Download LESSON OVERVIEW

The Group Recording sheet helps students’
organize their work to see the inductive pattern
Students work in small groups to explore the sum of the interior angles of various polygons
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Small group discussion guided by teacher questions
EXPLORE PHASE: Supporting Students’ Exploration of the Task
STRUCTURE
PRIVATE THINK TIME
• Distribute page two of Amazing Amanda. Students should be organized into collaborative groups of four. Have a student read the
task directions
• Ask for any words or terms that the students don’t understand. Clarify the meanings of the words or terms for the students.
• Assign a student to be individually responsible for completing the table for one of the polygons with 4, 5, 6 or 7 sides.
• Ask students to work individually for about 15 minutes so that they can make sense of the problem for themselves.
• Circulate around the classroom and clarify confusions. Be careful to NOT give away too much information or suggest conjectures.
SMALL GROUP (4 students) WORK
• After allowing 15 minutes for individuals to finish their tables distribute one copy of page three of the task to each group, the
“Group Recording Sheet”
• Using a “round robin/roundtable” collaborative strategy have the students transfer their work from their individual tables to the
group recording sheet, explaining their thinking to the group as they do so.
• Distribute page four of Amazing Amanda and allow students time to discuss the questions in their groups
• As students are working, circulate around the room.
o Be persistent in asking questions related to the mathematical ideas (see question suggestions in the following section),
exploration strategies, and connections between representations.
o Be persistent in asking students to explain their thinking and reasoning.
o Be persistent in asking students to explain, in their own words, what other students have said.
o Be persistent in asking students to use appropriate mathematical language.
*What do I do if students have difficulty getting started?
Ask them to draw their assigned polygon. Ask, “How many sides does your polygon have?” “How can we use the sum of the
angles in a triangle to figure out the sum of the interior angles of this polygon?” “How many non-overlapping triangles are
contained in your polygon?”
What do I do if students finish early?
• Challenge students to investigate whether their formula works for both concave and convex polygons.
• Ask a “quiet” group member to explain the work of the group. If s/he can’t explain, challenge the group to make sure that that each
group member understands, leave, and return later to ask again.
MONITORING STUDENTS’ RESPONSES
• As you circulate, attend to students’ mathematical thinking and to their conjectures, in order to identify those responses that will be
shared during the Share, Discuss, and Analyze Phases.
• Identify students who can correctly explain and demonstrate a formula for the sum of the measurements of the interior
angles of any polygon. Find students who used different methods, including different triangulation methods, and find
students with different formulas.
Identify a group member of several different groups that can explain the answers to each question.
Template developed by the LEARNING RESEARCH AND DEVELOPMENT CENTER
© LAUSD Secondary Mathematics 2008
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