Getting Started 
Misconception/Error The student is unable to calculate the actual length of the wing when given a scale drawing. 
Examples of Student Work at this Level The student:
 Provides the length of the scale drawing of the wing (8.125 cm).
 Attempts to determine the length of the diagonal side (e.g., the hypotenuse) of the wing.
 Multiplies the length by the width, providing an answer of 40.625Â Â or attempts to calculate the area of the scale drawing of the wing.
 Estimates the length of the wing from the drawing, counting every two squares as 192 cm, providing answers such as 768 cm.
 Multiplies 8.125 cm by 192, providing a wing length of 1560 cm.
 Multiplies 192 by four to find the actual length of 8 cm in the drawing but is unable to determine how to convert the fractional part of 8.125 cm to an actual length.

Questions Eliciting Thinking What is a scale drawing? How are scale drawings related to the size of the actual objects they represent?
Which measurement in the drawing corresponds to the width of the actual wing? If the width of the wing in the drawing is 5 cm, what would you multiply five by to find the width of the actual wing?
Is the length you found exact or is it an estimate? Do you know how to find the exact length? 
Instructional Implications Review the concepts of ratio and proportion. Remind the student that lengths shown in a scale drawing and corresponding actual lengths are proportionally related and that the scale factor is the same as the constant of proportionality. Assist the student in identifying the scale factor (e.g., k = 96) and writing an equation such as L = 96l where L is the length of an actual object given by l in the scale drawing. Guide the student to use the equation to find actual lengths given lengths in a scale drawing and vice versa. Consider implementing the MFAS tasks Saraâ€™s Hike and Making Coffee (6.RP.1.3).
Ask the student to solve problems involving proportional reasoning in a geometric context. For example:
 Given a right triangle with a base of five and a height of nine, find the height of a proportionally larger, triangle with a base of 12.
 Given a small right triangle with a base of four and a height of seven, use a scale factor of four to find the base and height of a proportionally larger triangle. Consider implementing the MFAS tasks for standard 7.RP.1.2.
Provide additional examples involving scale drawings. Assist the student in using a given scale (e.g., 1 cm corresponds to 3 m) to determine the scale factor and write an equation that models the relationship between lengths in the scale drawing and actual lengths (e.g., L = 3l).

Moving Forward 
Misconception/Error The student is unable to calculate the area of the wing when given a scale drawing. 
Examples of Student Work at this Level The student can correctly find the length of the actual wing. When asked to find its area, the student:
 Attempts to calculate the area of the scale drawing correctly or incorrectlyÂ (e.g., 20 , 20.3125 , or 40.625 ).
 Attempts to calculate the area of the wing using the correct measurements but the incorrect area formula providing an answer such as 374,400 .
 Adds length and width (e.g., 13.125 cm or 1260 cm).
 Attempts to calculate area using the correct formula but is unable to determine which measurements can be regarded as â€śheightâ€ť or â€śbase.â€ť
 Estimates the length of the diagonal then multiplies the values of length, width, and diagonal.
 Calculates the area of the scale drawing (correctly or incorrectly) and then multiplies the area by the scale factor, 96.

Questions Eliciting Thinking What is this shape called? How can you find its area?
What measurements do you need to find the area of a triangle? How do you find those measurements for the actual wing?
You found the area of the scale drawing correctly. Can you find the area of the actual wing? 
Instructional Implications Review the formula for the area of a triangle. Guide the student to identify the base and the height of a triangle, and emphasize that they always meet in a right angle. Be sure the student understands that the legs of a right triangle can serve as its base and height.
Guide the student to calculate the area of the actual wing by first finding its dimensions, both the length and width, and then applying the area of a triangle formula. Emphasize that the scale factor, 1:96, is the scale for length measurements, not area. Acknowledge that the ratio of areas (e.g., ) can be determined from this scale factor; but in order to use the ratio of areas to find the area of the actual wing, the area of the wing in the scale drawing must first be calculated. 
Almost There 
Misconception/Error The student is unable to provide proper units to describe length and/or area. 
Examples of Student Work at this Level The student provides no units or incorrect units. For example, the student describes the length of the wing as 780 , the area of the wing as 187,200 cm, or omits units.
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Questions Eliciting Thinking What is the significance of your answer? What does it mean? What is the unit of measure?
If you told someone that the area of a wing is 187,200, would they be able to understand how big the wing is? 
Instructional Implications Review the difference between length and area units of measure. Explain that, for example, 5 centimeters is a linear or onedimensional measure and can be used to describe lengths while 5 square centimeters is twodimensional and can be used to describe area. The unit of measure is essential to interpreting the meaning of a number in realworld contexts and should not be omitted. 
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 finds the length of the jetâ€™s wing as 780 cm by either:
 Writing and solving a proportion,
 Multiplying 8.125 cm by the scale factor (), or
 Identifying that 1cm in the drawing corresponds to 96 actual centimeters and multiplying 8.125 by 96.
The student finds the measure of the width of the wing (480 cm) and applies the formula for the area of a triangle, providing a correct answer of 187,200 .

Questions Eliciting Thinking If 2 cm in the drawing equals 192 cm on the actual wing, what does 1 cm in the drawing equal?
Can you set up a proportion that compares the measurements on the drawing to the measurements on the actual wing? 
Instructional Implications Provide the student with a measuring device and ask him or her to construct a scale drawing (on grid paper) of some object in the classroom.
Challenge the student to find the factor by which the area of the wing in the scale drawing can be multiplied to find the actual area of the wing. Ask the student to compare this value to the given scale factor (e.g., 2:192 or 1:96).
Pose the following questions to the student:
 If the vertical stabilizer on the tail of the jet was 465.6 cm long, how long would it be in a scale drawing given 2 cm in the drawing = 192 cm on the actual wing?
 If 2 cm in the drawing is equal to 192 cm on the real wing, does that mean that an area of 2 in the drawing is equal to an area of 192 on the real wing?
