Types of Triangles

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Objective

SWBAT classify triangles.

Big Idea

Students will classify triangles into groups and will later determine the attributes of different triangle types.

Student Exploration Part 1

50 minutes

Choosing Partners

Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. 

Triangle Sort (25 min)

To begin today's lesson, I handed out  a copy of Triangle Sort (from The Georgia Department of Education 4th Grade Math Unit 6) to each group of 2-3 students. Instead of giving students any directions, I wanted them to analyze the triangles and determine how they could use their current math knowledge to sort the triangles. I then handed out sticky notes to each group so that students could easily label each category of triangles. (I was hoping students would use their understanding of right, obtuse, and acute angles to classify the triangles. And... this is exactly what they did!)

Knowing that measuring every angle with a protractor would be difficult, I passed out card stock squares for students to use as square corners. Little did I know that some square corners weren't exactly square! In the future, I would just hand out index cards! 

Making Use of Structure

By leaving this activity open-ended, I knew students would engage in Math Practice 7: Look for and make use of structure. In order to categorize shapes, students will need to determine if there is a pattern or connection between shapes. They will also be closely analyzing shapes and drawing conclusions. 

Monitoring Student Understanding

While students were working, I conferenced with every group. My goal was to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3). 

  1. How are you making sense of these triangles? 
  2. Are you noticing a pattern? 
  3. What do you think? Why do you think that?
  4. How do you know it's not ______? (non-example)
  5. Can you explain your thinking to your partner to make sure he agrees?
  6. What are your categories?  
  7. Can you tell me why this triangle fits into this category?
  8. How did you come up with your labels?

Conferences

Here is an example of a conference at this time: Categorizing Triangles. I loved listening to the student explain how she used the square corner to reason through this categorization process.  

Checking Work

As students finished, I asked them to check their work with other groups. By this time, all groups had discovered the following labels: Triangle Categories.

Group Discussion (5 min)

Then, we moved on to a class discussion about their findings. First, I asked students what problems they encountered while classifying the triangles. Here are some of their responses: 

 

Writing Definitions (10 min)

I then explained: You all have done a beautiful job categorizing these triangles. Now, I'd like for you to use this information to construct definitions for a right triangle, acute triangle, and an obtuse triangle. I asked each group of students to get out a lined sheet of paper to document their definitions. Here's an example: Right, Acute, & Obtuse Definitions.

Here's an example of students going back to make their definitions more precise: Making Definitions More Precise.

Triangle Poster (10 min)

 To help students comprehend the difference between categorizing triangles based upon angles and categorizing triangles based upon side lengths, I created the following poster: Triangle Chart. All of the labeling took place during the lesson.

For the first half of this lesson, I folded over the right half of the poster so students could just focus on categorizing triangles by their angles. 

Using the student-created definitions, we discussed the meaning of right triangle. I labeled the right triangle with the following labels, "one 90 degree angel" and "two acute angles." We continued by labeling the acute and obtuse triangle in a similar manner. 

Student Exploration Part 2

50 minutes

Transition

I referred to the anchor chart and explained to students: There are two ways to classify triangles. You just dissevered one way... by the angles. If a triangle has a right angle, it is a right triangle. If a triangle has an obtuse angle, it is an obtuse triangle. And if a triangle has three acute angles, then it is an acute triangle. Now, we are going to investigate another way to classify triangles! At this point, I purposefully didn't tell students to investigate side lengths. I wanted them to figure this out on their own! 

The Second Triangle Sort (25 min)

I passed out an equilateral, an isosceles, and a scalene triangle to each group of students. Here's a copy of each: Triangle Types. I was very careful to avoid telling students the meaning of each triangle. Just like before, I want students to discover this on their own! I then asked students to get out rulers and protractors and explained the activity: Here's your next challenge! I'd like for you and your partners to use your tools to make observations about each type of triangle. Your goal is to come up with a definition for each triangle type! I wonder who is going to figure out what makes each of these triangles so special! 

Conferencing 

Just as before, I tried to conference with each group of students during this time. Here, Scalene Observations, a student explains how a scalene triangle has three different side lengths and it can be an obtuse triangle. 

This student, Isosceles Observations, found that an isosceles triangle and two congruent sides.

Here, Equilateral Observations, a student explains that an equilateral triangle has three equal sides and three acute angles. I encouraged him to get our a protractor to measure the angles: Finding Equivalent Angle Measurements.

Student Observations & Definitions 

Here are examples of the observations students recorded: 

Also, here's an example of student definitions: Student Example of Definitions.

Class Discussion (10 min)

I invited students to join me on the front carpet to discuss observations. At this point, I unfolded the Triangle Chart and asked students to help me label each of the triangles.

One student pointed out that an equilateral triangle has 3 equal sides. Another student said, "All the angles measure 60 degrees." Others explained, "The sides and angles are all congruent."

We continued by labeling the isosceles triangle and scalene triangle. Students will refer to this poster often during tomorrow's lesson. 

Song (10 min)

Next, I taught students a song to help them remember the types of triangles. This is only their second time singing it through: Triangle Song. By tomorrow, they will have it down perfectly! 

Final Demonstration (5 min)

For a final demonstration today, I showed students equilateral, scalene, and isosceles triangles: I explained: All triangles have something very special in common! I then cut off all the corners of each angle and lined them up to show that the sum of all triangle angles equal 180 degrees. I asked students: What do you notice about all triangles? After a few guesses, students came up with the following observation, "The sum of all angles in one triangle always equals 180 degrees." Here's the resulting poster: Triangle Angles

This final demonstration could have been stretched out into another investigation/lesson, however, I was running out of time to teach this unit so I just slipped it in. There will be several times in upcoming lessons that students refer to this poster. The goal was to simply introduce students to this concept.