The Sound of Polynomials

Display slide 7 and inform students they will be using online math manipulatives 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. Tell students that they will be using this resource to represent the terms of their polynomial expressions.

If this is your students first time using this tool, show slide 8 ask them to model: x² – 3x + x. Use the information below to help your students become familiar with how they are expected to use the tool:

• To create a negative block, select the “Negate” button at the top of the toolbar (after selecting the block one wants to make negative). The resulting block will turn red.

• Students can combine like terms by dragging and dropping a negative (red) block on top of the positive block. Let them know that this action will cause the blocks to disappear or “cancel each other out.” 

• To get rid of an unwanted block, select that block and then select the “Delete” button at the top of the toolbar.

• To clear their screen, students can select the refresh icon in their web browser or select the “Tidy” button at the top of the toolbar.

• Advise them that the blocks on the screen are very large and can be made smaller by using the “Zoom out” button (which looks like a magnifying glass with a negative symbol) in the top-right corner of the toolbar.

Use the “Exchange” and “Group” buttons when using these blocks as base-ten blocks. Similarly, use the “Rotate” button to model multiplication as area.

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 9 and introduce the Try It, Talk It, Color It, Check It strategy. Let students know that as they work on the problem, they will first try it on their own, then 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. Explain to students that they will have three colored cups that 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 to each student. Direct students to complete only the “Adding Polynomials” section of their handout. Once students begin, give pairs the green, yellow, and red cups. Clear up any misconceptions as they work. 

After 10 minutes, you can unhide and show slide 10 for students to check their answer and share their process or model the example and work through it together as a class. Use the colors of the cups as a gauge to make this decision.

Display slide 11 and direct students’ attention to the “Subtracting Polynomials” section of their handout. Tell students that they are going to continue working on simplifying polynomials using algebra tiles and the Try It, Talk It, Color It, Check It strategy. Again, clear up any misconceptions as they work.

After 10 minutes, you can unhide and show slide 12 (option 1) or slide 13 (option 2) for students to check their answer and share their process or model the example and work through it together as a class. Use the colors of the cups as a gauge to make this decision.

This is a natural place in the lesson to pause for the day. If that is the case, consider reminding students to bring their earbuds/headphones to class tomorrow, as they will be watching videos.