Complementary & Supplementary Angles

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Objective

SWBAT find the sum of angles.

Big Idea

Through an exploration process, students will practice using a protractor, recording observations, and constructing definitions for complementary and supplementary angles.

Opening

30 minutes

Today's Number Talk

For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using a number line model and hundreds grids. For each task today, students shared their strategies with peers (sometimes within their group, sometimes with someone across the room). It was great to see students inspiring others to try new methods and it was equally as great to see students examining each other work for possible mistakes!

Getting Started

Prior to the lesson, I placed magnetic money and fractions on the board to help students conceptualize our number talk today. 

I invited students to get a Student Number Line and Hundred Grids. I then drew a Number Line on the Board and marked 0, 1, and 2 on the line. I asked students to do the same on their own number lines.

Task #1: 7/10 + 0.75

To begin, I asked students to add 7/10 + 0.75. Students immediately went to work showing their thinking on their number lines and hundreds grids. To inspire students, I walked around the group and pointed out what students were doing: I see some students labeling their number lines with whole numbers... 0, 1, and 2. I see some students converting the fraction to a decimal number. 

After some time, I asked students to ask a nearby student, "What did you do?" I also took this opportunity to conference with students. 

Next, I asked students to explain their strategies while I modeled their thinking on the board. One student explained how she labeled her number line using fourths and tenths. She then started on 7/10 and added 7/10 to land on 14/10, which is equal to 140/100. Then she added 5/100 to get to 145/100. 

Task #2: 0.9 + 2/10

Next, we moved on to adding 0.9 + 2/10. To get students started, I asked: Who wants to use their number line first? And who wants to use their hundreds grids first? 

Again, students got right to work. Then, students turned and talked to compared answers. During this time, I conferenced with students to ensure understanding and inspire precise work. 

This time, I asked a couple students to demonstrate their thinking. The students showed how to decompose whole numbers on the number line using decimals and fractions. They then explained how they started at 0 and took nine jumps of 1/10 to get to 9/10. Then, they took two more jumps of 1/10 to land on 11/10, or 1 1/10. 

Teacher Demonstration

30 minutes

Complementary & Supplementary Angles

Although the CCSS standards don't specifically mention "complementary" and "supplementary" angles, the standards do indicate the importance of recognizing angle measure as additive, being able to decompose angles into parts in order to find a missing part, and understanding the relationship between angles and a circle. This lesson provided students with the opportunity to decompose complementary and supplementary angles to find the missing part. Also, students began to realize that four sets of complementary angles or two sets of supplementary angles are equal to 360 degrees. 

Review of Vocabulary

To review the meaning of right, acute, and obtuse angles, students sang our Angles Song. I then asked students to make a three column chart on the back of their orange (and white) number line mats with the following headings: right, acute, and obtuse. As we discussed angles, I referred to our posters on our math wall: Angle PosterAcute Angle PosterObtuse Angle PosterRight Angle Poster

I then introduced three more vocabulary words: Ray Poster, Straight Angle Poster, and a Reflex Angle

Importance of Using Different Tools

Prior to moving on with today's lesson, I wanted to make sure students could classify and estimate angle measurements without using a protractor. I also wanted them to learn how the square corner of a piece of paper could be used as tool to identify angles. This is all part of engaging students in Math Practice 5: Use appropriate tools strategically. I want students to learn how paper and estimation are both tools that can be used when analyzing angles. During our investigation today, I'll want students to use these tools to "detect possible errors by strategically using estimation" and the square corner of a paper to verify the angle measurements found using a protractor. 

Angles Review

To provide students with this practice, I created a Powerpoint Presentation called, Angles Review & Estimation.
We started on the following slide: Classifying Angles. I modeled how to use the square corner of a sticky note (or piece of paper) to "test" and classify angles. Next, I showed students how to use a wireless mouse to drag and classify angles on the slide. After modeling this process, I passed the wireless mouse (placed on a white board) to different students in the group. Each time a student classified an angle, we used the square corner of a sticky note to check student thinking. 
     
Angle Estimation   

We then moved on to the last six slides of the presentation to practice estimating angles. On the first slide, Angle Estimation Part A, there was an angle without a protractor. I asked students to guess the measurement. Students responded, "70 degrees!" "85 degrees!" "90 degrees!" 
Then, on the next slide, Angle Estimation Part B (which had the same angle as the last slide, only this time, there was also a protractor), I asked a student to use the wireless mouse to measure the angle. While the student lined up the protractor with the angle, the rest of class and I discussed how to properly use a protractor. We determined the actual measurement of the angle as 82 degrees. Excited voices filled the air as students commented, "I was only a couple degrees off!" 
We continued this process with a couple more angles using the last four slides of the presentaion.
    
Lesson Introduction & Goal
  

I explained to students: You are going to get to explore the rest of our math time. First, you're going to explore the difference between complementary and supplementary angles. I'm not going to tell you what they are or how they work! I'm going to let you investigate it! 

I projected the pages students would be using to guide their investigation: Complimentary Angles and Supplimentary Angles

I introduced today's goal: I can find the sum of angles and I modeled how to measure and add complementary angles first. I asked students to move on to investigating supplementary angles after investigating complementary angles. 

I explained: You're going to first measure angle A and then angle B. Then, you're going to write down the sum of angles A and B. Once you are done, I would like for you to write down 2-3 observations and then try creating a complementary angle on your own.

Students went back to their desks, grabbed their protractors, and were ready to explore! 

Choosing Partners

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

 

Student Practice

40 minutes

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. What are you lining up? (encouraging vocabulary use)
  2. Can you explain what you are noticing?
  3. What do you think? Why do you think that?
  4. How do you know it's not ______? (non-example)
  5. Is this acute or obtuse? How do you know?
  6. What are you finding out about complementary angles?
  7. What problem did you encounter?
  8. Can you explain your thinking to your partner to make sure he agrees? 

Complementary Angles

Students explored complementary angles by measuring and adding two angle measurements together. Through observations, students will identify and apply the generalization: When a right angle is decomposed into any two angles, the sum of the two angles will equal 90 degrees. 

Here are examples of student work: 

 

Supplementary Angles

Students explored supplementary angles by measuring and adding two angle measurements together. Through observations, students will identify and apply the generalization: When a straight angle is decomposed into any two angles, the sum of the two angles will equal 180 degrees. 

Here are examples of student work: 

Closing

10 minutes

To bring closure to this lesson, I asked all students to join me on the front carpet with their complementary and supplementary angle papers.

Poster

I then referred to the Complementary & Supplementary Angles Poster that I created using a projection of the students' investigation papers prior to today's lesson. We started by looking at Complementary Angles. I asked students to share the measurements of each angle from their investigation and I labeled the poster accordingly. 

Next, we discussed their observations. One student said, "All complementary angles add up to 90 degrees." Another student pointed out, "Complementary angles are always acute." The last student said, "They all start in the corners." I then pointed out the correlation between Corner & Complementary angles.

This was also a perfect opportunity to point out the correlation between Side and Supplementary Angles. 

We then discussed student observations of supplementary angles. One student said, "All pairs of supplementary angles add up to 180 degrees." 

Here's how the poster looked at the end of our closing procedures: Completed Complementary & Supplementary Angle Poster.