Name: ______Date: ______
4.MD.7
The circle to the right is divided into
three angles: angle AMT, angle RMT,
and angle AMR.
• The sum of the three angles is 360º.
• Angle RMT measures 170º.
• Angle AMT is about twice as large
as angle AMR.
What are three possible measurements
for angle AMT and angle AMR?
possibility #1 / possibility #2 / possibility #3angle AMT / angle AMR / angle AMT / angle AMR / angle AMT / angle AMR
_____ º / _____ º / _____ º / _____ º / _____ º / _____ º
Name: ______Date: ______
4.MD.7
The circle to the right is divided into
three angles: angle AMT, angle RMT,
and angle AMR.
• The sum of the three angles is 360º.
• Angle RMT measures 170º.
• Angle AMT is about twice as large
as angle AMR.
What are three possible measurements
for angle AMT and angle AMR?
possibility #1 / possibility #2 / possibility #3angle AMT / angle AMR / angle AMT / angle AMR / angle AMT / angle AMR
_____ º / _____ º / _____ º / _____ º / _____ º / _____ º
Elementary Mathematics Office • Howard County Public School System • 2013-2014
Teacher notes:• This task is designed to be completed without the use of a protractor. The target concept for this task is described in 4.MD.7: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram. As such, students need to use knowledge of angles to determine a given angle’s measurement, not to measure the angles.
• Students may need to do calculations on paper, either to solve or to check their work. Since there is limited space on the half-sheet task, you should provide students with extra paper on which they can do necessary calculations.
• The total of the two angles that the students are working with is 190º. When they list pairs of possible measurement for AMT and AMR, there are a number of criteria to consider. The student’s pairs of possible measurements should 1) add to 190º and 2) have one measurement that is approximately double the other measurement. As you evaluate the student’s answers for scoring, use those criteria when determining the degree to which the student’s work shows “full” “substantial”, “partial”, or “little” accomplishment. If it is clear that a given error is due to a misunderstanding of a learned fact or calculation error (such as incorrect regrouping when subtracting 360 –170), but the student’s overall work shows that an understanding of the relationship between angles, he or she can still be rated as having “got” the target concept.
• It would be beneficial to have a post-scoring review discussion of this task with your class. One focus could be how the students calculated the total value of the two angles AMT and AMR. This amount has to be 190º, and students who did not know this would benefit from discussion (and instruction) and how to determine that value. In addition, students would be able to share their reasoning for how they determined their possibilities for the two individual angles.
Not yet: Student shows evidence of misunderstanding, incorrect concept or procedure. / Got It: Student essentially understands the target concept.
0 Unsatisfactory:
Little Accomplishment
The task is attempted and some mathematical effort is made. There may be fragments of accomplishment but little or no success. Further teaching is required. / 1 Marginal:
Partial Accomplishment
Part of the task is accomplished, but there is lack of evidence of understanding or evidence of not understanding. Further teaching is required. / 2 Proficient:
Substantial Accomplishment
Student could work to full accomplishment with minimal feedback from teacher. Errors are minor. Teacher is confident that understanding is adequate to accomplish the objective with minimal assistance. / 3 Excellent:
Full Accomplishment
Strategy and execution meet the content, process, and qualitative demands of the task or concept. Student can communicate ideas. May have minor errors that do not impact the mathematics.
Adapted from Van de Walle, J. (2004) Elementary and Middle School Mathematics: Teaching Developmentally. Boston: Pearson Education, 65
Elementary Mathematics Office • Howard County Public School System • 2013-2014