Find the measure of the 2 different angles of the tan pattern block piece. You may use the information you found out about the angles of the other pattern block pieces. Use precise mathematical language in your write up of your solution. Use diagrams to help explain your reasoning.
This was used as a problem-solving assessment task after students studied central angles and other aspects of angles. They used the idea of central angles to find the measures of the angles of the hexagon, trapezoid, square and triangles. It was interesting to see which students were flexible in coming up with other strategies for finding the obtuse angle of the tan parallelogram. Using information recently learned is a valuable tool for students to practice. In this problem they will need to use the information about the measure of the other Pattern Block angles to find the measure of the obtuse angle of the tan parallelogram. This task can elicit a good deal of geometric language. It shows how flexible students can be in finding a strategy to solve a problem when a familiar strategy fails to work. This task connects much of what is studied in a beginning angle unit. The student will find that the idea of central angles is a viable strategy to find the measure of the acute angle of the tan parallelogram, but not for the obtuse angle. The student will need to use previously learned information about angles (and possibly the other pieces) to come up with a workable strategy. 45 minutes This unit on angles coordinated with a unit on light reflection in science. Students needed to be able to measure the angle of incidence and the angle of reflection as a light beam was reflected off a mirror. It also can be related to the skill needed in playing table pool or in designing a miniature golf course to see if a "hole in one" was possible. Students will need to have had some experience with angles before they can attack this problem.
- Pattern blocks
- Blank paper
- Pencil
The acute angle measures 30 degrees (30 divides 360 evenly) and the obtuse angle measures 150 degrees (150 does not divide 360 evenly).
The student applied inappropriate concepts in solving the problem. The strategy of estimating the size of the angle from a 45-degree angle will not solve the problem. The student comes up with two measures for the obtuse angle and does not reconcile the two solutions.
The student solved part of the problem indicating that the other part of the problem was not understood. S/he has a strategy that is partially useful, leading to part of the solution, but not to a full solution of the problem. There is some evidence of mathematical reasoning. The solution is not clearly explained.
The solution shows the student has a broad understanding of angles. The strategy leads to a solution of the problem. His/her mathematical reasoning is effective. There is a clear explanation with appropriate mathematical terminology, notation and representation.
The student uses a strategy that connects the knowledge of supplementary angles to the solution. S/he also solves the problem two different ways to verify his/her solution. There is precise and appropriate use of mathematical terminology (except for "decahedron" and "divided 2 by 360") and notation.
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