Lesson Plan Template: Confirmatory or Structured Inquiry
Learning Objectives: What will students know and be able to do as a result of this lesson?
Given three side lengths, student will be able to determine if those sides can form a triangle.
Prior Knowledge: What prior knowledge should students have for this lesson?
- Have a working definition of a polygon
- Know that polygons are closed figures
- Know how to classify polygons by their sides
- Readily recognize a triangle
Guiding Questions: What are the guiding questions for this lesson?
What are some characteristics of triangles? (closed, three sides, three angles, angles sum to 180 degrees, etc.)
Now, suppose a triangle has three sides with lengths a, b, and c.
- Will any set of numbers a, b, and c make a triangle, or do we need a special set of side lengths?
- What relationship do you think exists between a, b, and c? (HINT: It will be an inequality relationship.)
Introduction: How will the teacher introduce the lesson to the students?
Teacher places three strips on a magnetic white board and asks the students what figure could be formed using the three strips for sides. When the students immediately answer "triangle," the teacher will probe for characteristics of triangles. The goal is to lead students to agree that only CLOSED three sided figures are triangles.
Investigate: What question(s) will students be investigating? What process will students follow to collect information that can be used to answer the question(s)?
Step 1: Give each group an activity log. Triangle_Inequality_Investigation_LogSheet.pdf
Have students put the names of all group members on the log. Then pass out a set of foam strips to each group. Have students confirm that there are eight strips in their bags. Further confirm that each set of strips contains strips marked 10, 9, 8, 7, 6, 5, 4, and 3. Explain the number on the strip indicates its length in centimeters. Demonstrate this by measuring a strip under the document camera.
Step 2: Ask students to remove strips 10, 9 and 8. Ask them to form a triangle with the strips by laying each strip down so its end is touching the other strips at their endpoints. Now have them record this combination in their activity log. Be sure that students are completing the entire row of information for each set of side lengths.
Step 3: Ask students to remove strips 3, 6 and 10 from their bags. Again have them form a triangle. When they are not successful, there will be controversy. Some students will insist that they can make a triangle, so it will be necessary to return to the original directions that the ENDPOINTS must be touching. Also, remind students that a triangle is a closed figure.
Analyze: How will students organize and interpret the data collected during the investigation?
Step 4: When students complete their exploration and have recorded their findings their log sheets, ask them to study the results and form a conjecture about triangles and their side lengths. In particular, tell students to use their data to guide them as they write a rule for determining whether a set of three side lengths will form a triangle. (The teacher may need to direct students to focus on the columns headed "Sum of short and middle sides" and "longest side." Ask them how the sums and the longest sides are related in the sets that form triangles. Then ask how those same numbers are different for the sets of side lengths that do not form triangles. This can be a difficult task for students as they are not experienced writing a rule.
Step 5: Have students go back and test their rule on any four of the strip sets listed in their log. Did their rule work? If not, why? How can they change their rule so that it will work? Tell students to test their new rule again. They should continue modifying their rule and testing it until their rule works for all the side length combinations on their activity sheet.
Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Teacher goes back to the three strips that were originally used to open the day's discussion and introduce the lesson. Ask students to apply their rules to these three lengths. Each student will turn in a written response to the question: "Can these three side lengths form a triangle? Why or why not?"
Student responses should include the rule their group developed for determining if a set of side lengths could form a triangle. This written response is each student's "exit slip" out the door at the end of the class period.
Each student's Exit Slip should state something like the following:
"Any side of a triangle is less than the sum of the other two sides." (Triangle Inequality Theorem)
In equation form, the Triangle Inequality Theorem looks like this:
Work the odd-numbered problems on the worksheet:
- Using pencil, paper, and a rule, ask students to draw a triangle on a sheet of 8.5 x 11 paper.
- Ask students to measure side lengths in centimeters using a metric ruler.
- Ask students to label the sides with the measured lengths.
- Teacher will circulate to inspect the results, to verify that:
- triangles were drawn
- students understand the concept of side length
Feedback to Students
Teacher will assess students' understanding informally as they work through the activity. The Exit Slip will allow the teacher to determine what aspects of the concept need to be addressed again the next day.