##
* *Reflection: Checks for Understanding
Tricky Triangles - Section 1: Review and Refresh

I check for student understanding using many different methods. One technique I use is group dialogue and discussion. I encourage the students to be as specific as possible when they are sharing their thoughts. If students speak in vague terms, it is natural for teacher to assume they are trying to say something different/ more accurate than they actually are.

In the triangle review and refresh portion of this lesson, students made some statements that allowed me to recognize and clarify misconceptions.

• "All sides of a triangle add to 180" - I wrote this statement on the board and asked the student if there was something that should be revised. When she didn't immediately recognize her mistake, I surveyed the class to see how many thought something could be changed. It was clear that some students knew the word side was used rather than angle, but others did not. I asked a student to come up and label a triangle to show this is true. A student came to the board and labeled each side of the triangle 60 degrees, 60 degrees, 60 degrees. Rather than writing the measurements at the corners of the triangle, they were placed on the sides. This opened a huge conversation about labeling, accuracy, and degrees compared with distance. The misconception that was shared proved more thorough teaching than I had planned.

• "A triangle has 3 edges and 3 corners". This error in student thinking triggered a discussion about 2-D and 3-D shapes. Students may compare attributes such as edges with sides. However, they they are not the same, and I want to help students become more precise in their language.

Open discussion and dialogue, along with time to review and refresh provide opportunities for me to check student understanding without a formal/written assessment. At these times I often learn more about the students' understanding than with formal questioning.

*Beware of student misconceptions*

*Checks for Understanding: Beware of student misconceptions*

# Tricky Triangles

Lesson 7 of 10

## Objective: SWBAT identify, classify, and solve problems involving triangles.

*40 minutes*

#### Review and Refresh

*15 min*

Based on evidence from student work as well as what I've seen in students' reflections, this lesson was designed to provide students with additional opportunities to work with triangles.

To start the lesson, I write TRIANGLES on the board and ask students to share what we know about the properties of triangles. I list their responses on the board to use as an anchor chart throughout the lesson.

• 3 sides, 3 angles

• All angles add to 180 degrees

• Triangles can be named for their sides (equilateral, isosceles, scalene)

• Triangles can be named for their angles (acute, right, obtuse)

This review and refresher allows students share what they know about the properties of triangles. It also provides an opportunity for misconceptions to surface. In the reflection for this section, some of these misconceptions are explained.

Next, I show students the triangles contain 180 degrees model from the Math is Fun website. This page allows us to manipulate a triangle into infinite shapes and sizes. As new triangles are created, the angle measures and total are shown, always adding to 180 degrees.

Before students are sent off to practice finding a missing angle, we work together to make sense of the triangle diagrams; discussing what the various symbols mean. I also explain to students that if 2 sides are equal, than 2 angles will be too. I do this quickly and add the measurements to the board to help students when they get to the 3rd and 4th examples. At this point, they do not need to memorize this characteristic of triangles so I provide students with this information.

*expand content*

#### Independent Practice

*20 min*

Students work in pairs to find the missing angle of a triangle. They use diagrams to organize their thinking (part, part, part whole) and check their results using angle rulers.

Challenges are provided for students to extend their thinking. These "riddles" are from the Matholopis website, and are labeled as *5th grade hard*.

It is important to provide students with these challenges. Often times I think we shy away from things that seem like they are too hard for the students, claiming they won't be able to solve the problem.

I like to provide students with a challenging task to push their thinking.

*expand content*

#### Group Share

*5 min*

The schedule this week has continuously altered the time we have for math class. The ticket out today, was a short group share that I left open ended.

*"Ask me a question about triangles".*

We were able to answer just one group's question.

"When we were working with finding the missing angle, we got 82.1 when we did the math. When we checked it with the angle ruler, we got 80 degrees. Do we trust the math or the measurement more?"

This lead to a discussion about accuracy, scale, and precision. I told students to trust their math, because with the angle ruler, there is a chance of user error, since the tool is new to them. They are more accurate with addition and subtraction.

*expand content*

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- LESSON 1: Discovering Volume (Part 1)
- LESSON 2: Discovering Volume (Part 2)
- LESSON 3: Volume: Decomposing Irregular Shapes
- LESSON 4: Math Scavenger Hunt
- LESSON 5: Finding Volume of Combined Prisms
- LESSON 6: Volume Word Problems
- LESSON 7: Tricky Triangles
- LESSON 8: Benchmark Assessment
- LESSON 9: Quadrilateral Properties & Attributes
- LESSON 10: Solving Quadrilateral Problems