|Grade span:||9 to 12|
Description:This sample lesson, rooted in geometric art, provides students opportunities to explore number patterns and basic geometry concepts. Students engage in a fun, creative mathematics activity, enhanced by a classroom configured into centers. Students work together, compare drawings, and discuss their findings. As a result, they develop and refine their processing, communication, and exploratory skills - real-life skills that mathematicians use routinely. Students employ their creative skills in an activity that is structured, but also requires investigation based on student interest and curiosity.
- Investigate number and diagram patterns
- Communicate about mathematics (e.g., use mathematical language, share mathematical insights)
- Follow a set of pre-determined rules
- Represent number patterns with pictures
- PDF - Student Worksheet (PDF)
- Pencils (including colored)
- Paper (graphing and other as needed)
- Print out accompanying PDF and familiarize yourself with the task students will be involved with. If necessary, make time to share the lesson with a day time mathematics instructor and to converse about the standards and mathematics involved.
- Organize students in small groups that will allow them appropriate discussion partners. The success of this lesson depends, in part, on each student's ability to feel free to explore and discuss his or her ideas within a math center. [link to Math Centers home page for further explanation and support]
- Make sure all materials are available for all students.
- Prepare a brief introduction of the task the students will be involved with. You might ask if any students have a particular interest in art. Some pictures of geometric art might be of interest and can serve as a useful bridge to the content (an internet search on "geometric art" yields many examples). Clarifying the task and peaking students' interest in the problem are the goals of this discussion.
What to Do:
- Give a brief introduction of the task.
- Allow students time to read through the worksheet. Let students talk with each other about the task at hand, and ask any questions they have to their peers. [link to Implementation Considerations, "Encourage students to communicate about math"]
- If students need more structure, you can provide an example for them to try. Here are a couple of examples:
- Have students try the same numbers (2, 3, 4) but in a different order (e.g., 3, 2, 4).
- Have students try another simple 3-number pattern, like 2, 4, 6. Ask what happens if they use all even numbers. This might give students a starting place, and help get them "unstuck."
- As you circulate, try to stay active in student's work. Don't get bogged down at one center for a long period of time. Make sure students try various number sequences. All even and all odd numbers might be interesting for some. Also, not all helix-a-graphs return to the starting point. Challenge students to figure out which number patterns generate graphs that never end.
- Before the end of the session, provide time for students to share their helix-a-graphs with the entire class. Even if students need more time, be sure to end the session with a chance for student sharing. You can prompt students to share any conjectures about number patterns or ideas they are still investigating. You might need to model this for students using a think-a-loud (e.g., Say, "I am interested in what happens if I use the same three digits, but in a different order every time. So far, every time I use the same numbers in different orders, my helix-a-graphs have exactly the same shape.")
Evaluate (Outcomes to look for):
- All students are engaged and actively creating helix-a-graphs
- Students are communicating effectively about mathematics (e.g., using mathematical language, comparing their own thinking with other student thinking, gaining clarification from each other)
- Students are engaging in an open-ended investigation. Ideally, students should be comfortable with an activity with little or no scaffolding (this may take practice).
- Students are working effectively with a small group and using group members as a resource.
- There is a "buzz" of student activity and commitment to the task
Click this link to see additional learning goals, grade-level benchmarks, and standards covered in this lesson.