Rotation Patterns
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to identify transformations used to build a shape, which will be useful when students perform transformations in a later activity. While students may notice and wonder many things about these figures, identifying transformations used to build a shape and using knowledge of the original figure to classify the new shape are the important discussion points.
This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is the properties of the isosceles right triangle needed to classify the final shape.
Launch
Arrange students in groups of 2. Display the image 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 with their partner.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The quadrilateral is made of four triangles.
- Triangle ABC can be rotated to line up with the other triangles.
- Triangle ABC can be reflected to line up with the other triangles.
- A 90-degree rotation of the quadrilateral would line up with the current quadrilateral (the quadrilateral is a square).
Students may wonder:
- Is the quadrilateral a square?
- Is triangle ABC an isosceles right triangle?
- Would rotating any triangle 90 degrees repeatedly create a square?
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 using transformations to build a shape does not come up during the conversation, ask students to discuss this idea.
Math Community
After the Warm-up, display the revised Math Community Chart created from student responses in Exercise 3. Tell students that today they are going to monitor for two things:
- “Doing Math” actions from the chart that they see or hear happening.
- “Doing Math” actions that they see or hear that they think should be added to the chart.
Standards
- 8.G.1.a·Lines are taken to lines, and line segments to line segments of the same length.
- 8.G.1.b·Angles are taken to angles of the same measure.
- 8.G.A.1.a·Lines are taken to lines, and line segments to line segments of the same length.
- 8.G.A.1.b·Angles are taken to angles of the same measure.
15 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Rotation Patterns
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to identify transformations used to build a shape, which will be useful when students perform transformations in a later activity. While students may notice and wonder many things about these figures, identifying transformations used to build a shape and using knowledge of the original figure to classify the new shape are the important discussion points.
This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is the properties of the isosceles right triangle needed to classify the final shape.
Launch
Arrange students in groups of 2. Display the image 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 with their partner.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The quadrilateral is made of four triangles.
- Triangle ABC can be rotated to line up with the other triangles.
- Triangle ABC can be reflected to line up with the other triangles.
- A 90-degree rotation of the quadrilateral would line up with the current quadrilateral (the quadrilateral is a square).
Students may wonder:
- Is the quadrilateral a square?
- Is triangle ABC an isosceles right triangle?
- Would rotating any triangle 90 degrees repeatedly create a square?
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 using transformations to build a shape does not come up during the conversation, ask students to discuss this idea.
Math Community
After the Warm-up, display the revised Math Community Chart created from student responses in Exercise 3. Tell students that today they are going to monitor for two things:
- “Doing Math” actions from the chart that they see or hear happening.
- “Doing Math” actions that they see or hear that they think should be added to the chart.
Standards
- 8.G.1.a·Lines are taken to lines, and line segments to line segments of the same length.
- 8.G.1.b·Angles are taken to angles of the same measure.
- 8.G.A.1.a·Lines are taken to lines, and line segments to line segments of the same length.
- 8.G.A.1.b·Angles are taken to angles of the same measure.