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Lesson 5E Lesson
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The Sound of Polynomials

Adding and Subtracting Polynomials

Samaya Williams, James Doyle, Sherry Franklin, Kelsey Willems, Dustin Ragland | Published: July 18th, 2024 by K20 Center

  • Grade Level Grade Level 9th, 10th, 11th
  • Subject Subject Mathematics
  • Course Course Algebra 1, Algebra 2
  • Time Frame Time Frame 120–140 minutes
  • Duration More 3 class periods

Summary

In this lesson, students practice adding and subtracting polynomial expressions. They watch a video about a complicated food order and discuss the idea of combining like items to simplify the order. Students use math manipulatives to explore how to use addition and subtraction to simplify polynomial expressions. By participating in a Scavenger Hunt Notes activity, students create their own notes about adding and subtracting polynomials. Students watch an ICAP video of an education specialist from Ableton, who was a former tour musician. He shares his knowledge of the music industry, using technology to engineer and produce music, and he explains how Chebyshev polynomials of the first kind can be used to manipulate sound and music. After watching the video, students apply adding and subtracting polynomials to hear the sound of the simplified polynomial. Finally, students demonstrate what they have learned about adding and subtracting polynomials in an Exit Ticket.

Essential Question(s)

How can you use addition and subtraction to simplify polynomial expressions?

Snapshot

Engage

Students make the connection of grouping like items and figure out how that concept applies to simplifying polynomial expressions.

Explore

Students use a digital math manipulative to explore using addition and subtraction to simplify polynomial expressions.

Explain

Students participate in a Scavenger Hunt Notes activity to complete notes on using addition and subtraction to simplify polynomial expressions.

Extend

Students watch an ICAP video to see how polynomial expressions affect or change sound, then work in groups to apply their knowledge to listen to their simplified polynomials using a web tool.

Evaluate

Students demonstrate what they have learned about adding and subtracting polynomials in an Exit Ticket.

Materials

  • Lesson Slides (attached)

  • Polynomials and Algebra Tiles handout (attached, 1 per student, 2-sided)

  • Scavenger Hunt QR Codes handout (attached, print 1-sided, print on colored paper)

  • Frayer Model handout (attached, 1 per student)

  • Frayer Model (Teacher Guide) document (optional, attached)

  • Alternative Scavenger Hunt QR Codes handout (optional, attached, print 1-sided, print on colored paper)

  • Alternative Frayer Model handout (optional, attached, 1 per student)

  • Polynomials and Sound handout (attached, 1 per student)

  • Learning Synths Playground handout (optional, attached)

  • Exit Ticket handout (cut in half, one half page per student)

  • Pencils

  • Clipboards (one per student)

  • Devices with Internet access

  • Algebra tiles (optional)

  • Green cups (1 per group)

  • Yellow cups (1 per group)

  • Red cups (1 per group)

  • Blank sheet of paper (1 per student)

  • Earbuds (1 per student, optional)

  • Colored pencils 

  • Markers

Engage

10 Minute(s)

Present the lesson using the attached Lesson Slides.

Display slide 3 and ask students to watch a video about ordering at a fast-food restaurant. Show students the MADtv Fast Food Ordering video. 

Once the students have watched the video, display slide 4 and ask students to figure out an easier way the customer could have communicated his order.

If students don’t mention grouping things that have been ordered, guide them to the possible answer of grouping like items.

Share slides 5–6 to introduce the essential question and the learning objective to connect the idea of grouping like items to simplifying polynomials.

Explore

30 Minute(s)

Display slide 7 and inform students they will be using an online math manipulative to answer questions about the given polynomials. Have students navigate to k20.ou.edu/algebratiles to access the Mathsbot dienes blocks, also known as base-ten blocks. Follow the steps itemized below:

  1. Instruct students to use these resources to represent terms of the polynomial expressions.

  2. Inform students that to create a negative, they will need to click the ” x-1” button at the top of the tool bar.

  3. Advise them to combine like terms by dropping a negative (or red block) on top of the positive block.

  4. Let them know that this action will cause the blocks to disappear or cancel each other out.

  5. Instruct them to get rid of a block by clicking on the block and selecting “delete.”

  6. Instruct them to hit “refresh” in the web browser to clear their screen.

  7. Advise them that the blocks on the screen are very large and can be made smaller by using the “negative magnifying glass” in the top right corner of their screen.

Consider modeling these steps for the class and have the students mimic at the same time. Note that this modeling will give students the opportunity to practice using the tool they will use for the activity.

Display slide 8 and introduce the Try It, Talk It, Color It, Check It instructional strategy. Let students know that as they work on the problem, they will first try it on their own, discuss it with a partner, and then choose a colored cup to represent their confidence in efficiently summarizing how many blocks of each kind they have all together. They will have three colored cups. Tell the students that the colors represent the following confidence levels:

  • Green: They can summarize their thought processes.

  • Yellow: They are a bit uncertain about how to summarize their thought processes.

  • Red: They need help summarizing their thought processes.  

Pass out the Polynomials and Algebra Tiles handout, the green, yellow, and red cups, and a device to each student. Inform students to complete only the addition side of the handout. Give students time to work through the addition side of their handout before moving on. Clear up any misconceptions as they work. 

After 10 minutes, you can unhide slide 9 for students to check their answer and share their process.

Display slide 10 and inform students they will continue working on simplifying polynomials using algebra tiles and the Try It, Talk It, Color It, Check It instructional strategy. But this time, they will focus on subtraction on the back of the handout. Remind students that, as they work on the problem, they should first try it on their own, discuss it with a partner, and then choose a color to represent their confidence in efficiently summarizing their thought process.

Have students use the dienes blocks on the Mathsbot website they used for addition. Give students time to work through the subtraction side of their handouts before moving on. Clear up any misconceptions as they work. 

 After 10 minutes, you can unhide slide 11 for students to check their answer and share their process.

Explain

40 Minute(s)

Start day 2 with a review of the essential question and learning objective (slides 5 and 6). Then, go through the following steps:

  1. Inform students that they will be taking notes on what they explored the day before.

  2. Display slide 12 and introduce the students to the Scavenger Hunt Notes instructional strategy.

  3. Explain to the students that there are QR codes taped around the room to help them take notes.

  4. Have the students start anywhere they would like. Encourage them to spread out.

  5. Pass out a Frayer Model handout and clipboard to each student.

  6. Make sure each student or group of students has a device to scan the QR codes.

  7. Using the QR codes on the wall, have students walk around the room filling in the boxes of their Frayer Model with the information from the corresponding videos.

  8. During the scavenger hunt, in the top-left corner of the Frayer Model handout, ask students to write a definition of polynomial expression. This

    concept is addressed in the video at station 1.

  9. In the top-right corner of the Frayer Model handout, have students write the steps for simplifying polynomials by adding or subtracting.

  10. Ask them to identify what is the most important thing to remember when subtracting polynomials. This concept is addressed at stations 2 and 3.

  11. In the bottom left and right corners of the Frayer Model handout, ask students to simplify the polynomial expressions on the Scavenger Hunt QR Codes handout using either the vertical or horizontal methods.

  12. Inform students that both station 4, adding, and station 5, subtracting, have two QR codes.

  13. Instruct them to watch both videos before deciding whether they want to solve the problem horizontally or vertically on their Frayer Model.

  14. Provide students with 20–30 minutes to complete the activity. 

Once all students have completed the Scavenger Hunt, display slide 13 and facilitate a class discussion to review the Frayer Model. 

Ask students to share what they put on their Frayer Model to help them understand what a polynomial expression is. Use slide 14 to reveal the answers, then have them check their work. 

Then, display slides 15 and 16 to go over the steps of simplifying polynomials. Remind students of the most important thing to remember when subtracting polynomials. Click slide 16 a second time to share the answer with the students.

 Use slides 17–20 to show the answers of the problems in the addition and subtraction sections of the Frayer Model.

Extend

30 Minute(s)

Display slide 21 and introduce the students to the Chebyshev polynomials and the effects these polynomials have on music when they are added and subtracted.

Display slide 22 and inform students they will watch an ICAP video of Dustin Ragland, an “Education Specialist for Ableton,” where he shares his knowledge of the music industry, using technology to engineer and produce music. He explains how Chebyshev polynomials of the first kind can be used to manipulate sound and music. As students watch the video, consider pausing the video as students see the questions on the screen and facilitate brief discussion about what they think the answer to each question will be.

Once the video ends, divide students into groups of no more than four using the method you prefer. Display slide 23 then give each student a copy of the attached Polynomials and Sound handout. Have groups simplify the four expressions on their handout. Each expression is a sum or difference of Chebyshev polynomials.

Show slide 26 and direct students to navigate to the Polynomials and Sound website on their devices. As a class, use slides 26–28 to walk through the steps of entering the T8(x) Chebyshev polynomial into the web tool. Adjusting the slider to the far right turns on the noeffect and effect volumes, while adjusting the slider to the far left turns off the noeffect and effect volumes. Have students think about how to enter negative coefficients and constants, which are the guiding questions on slide 27. Try to ask prompting questions instead of directly telling them how to enter this information.

Once the class has entered the polynomial and there is a unified sound in the room, display slide 29 and have students adjust the sliders such that one is to the far right (on) while the other is to the far left (off) and listen carefully. Ask for volunteers to describe how the sound changes. Remind students that the “before” is when the noeffect volume slider is to the far right (on), and the “change” is when the effect volume slider is to the far right (on), while the other is off.

If students need additional practice using the web tool, move to slide 30 and have students try to enter the T5(x) Chebyshev polynomial into the web tool. Otherwise, skip slide 30. Students can use the back of their handout for quick reference regarding how to use the web tool.

Again, once you are hearing a unified sound in the room, indicating that students are understanding how to use the web tool, show slide 31. Now is an excellent time to use headphones if students haven’t been already. Direct students to now individually enter the results from their handout and listen for the changes in sound.

Navigate to slide 32. Hold a quick class discussion and have a couple of students share their answers about how they describe the change of their sound. Use the following questions to help with sharing out for one subtraction and one addition problem: 

  • How are the sounds different?

  • What descriptive words would you use for each sound? For example, would nasal, cold, scary, happy, etc., describe the change in sound?

Evaluate

10 Minute(s)

Display slide 34 and use the Exit Ticket strategy to individually assess what students have learned from the lesson. Give each student a half-sheet of the attached Exit Ticket handout or give students a sticky note, an index card, etc., for them to write their response. 

Collect student responses and use them to determine whether they need additional practice or are ready for the next lesson.

Resources

Publisher

K20 Center

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Downloads

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Standards

Oklahoma Academic Standards Mathematics (Algebra 1)
A1.A.3.2: Simplify polynomial expressions by adding, subtracting, or multiplying.
Oklahoma Academic Standards Mathematics (Algebra 2)
A2.A.2.2: Add, subtract, multiply, divide, and simplify polynomial expressions.

Facilitator Resources

Click on a file type icon to download an attachment.

  • Alternative Frayer Model—The Sound of Polynomials
  • Alternative Scavenger Hunt QR Codes—The Sound of Polynomials
  • Frayer Model (Teacher Guide)—The Sound of Polynomials
  • Lesson Slides—The Sound of Polynomials
  • Scavenger Hunt QR Codes—The Sound of Polynomials

Learner Handouts

Click on a file type icon to download an attachment.

  • Exit Ticket—The Sound of Polynomials
  • Frayer Model—The Sound of Polynomials
  • Learning Synths Playground—The Sound of Polynomials
  • Polynomials and Algebra Tiles—The Sound of Polynomials
  • Polynomials and Sound—The Sound of Polynomials

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