Tessellations of the Plane
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to make observations of tessellations, which will be useful when students describe and create their own tessellations in a later activity. While students may notice and wonder many things about these images, tessellations covering the plane with no gaps and the transformations of shapes are the important discussion points.
Studying these patterns and understanding how and why they repeat to fill up the plane is an example of expressing regularity in repeated reasoning (MP8). In this case, the repeated reasoning is continuing to lay out the shapes in the same pattern.
Launch
Arrange students in groups of 2. Display the images 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
Students may notice:
- Four of the patterns use only 1 shape. Two of them use 2 different shapes.
- The pattern could continue to the left and right or up and down.
Students may wonder:
- Are the colors of the shapes important?
- Do the arrows count as 1 shape or 2, since they are pointing in different directions?
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 images. 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 the concept of shapes covering the plane without gaps does not come up during the conversation, ask students to discuss this idea.
If time allows, discuss:
- “How do I know what happens as the tessellation continues to grow off of the page?” (There is often a pattern, but we would have to indicate that the pattern continues.)
- “Are the colors of the shapes important?” (They are important for seeing patterns and making the pictures prettier, but they could be changed and the pattern would still be the same.)
- Tessellations of the plane and of spheres have been used by many cultures. Show students pictures of the Kutubiyya Mosque minaret in Marrakesh, Morocco, the Alhambra in Spain, or sphere tessellations such as those found in Japanese temari, and have students describe the patterns and transformations they see.
Standards
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
20 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Tessellations of the Plane
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to make observations of tessellations, which will be useful when students describe and create their own tessellations in a later activity. While students may notice and wonder many things about these images, tessellations covering the plane with no gaps and the transformations of shapes are the important discussion points.
Studying these patterns and understanding how and why they repeat to fill up the plane is an example of expressing regularity in repeated reasoning (MP8). In this case, the repeated reasoning is continuing to lay out the shapes in the same pattern.
Launch
Arrange students in groups of 2. Display the images 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
Students may notice:
- Four of the patterns use only 1 shape. Two of them use 2 different shapes.
- The pattern could continue to the left and right or up and down.
Students may wonder:
- Are the colors of the shapes important?
- Do the arrows count as 1 shape or 2, since they are pointing in different directions?
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 images. 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 the concept of shapes covering the plane without gaps does not come up during the conversation, ask students to discuss this idea.
If time allows, discuss:
- “How do I know what happens as the tessellation continues to grow off of the page?” (There is often a pattern, but we would have to indicate that the pattern continues.)
- “Are the colors of the shapes important?” (They are important for seeing patterns and making the pictures prettier, but they could be changed and the pattern would still be the same.)
- Tessellations of the plane and of spheres have been used by many cultures. Show students pictures of the Kutubiyya Mosque minaret in Marrakesh, Morocco, the Alhambra in Spain, or sphere tessellations such as those found in Japanese temari, and have students describe the patterns and transformations they see.
Standards
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.