Math Spring Operational 2015
Geometry PBA Item #13 Hexagon Claims M41170 Prompt
Rubric
Task is worth a total of 3 points M41170 Rubric Score Description 3 Student response includes the following 3 elements. • Reasoning component = 3 points
o Correct and convincing reason explaining why Justine’s claim for lines of symmetry is incorrect
o Correct and convincing reason explaining why Justine’s claim for rotational symmetry is incorrect
o Correct use of notation and vocabulary to explain reasoning Sample Student Response: Justine is incorrect because there are other lines of symmetry and rotational symmetry she did not consider. Each line containing a vertex and O is a line of symmetry. However, she did not account for three more lines of symmetry, the lines containing the midpoints of the sides and O. An angle with measure 60˚, such as does show rotational symmetry and so does 120˚, 180˚, 240˚, 300˚, and 360˚. There are additional angles that show rotational symmetry that Justine did not include.
2 Student includes a response to one or both of Justine’s claims but is not sufficiently convincing. 1 Student response includes a quick assessment of the claims but little to support the response. 0 Student response is incorrect or irrelevant.
Anchor Set A1 – A8 A1 Score Point 3
Annotations
Anchor Paper 1 Score Point 3
This response receives full credit. The student includes all three of the required elements.
• The response provides a correct and convincing reason why Justine’s claim for lines of symmetry is incorrect (lines that pass through the midpoint of any of the sides of the hexagon, such as line y, are also lines of symmetry.)
• The response provides a correct and convincing reason why Justine’s claim for rotational symmetry is incorrect (this is a regular six sided figure, the angles of 0 rotation that show rotational symmetry are any multiples of 360 , or 60°.) 6
• The response uses correct notation and vocabulary to explain reasoning. The response correctly uses the term (midpoint) in describing the lines of symmetry.
A2 Score Point 3
Annotations
Anchor Paper 2 Score Point 3
This response receives full credit. The student includes all three of the required elements.
• The response provides a correct and convincing reason why Justine’s claim for lines of symmetry is incorrect (because a line of symmetry can be the midpoint of one of the lines to the midpoint of its opposite line.)
• The response provides a correct and convincing reason why Justine’s claim for rotational symmetry is incorrect (the angle of rotation can be 60° 180° 360° 300° or 240°). The response understands that the angle of rotation can be any multiple of 60 degrees for a regular hexagon.
• The response uses correct notation and vocabulary to explain reasoning. The response correctly uses the term (midpoint) in describing the lines of symmetry.
A3 Score Point 2
Annotations
Anchor Paper 3 Score Point 2
This response receives partial credit. The student responds to only one of Justine’s claims.
• The response provides a correct and convincing reason why Justine’s claim for lines of symmetry is incorrect (because y and x bisect the hexagon . . . also makes the perpendicular bisectors lines of symmetry.)
The response does not discuss whether Justine’s claim of rotational symmetry is correct or incorrect.
To receive a full-credit score point of 3, the response must address both of Justine’s claims and provide supportive, convincing reasoning for both.
A4 Score Point 2
Annotations
Anchor Paper 4 Score Point 2
This response receives partial credit. The student response responds to both of Justine’s claims but is not sufficiently convincing.
The response provides a correct conclusion for Justine’s claim of rotational symmetry with convincing reasoning (there are other angles of rotation, such as between B and A is 60°). The response gives an example of an angle that proves rotational symmetry.
The response provides a correct conclusion for Justine’s claim for lines of symmetry without convincing reasoning (incorrect because there are other lines of symmetry, such as DA.) The line of symmetry given includes two vertices and does not support the conclusion that other lines of symmetry exist that do not include vertices.
A5 Score Point 1
Annotations
Anchor Paper 5 Score Point 1
This response receives partial credit. The student makes a quick assessment of the claims but provides little to support the response.
The response provides a correct conclusion to Justine’s claim of rotational symmetry; however, the supportive reasoning is partially incorrect (incorrect . . . rotational angle symmetry occurs with angle measures 90, 180, 270, and 360.) In a regular hexagon rotational symmetry will occur only with angles that are multiples of 60 degrees. The values 90 and 270 are incorrect; therefore this response only receives credit for a score point 1.
Note: If the two incorrect values were not given as examples this response would have received credit for a score point 2.
The response does not discuss whether Justine’s claim for lines of symmetry is correct or incorrect.
A6 Score Point 1
Annotations
Anchor Paper 6 Score Point 1
This response receives partial credit. The student makes a quick assessment of the claims but provides little to support the response.
The response provides correct conclusions for Justine’s claims of lines of symmetry and rotational symmetry but does not give a sufficient explanation for either (because theres more rotational symetry then 120 and theres more lines of symmetry).
To receive a higher score point, the response must give examples of other lines of symmetry and/or provide examples of other angles that also prove rotational symmetry.
A7 Score Point 0
Annotations
Anchor Paper 7 Score Point 0
This response receives no credit. The student does not include a correct conclusion with correct reasoning for either of the two claims.
Although the response provides a correct conclusion for Justine’s claim of rotational symmetry, the reasoning is incorrect (incorrect because 90° also shows rotational symmetry.) An angle measurement of 90 degrees does not show rotational symmetry in a regular hexagon. Only angle measurements that are multiples of 60 degrees [60, 180, 240, 300, and 360] will show rotational symmetry for a regular hexagon. An angle measurement of 120 degrees will not receive credit by itself, as this angle is already provided in the prompt.
The response does not discuss whether Justine’s claim for lines of symmetry is correct or incorrect. A8 Score Point 0
Annotations
Anchor Paper 8 Score Point 0
This response receives no credit. The student does not include a correct conclusion with correct reasoning for either of the two claims.
The response provides an incorrect conclusion for Justine’s claim for the lines of symmetry (Justine is right.) The reasoning provided for the lines of symmetry is in conflict with the actual conclusion. The response states, (There are 6 lines of symmetry), which is correct, but this statement conflicts with the incorrect conclusion.
The claim states that the only lines of symmetry for the hexagon must contain a vertex and the center point O. There are only 3 lines of symmetry that contain both a vertex and the center point of the hexagon; however, there are also 3 other lines of symmetry that use the midpoint of the side of the hexagon and the center point.
The response does not discuss Justine’s claim for rotational symmetry. The explanation (Each symmetric line makes a 120 degree angle) is incorrect [as a line of symmetry forms a 180 degree angle] and relates more to the lines of symmetry claim than the rotational symmetry claim.
Practice Set P101 - P105
P101
P102
P103
P104
P105
Practice Set
Paper Score
P101 3
P102 2
P103 1
P104 3
P105 1