.3.7). |