7th Grade Math : Unit #7 - Geometric Figures : Lesson #9

Triangle Inequality Theorem

Objective: Students will be able to determine if three side lengths can form a triangle.
Standards: 7.G.A.2 MP1 MP2 MP3 MP4 MP5
Subject(s): Math
60 minutes
1 Launch - 10 minutes

OpenerAs students enter the room, they will immediately pick up and begin working on the opener – Instructional Strategy - Process for openers.  This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is mathematical practice 3

Learning Target:  After completion of the opener, I will address the day’s learning targets to the students.  For today’s lesson, the intended target is “I can determine whether three side lengths can form a triangle.” Students will jot the learning target down in their agendas (our version of a student planner, there is a place to write the learning target for every day). 

Opener Reflection
Connection to Prior Knowledge

I use the openers daily in order to establish and keep routine in my classroom.  Students know the expectation is to come in, pick up an opener and get started right away.  This frees me up to deal with any issues that may arise between classes, or to help previously absent students. 

The content in this particular opener is skill work on fractions.  Fractions were not students' favorite topic, and I think it is important to work on skills every once in a while.  Thus, students were working on simiple add/subtract/multiply/divide fraction problems.  This was a good review for kids - lots of hands went up, but I just asked a few guiding questions to get them going - which one do we need a common denominator for? How do we divide fractions?

2 Explore - 45 minutes
Discovery Reflection
Developing a Conceptual Understanding

This discovery activity really allows kids to write the rules for determining the possible side lengths of a triangle themselves. I walked the kids through one of the colors (red) so that they understood my expectations, but then I set them free to finish the table and answer the four questions - I have included a short video clip of the kids in action: Discovery Activity Clip. Today the kids did a great job of generating the answers for the reflective questions - see the Class Notes and Student Work for more. 

The discovery activity was a great segway into the notes, and the discussion on how to set the parameters for a third side.  I was hoping they would be able to set the parameters on their own, but they struggled a bit - so I gave them 6 choices of a third side and asked that they talk at their tables about which of my options could be possibilities.  Then I was able to get them thinking about what x had to be between, and from there they were able to figure out how to set up the inequality for the possible third side length.

3 Summary + Homework - 5 minutes

Instructional Strategy - Table DiscussionTo summarize this lesson, I am going to ask that students have a table discussion on the question – Think about the angles across from each side of a triangle – just knowing the side lengths, you can order the angles from largest to smallest – figure out how.  For this summary, I am going to have students discuss at their tables, and I am going to ask someone from each table to share out.  After every one shares, I will address the right/wrong answers.

Homework:  After the table discussion I will pass out the homework for the students to get started on. Eventhough the assignment is long, it should go quick!



Summary Reflection
Adjustments to Practice

I had several tables ask if they could have their straw bags back in order to figure out the answer to my question - so I thought that was awesome.  I considered just drawing them a triangle on the board, but I was excited that they wanted to figure it out for themselves.  Once they had their straws, students were able to answer the question with ease.  I think in the future I may add a column to the table about the angles, so that they make note of it during the discovery.