##
* *Reflection: Discourse and Questioning
Classification of Triangles - Section 2: Student Exploration

Discourse and questioning is a key component to every math lesson. Here's an example of a conference where questioning leads the student to a deeper conceptual understanding of angle classification: Identifying Triangle 3. Many times during this conference, I could have told him the answer, but instead I had to "bite my tongue" and provide the necessary wait time!

*Discourse and Questioning: Developing a Deeper Understanding*

# Classification of Triangles

Lesson 5 of 7

## Objective: SWBAT classify triangles by their properties.

## Big Idea: Students will use a Powerpoint Presentation and pictures of real-world triangles to classify triangles by properties.

*100 minutes*

#### Opening

*40 min*

**Goal & Introduction**

To being today, I introduced today's goal: *I can classify triangles by their properties. *We then discussed the meaning of properties using the following Properties Poster.

**Review**

Next, we reviewed the meaning of a right triangle, obtuse triangle, and acute triangle. We then sang our Triangle Song to review how to classify triangles based on the number of congruent sides.

**Powerpoint Presentation**

To review how to classify triangles, I created a Google Powerpoint, Triangle Types Presentation, and shared it with students. Next, students opened the presentation in Google Documents and copied the presentation to make the presentation their own.

On the first slide, we discussed how all triangles are 3-sided figures. Then, we moved on to the next slide, Right Isosceles Triangle, and I asked:* Based on your investigation yesterday, who who can tell me what you think the properties of a right isosceles triangle are? *Students referred to the Triangle Chart from yesterday and said, "It has a right angle," and "It has two congruent sides." We then listed these properties in the text box on this slide and used the shape tools to construct a right isosceles triangle.

We continued in the same fashion with the following slides: discussing and listing the properties of each triangle as a class and then students created examples. After a few slides, I let students continue on their own. My students have their own laptops this year so they are pretty quick when it comes to completing a presentation like this. Here is an example of a student-teacher conference during this time: Student Constructing an Acute Isosceles Triangle.

**Impossible Triangles **

As students got to slides 10 and 11 (right equilateral triangle and obtuse equilateral triangle), students discovered that they were impossible! I loved letting them discover this on their own!

**Student Example**

Here's an example of a student's completed presentation: Student Example of Presentation.

*expand content*

#### Student Exploration

*40 min*

**Real World Connection**

To engage students in Math Practice 4: Model with mathematics, I printed pictures of triangles in every day life, Every Day Triangles. I wanted students to make the connection between math in the classroom and math in the real world.

After numbering each picture, 1-17, I placed the Pictures on the Back Table. This way, groups of students could choose a picture to explore one at a time. I have found, whenever I incorporate student choice into lessons, student engagement almost always increases!

**Choosing Partners**

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

**Recording Sheet**

To begin, I asked all students to number a lined sheet of paper, 1-17. We then titled our recording sheet, "Real World Triangles!" Here's an example of a student's completed recording sheet: Student Recording Sheet.

I explained: *Today, I want you to classify triangles outside of our classroom! On the back table, you'll find pictures of a bike, a sidewalk, a sailboat, and other real world objects. It's important for you to know that triangles aren't just a part of math! One at a time, you and your partner can choose a real world triangle off the back table. Then, you'll use your tools, such as a protractor, square corner, or ruler to classify each triangle. Make sure you record Triangle #1 next to number one on your recording sheet. *

Students couldn't wait to begin!

**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).

*What type of triangle is this?**How do you know?**What properties helped you classify this triangle?**What do you call two sides that are equal? (congruent)**How many obtuse angles can an obtuse triangle have?*

**Conferences**

Here, Identifying Triangle 1, two students use their tools to estimate the angle and side measurements of this triangle. They found that all the angles and sides are roughly the same which means it is an acute equilateral triangle.

Here, Identifying Triangle 12, two students work together to determine that this triangle is an obtuse isosceles triangle.

**Checking Student Work**

As students finished their triangle exploration, we corrected the recording sheet altogether as a class.

*expand content*

#### Student Practice

*20 min*

**Practice Page**

Transferring learning using other applications is a huge part of math! To formatively assess students on their ability to classify triangles, I passed out a practice page from Math-Aids.com.

**Conferencing**

During this time, I conferenced with as many students as possible. Here, Identifying Angles, a student benefits from turning the page in order to "see" each angle.

**Completed Work**

Most students were successful at completing this page. Here's an example of a student's completed work: Student Practice Page.

*expand content*

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- UNIT 1: Measuring Mass and Weight
- UNIT 2: Measuring Capacity
- UNIT 3: Rounding Numbers
- UNIT 4: Place Value
- UNIT 5: Adding & Subtracting Large Numbers
- UNIT 6: Factors & Multiples
- UNIT 7: Multi-Digit Division
- UNIT 8: Geometry
- UNIT 9: Decimals
- UNIT 10: Fractions
- UNIT 11: Multiplication: Single-Digit x Multi-Digit
- UNIT 12: Multiplication: Double-Digit x Double-Digit
- UNIT 13: Multiplication Kick Off
- UNIT 14: Area & Perimeter

- LESSON 1: Right, Acute, & Obtuse Angles
- LESSON 2: Complementary & Supplementary Angles
- LESSON 3: Measuring Angles Inside Shapes
- LESSON 4: Types of Triangles
- LESSON 5: Classification of Triangles
- LESSON 6: Regular vs. Irregular Polygons
- LESSON 7: Classification of Quadrilaterals