M1 End-of-Module Assessment Task - OpenCurriculum
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Name
Date
1. Each of the illustrations on the next page shows in black a plane figure consisting of the letters F, R, E, and D evenly spaced and arranged in a row. In each illustration, an alteration of the black figure is shown in red. In some of the illustrations, the red figure is obtained from the black figure by a geometric transformation consisting of a single rotation. In others, this is not the case. a. Which illustrations show a single rotation?
b. Some of the illustrations are not rotations or even a sequence of rigid transformations. Pick one such illustration and use it to explain why it is not a sequence of rigid transformations.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
269 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
270 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
2. In the figure below, ̅̅̅̅ bisects Find the measure of angle
and
.
.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
271 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
3. In the figure below, ̅̅̅̅ is the angle bisector of Prove that
. ̅̅̅̅̅̅ and ̅̅̅̅̅̅ are straight lines and ̅̅̅̅
̅̅̅̅ .
.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
272 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
End-of-Module Assessment Task
GEOMETRY
4. The triangles
and
in the figure below such that ̅̅̅̅
̅̅̅̅ , ̅̅̅̅
̅̅̅̅ , and
a. What criteria for triangle congruence (ASA, SAS, SSS) implies that
b. Describe a sequence of rigid transformations that shows
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
.
?
.
Congruence, Proof, and Constructions 5/29/14
273 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
5. a.
Construct a square
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
with side ̅̅̅̅. List the steps of the construction.
Congruence, Proof, and Constructions 5/29/14
274 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
b.
Three rigid motions are to be performed on square . The first rigid motion is the reflection ̅̅̅̅ through line . The second rigid motion is a 90° clockwise rotation around the center of the square. Describe the third rigid motion that will ultimately map image of each rigid motion in the provided blanks.
back to its original position. Label the
Rigid Motion 1 Description: Reflection through line ̅̅̅̅
Rigid Motion 2 Description: 90° clockwise rotation around the center of the square.
Rigid Motion 3 Description:
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
275 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
6. Suppose that Prove that
is a parallelogram and that is a parallelogram.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
and
are the midpoints of ̅̅̅̅ and ̅̅̅̅ , respectively.
Congruence, Proof, and Constructions 5/29/14
276 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
A Progression Toward Mastery Assessment Task Item
1
a–b G-CO.2
STEP 1 Missing or incorrect answer and little evidence of reasoning or application of mathematics to solve the problem.
STEP 2 Missing or incorrect answer but evidence of some reasoning or application of mathematics to solve the problem.
STEP 3 A correct answer with some evidence of reasoning or application of mathematics to solve the problem, or an incorrect answer with substantial evidence of solid reasoning or application of mathematics to solve the problem.
STEP 4 A correct answer supported by substantial evidence of solid reasoning or application of mathematics to solve the problem.
The response identifies illustration 2 OR 5 for part (a) AND shows no understanding of what a sequence of rigid transformations entails in part (b).
The response correctly identifies illustrations 2 AND 5 for part (a) AND shows little understanding of what a sequence of rigid transformations entails in part (b).
The response correctly identifies illustrations 2 AND 5 for part (a) AND shows an understanding of what a sequence of rigid transformations entails, but states a less than perfect solution.
The response correctly identifies illustrations 2 AND 5 for part (a) AND correctly reasons why any one of illustrations 1, 3, 4, or 6 is not a sequence of rigid transformations.
2
G-CO.10
The response shows little or no understanding of angle sum properties and no correct answer OR states the correct answer without providing any evidence of the steps to get there.
The response shows the appropriate work needed to correctly calculate the measure of angle A, but makes either one conceptual error and one computational error, two conceptual errors, or two computational errors.
The response shows the appropriate work needed to correctly calculate the measure of angle A, but makes one conceptual error, such as labeling = 132 OR one computational error such as finding .
The response shows all the appropriate work needed to correctly calculate the measure of angle A.
3
G-CO.10
A proof is written that demonstrates little or no understanding of the method needed to achieve the conclusion.
A proof is written that demonstrates an understanding of the method needed to reach the conclusion, but two steps are missing or incorrect.
A proof is written that demonstrates an understanding of the method needed to reach the conclusion, but one step is missing or incorrect.
A complete and correct proof is written that clearly leads to the conclusion that .
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
277 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
4
a–b G-CO.7 G-CO.8
5
a–b G-CO.3 G-CO.13
6
G-CO.11
A response shows little or no evidence of understanding for part (a) or (b).
A response shows the correct triangle congruence criteria listed in part (a) and the sequence contains more than one error (b).
A response shows the correct triangle congruence criteria listed in part (a) and the sequence contains an error (b).
A response shows the correct triangle congruence criteria listed in part (a) and any valid sequence of transformations in (b).
A drawing that is not an appropriate construction and an underdeveloped list of steps is given and in part (b) there are errors with the vertex labels and the description for Rigid Motion 3.
A construction is drawn, but two steps are either missing or incorrect in the construction or list of steps; in part (b), correct vertex labels are written in the diagram of but an incorrect Rigid Motion 3 description OR the Rigid Motion 3 description is correct, but the vertex labels are incorrect.
A construction is drawn, but one step is missing or incorrect in the construction or list of steps, such as the marks to indicate the length of side ̅̅̅̅; in part (b), correct vertex labels are written in the diagram, but an incorrect Rigid Motion 3 description OR the Rigid Motion 3 description is correct, but the vertex labels are incorrect.
A correct construction is drawn showing all appropriate marks and the steps of the construction are written out correctly; in part (b), correct vertex labels are written in the diagram of, as well as a correct Rigid Motion 3 description.
A proof is written that demonstrates little or no understanding of the method needed to achieve the conclusion.
A proof is written that demonstrates an understanding of the method needed to reach the conclusion, but two steps are missing or incorrect.
A proof is written that demonstrates an understanding of the method needed to reach the conclusion, but one step is missing or incorrect.
A complete and correct proof is written that clearly leads to the conclusion that is a parallelogram.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
278 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
279 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
280 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
281 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
282 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
283 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
284 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
285 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
End-of-Module Assessment Task
M1
GEOMETRY
Name
Date
1. Each of the illustrations on the next page shows in black a plane figure consisting of the letters F, R, E, and D evenly spaced and arranged in a row. In each illustration, an alteration of the black figure is shown in red. In some of the illustrations, the red figure is obtained from the black figure by a geometric transformation consisting of a single rotation. In others, this is not the case. a. Which illustrations show a single rotation?
b. Some of the illustrations are not rotations or even a sequence of rigid transformations. Pick one such illustration and use it to explain why it is not a sequence of rigid transformations.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
269 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
270 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
2. In the figure below, ̅̅̅̅ bisects Find the measure of angle
and
.
.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
271 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
3. In the figure below, ̅̅̅̅ is the angle bisector of Prove that
. ̅̅̅̅̅̅ and ̅̅̅̅̅̅ are straight lines and ̅̅̅̅
̅̅̅̅ .
.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
272 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
End-of-Module Assessment Task
GEOMETRY
4. The triangles
and
in the figure below such that ̅̅̅̅
̅̅̅̅ , ̅̅̅̅
̅̅̅̅ , and
a. What criteria for triangle congruence (ASA, SAS, SSS) implies that
b. Describe a sequence of rigid transformations that shows
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
.
?
.
Congruence, Proof, and Constructions 5/29/14
273 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
5. a.
Construct a square
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
with side ̅̅̅̅. List the steps of the construction.
Congruence, Proof, and Constructions 5/29/14
274 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
b.
Three rigid motions are to be performed on square . The first rigid motion is the reflection ̅̅̅̅ through line . The second rigid motion is a 90° clockwise rotation around the center of the square. Describe the third rigid motion that will ultimately map image of each rigid motion in the provided blanks.
back to its original position. Label the
Rigid Motion 1 Description: Reflection through line ̅̅̅̅
Rigid Motion 2 Description: 90° clockwise rotation around the center of the square.
Rigid Motion 3 Description:
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
275 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
6. Suppose that Prove that
is a parallelogram and that is a parallelogram.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
and
are the midpoints of ̅̅̅̅ and ̅̅̅̅ , respectively.
Congruence, Proof, and Constructions 5/29/14
276 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
A Progression Toward Mastery Assessment Task Item
1
a–b G-CO.2
STEP 1 Missing or incorrect answer and little evidence of reasoning or application of mathematics to solve the problem.
STEP 2 Missing or incorrect answer but evidence of some reasoning or application of mathematics to solve the problem.
STEP 3 A correct answer with some evidence of reasoning or application of mathematics to solve the problem, or an incorrect answer with substantial evidence of solid reasoning or application of mathematics to solve the problem.
STEP 4 A correct answer supported by substantial evidence of solid reasoning or application of mathematics to solve the problem.
The response identifies illustration 2 OR 5 for part (a) AND shows no understanding of what a sequence of rigid transformations entails in part (b).
The response correctly identifies illustrations 2 AND 5 for part (a) AND shows little understanding of what a sequence of rigid transformations entails in part (b).
The response correctly identifies illustrations 2 AND 5 for part (a) AND shows an understanding of what a sequence of rigid transformations entails, but states a less than perfect solution.
The response correctly identifies illustrations 2 AND 5 for part (a) AND correctly reasons why any one of illustrations 1, 3, 4, or 6 is not a sequence of rigid transformations.
2
G-CO.10
The response shows little or no understanding of angle sum properties and no correct answer OR states the correct answer without providing any evidence of the steps to get there.
The response shows the appropriate work needed to correctly calculate the measure of angle A, but makes either one conceptual error and one computational error, two conceptual errors, or two computational errors.
The response shows the appropriate work needed to correctly calculate the measure of angle A, but makes one conceptual error, such as labeling = 132 OR one computational error such as finding .
The response shows all the appropriate work needed to correctly calculate the measure of angle A.
3
G-CO.10
A proof is written that demonstrates little or no understanding of the method needed to achieve the conclusion.
A proof is written that demonstrates an understanding of the method needed to reach the conclusion, but two steps are missing or incorrect.
A proof is written that demonstrates an understanding of the method needed to reach the conclusion, but one step is missing or incorrect.
A complete and correct proof is written that clearly leads to the conclusion that .
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
277 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
4
a–b G-CO.7 G-CO.8
5
a–b G-CO.3 G-CO.13
6
G-CO.11
A response shows little or no evidence of understanding for part (a) or (b).
A response shows the correct triangle congruence criteria listed in part (a) and the sequence contains more than one error (b).
A response shows the correct triangle congruence criteria listed in part (a) and the sequence contains an error (b).
A response shows the correct triangle congruence criteria listed in part (a) and any valid sequence of transformations in (b).
A drawing that is not an appropriate construction and an underdeveloped list of steps is given and in part (b) there are errors with the vertex labels and the description for Rigid Motion 3.
A construction is drawn, but two steps are either missing or incorrect in the construction or list of steps; in part (b), correct vertex labels are written in the diagram of but an incorrect Rigid Motion 3 description OR the Rigid Motion 3 description is correct, but the vertex labels are incorrect.
A construction is drawn, but one step is missing or incorrect in the construction or list of steps, such as the marks to indicate the length of side ̅̅̅̅; in part (b), correct vertex labels are written in the diagram, but an incorrect Rigid Motion 3 description OR the Rigid Motion 3 description is correct, but the vertex labels are incorrect.
A correct construction is drawn showing all appropriate marks and the steps of the construction are written out correctly; in part (b), correct vertex labels are written in the diagram of, as well as a correct Rigid Motion 3 description.
A proof is written that demonstrates little or no understanding of the method needed to achieve the conclusion.
A proof is written that demonstrates an understanding of the method needed to reach the conclusion, but two steps are missing or incorrect.
A proof is written that demonstrates an understanding of the method needed to reach the conclusion, but one step is missing or incorrect.
A complete and correct proof is written that clearly leads to the conclusion that is a parallelogram.
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
278 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
279 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
280 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
281 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
282 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
283 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
284 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
M1
GEOMETRY
Module 1: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Congruence, Proof, and Constructions 5/29/14
285 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
