Getting Started |
Misconception/Error The student sketches or draws rather than constructs. |
Examples of Student Work at this Level The student draws a circle or an arc that does not seem to be related to the task.
The student draws a segment and judges by observing that this segment is congruent to the given segment.
The student uses a ruler to measure and draw a segment of the same length as the given segment. |
Questions Eliciting Thinking What is the difference between drawing and constructing?
When doing a geometric construction, what tools are typically used?
What is the difference between a straightedge and a ruler?
What is it that you are supposed to construct?
Suppose you start with a working line. Could you construct a segment on this line that is congruent to the given segment? |
Instructional Implications Explain to the student the difference between drawing and constructing. Show the student the tools traditionally used in geometric constructions and explain the purpose of each. Be sure the student understands the difference between a ruler and a straightedge.
Guide the student through the steps of constructing a segment congruent to a given segment. Have the student label the congruent segment as , as given in the instructions. Have the student remove any unnecessary marks or marks made in error from his or her paper. Ask the student to write out the steps of the construction and keep them for future reference.
Ask the student to use the given to construct other segments such as so that MN = 2(AB). |
Moving Forward |
Misconception/Error The student attempts the construction but makes a significant error. |
Examples of Student Work at this Level The student does not construct the segment on a working line. Instead the student uses the compass to make an arc on the paper. Then the student sets the compass radius to the length of the given segment and, with the point of the compass on the previously drawn arc, makes another arc. The student draws a segment with endpoints on the arcs.
The student makes a working line below the given segment and marks the endpoints of the “constructed” segment on the working line by visually comparing to the given segment. |
Questions Eliciting Thinking Can you explain how you constructed the congruent segment?
How did you ensure that your measurement was precise?
Is there a way to transfer the length of the given segment onto your working line that is more precise?
Did you use the compass? What should it be used for? |
Instructional Implications Explain to the student the need to precisely locate points in constructions and that points can be precisely located at the intersection of two construction marks. Guide the student to begin segment constructions with a working line and to use the compass to measure needed lengths.
Guide the student through the steps of constructing a segment congruent to a given segment. Have the student label the congruent segment as , as given in the instructions. Have the student remove any unnecessary marks or marks made in error from his or her paper. Ask the student to write out the steps of the construction and keep them for future reference.
Ask the student to use the given to construct other segments such as so that MN = 2(AB). |
Almost There |
Misconception/Error The student correctly completes the construction but does not label the construction or leaves unnecessary marks on the paper. |
Examples of Student Work at this Level The student correctly constructs a segment congruent to the given one but does not label as or labels it .
The student correctly constructs and labels a segment congruent to the given one but leaves several arcs marked on the working line that are not needed for the construction. |
Questions Eliciting Thinking Where is in your construction?
What are these arcs for? Did you use them in your construction? |
Instructional Implications Ask the student to label the congruent segment as , as given in the instructions, and to remove any unnecessary marks or marks made in error from his or her paper.
Give the student two segments of lengths a and b, respectively. Challenge the student to construct segments of length a + b, 3b, and 3a – b. |
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 uses the straightedge to construct a working line. The student marks endpoint P on the working line and then measures AB with the compass. The student places the point of the compass on point P and makes an arc that intersects the working line. The student marks the point of intersection of the working line and the arc as point Q. This procedure is indicated and described on the worksheet. |
Questions Eliciting Thinking For the line and point P that you drew, how many places on the line could Q appear? |
Instructional Implications Give the student two segments of lengths a and b, respectively. Challenge the student to construct segments of length a + b, 3b, and 3a – b.
For a given point P, ask the student to construct all possible locations of the point Q (without first constructing a working line on which Q must lie). Introduce the student to the concept of a locus of points (i.e., a set of points that satisfies a certain condition). |