Triangle Inequality Lesson Study
The Triangle Inequality was the third lesson study I participated in during my internship year. I had the privilege to teach this lesson in hopes to recieve some feedback from fellow MSU mathematics interns at the same placement school, Waverly Middle School.
This lesson study was an explore-based lesson requiring students to discover the Triangle Inequality through using straws as manipulatives.
Once the lesson had been planned, taught, debreifed, and revised the lesson, my team created a poster with revisions and student work from the lesson and presented it at a poster fair in one of my Teacher Education class. (Our team shown to the left at the poster fair)
This lesson study was an explore-based lesson requiring students to discover the Triangle Inequality through using straws as manipulatives.
Once the lesson had been planned, taught, debreifed, and revised the lesson, my team created a poster with revisions and student work from the lesson and presented it at a poster fair in one of my Teacher Education class. (Our team shown to the left at the poster fair)
Discovering the Triangle Inequality with Straws
Triangle Inequality Lesson Plan:
march_5_-_straw_lp.pdf | |
File Size: | 39 kb |
File Type: |
Goal: Students will be able to determine whether three side lengths construct a triangle or not.
Bellwork and Exit Slip:
Original Straw Activity Handout:
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Revised Bellwork and Exit Slip:
Revised Straw Activity Handout:
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Examples of one student's growth from bellwork to exit slip.
Common Misconception:
Side a + Side b = Side c (a and b are the shortest sides) does create a triangle
In general, students answered the bellwork questions correctly. However, they were not able to give an explanation to their answer. At the end of the lesson when students were answering the exit slip questions (same as the bellwork questions) almost every student answered the questions correctly and most students were able to provide a correct reason to their answer. This shows that students gained a deeper understanding of the triangle inequality throughout the lesson.
Side a + Side b = Side c (a and b are the shortest sides) does create a triangle
In general, students answered the bellwork questions correctly. However, they were not able to give an explanation to their answer. At the end of the lesson when students were answering the exit slip questions (same as the bellwork questions) almost every student answered the questions correctly and most students were able to provide a correct reason to their answer. This shows that students gained a deeper understanding of the triangle inequality throughout the lesson.
Our team’s take-aways:
- The use of manipulatives enhanced student understanding about the requirements to create a triangle, more specifically the triangle inequality.
- The structure of a task will significantly determine the conclusions students create.
- Manipulatives can create misconceptions.
Revisions:
- Shortest -> Longest Side Length visible on table.
- Yes/No Table for Side Lengths
- Generate Questions about what they notice from Yes/No table
- Partner Activity with Questions
- Students construct their own triangle lengths to give to their partner to solve.
- Whole Group Table
- More Variety in Student Responses
- Add 4th Question with two of same side length that equaled the other.
- Addresses misconception about equal.
Why will these revisions will improve students’ learning?
The revisions on the worksheet were to create productive exploration. Originally, there were numerous groups that were randomly exploring. Having students explore is always positive, but it is important to remember that there must be a reason for the exploration. Creating a yes and no table allows students to notice trends that make side lengths triangles. To build off this, students can generate questions about what they notice from the side lengths in each yes and no table. This allows the cognitive demand to increase through students developing their own understanding from the tables. This can be extended to creating their own triangle side lengths for their peers to test on their own. This will generate more of a productive conversation in the whole class discussion. There is more chance to develop a firm understanding of what side lengths constitute a triangle.
The revisions on the worksheet were to create productive exploration. Originally, there were numerous groups that were randomly exploring. Having students explore is always positive, but it is important to remember that there must be a reason for the exploration. Creating a yes and no table allows students to notice trends that make side lengths triangles. To build off this, students can generate questions about what they notice from the side lengths in each yes and no table. This allows the cognitive demand to increase through students developing their own understanding from the tables. This can be extended to creating their own triangle side lengths for their peers to test on their own. This will generate more of a productive conversation in the whole class discussion. There is more chance to develop a firm understanding of what side lengths constitute a triangle.