Naming the Moves
10 min
Teacher Prep
Setup
Narrative
This is the first Notice and Wonder activity in the course. Students are shown an image and asked: “What do you notice? What do you wonder?”
Students are given time to write down what they notice and wonder about the image and then time to share their thoughts. Their responses are recorded for all to see. Often, the goal is to elicit observations and curiosities about a mathematical idea students are about to explore. Pondering the two open questions allows students to build interest about and gain entry into an upcoming task.
The purpose of this Warm-up is to describe a transformation, which will be useful when students describe transformations with more precise language in a later activity. While students may notice and wonder many things about this image, the angle of rotation and vocabulary used are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 2. Display the two quadrilateral figures for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner.
Student Task
What do you notice? What do you wonder?
Sample Response
Things students may notice:
- You can turn Figure A to get Figure B.
- Figure A and Figure B are both quadrilaterals.
- Figure A and B share a vertex.
- You cannot slide Figure A to get Figure B.
- The rotation is more than 90∘.
Things students may wonder:
- Can you get from Figure A to Figure B with only 1 move?
- Does this shape have a special name?
- Are the shapes the same?
- How many degrees is the rotation from Figure A to Figure B?
- Which figure is the original?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If determining the angle of rotation does not come up during the conversation, ask students to discuss this idea.
Introduce or reiterate the language of clockwise (for rotating in the direction the hands on a clock move) and counterclockwise (for rotating in the opposite direction). In this case, the direction of rotation is not specified but it is natural to view Figure A being rotated counterclockwise onto Figure B. Make sure to introduce the language of the center of rotation (the vertex shared by A and B is the center of rotation).
Anticipated Misconceptions
Students may not be sure which angle to measure. They may measure the acute angle between Shape A and Shape B. Ask these students to trace Shape A on tracing paper and rotate it by that angle to see that this does not give Shape B.
Standards
- 4.MD.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- 4.MD.C.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations:
10 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Naming the Moves
10 min
Teacher Prep
Setup
Narrative
This is the first Notice and Wonder activity in the course. Students are shown an image and asked: “What do you notice? What do you wonder?”
Students are given time to write down what they notice and wonder about the image and then time to share their thoughts. Their responses are recorded for all to see. Often, the goal is to elicit observations and curiosities about a mathematical idea students are about to explore. Pondering the two open questions allows students to build interest about and gain entry into an upcoming task.
The purpose of this Warm-up is to describe a transformation, which will be useful when students describe transformations with more precise language in a later activity. While students may notice and wonder many things about this image, the angle of rotation and vocabulary used are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 2. Display the two quadrilateral figures for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner.
Student Task
What do you notice? What do you wonder?
Sample Response
Things students may notice:
- You can turn Figure A to get Figure B.
- Figure A and Figure B are both quadrilaterals.
- Figure A and B share a vertex.
- You cannot slide Figure A to get Figure B.
- The rotation is more than 90∘.
Things students may wonder:
- Can you get from Figure A to Figure B with only 1 move?
- Does this shape have a special name?
- Are the shapes the same?
- How many degrees is the rotation from Figure A to Figure B?
- Which figure is the original?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If determining the angle of rotation does not come up during the conversation, ask students to discuss this idea.
Introduce or reiterate the language of clockwise (for rotating in the direction the hands on a clock move) and counterclockwise (for rotating in the opposite direction). In this case, the direction of rotation is not specified but it is natural to view Figure A being rotated counterclockwise onto Figure B. Make sure to introduce the language of the center of rotation (the vertex shared by A and B is the center of rotation).
Anticipated Misconceptions
Students may not be sure which angle to measure. They may measure the acute angle between Shape A and Shape B. Ask these students to trace Shape A on tracing paper and rotate it by that angle to see that this does not give Shape B.
Standards
- 4.MD.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- 4.MD.C.5·Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations: