Authentic Lessons for 21st Century Learning

Awesometh Degree of a Function

Polynomials

K20 Center, Alexandra Parsons | Published: June 8th, 2022 by K20 Center

Summary

This lesson is an introduction to polynomials. Solving polynomials is not included in this lesson, and would be the next lesson after this one. Academic language as well as patterns in polynomial family functions is explored. Prerequisite knowledge would be an understanding of functions and exponents in general, as well as the ability to graph (or work a graphing calculator).

Essential Question(s)

How do we know if a pattern is correct or not?

Snapshot

Engage

Students will brainstorm prior knowledge with a two-minute paper.

Explore

Students will construct polynomials and look for patterns.

Explain

Students will share the patterns found and will learn academic language associated with the patterns.

Extend

Students will determine if statements are always, sometimes, or never true.

Evaluate

Students will write a word splash paragraph over the content.

Materials

  • Graphing calculator, or other graphing software (Explore)

  • Card sort set, cut out (one for each student; Explore)

  • Data sheet (one for each student; Explore)

  • Whiteboard; something to write on for all students to see (Explain)

  • Always, Sometimes, Never Worksheet (one for each student; Extend)

  • Lined paper (Engage and Evaluate)

Engage

Have the words "Polynomial Functions" displayed on the board when students come in. Have them take out a piece of paper, and do a Two-Minute Paper over everything they know - or think they know - about polynomial functions.

After the two minutes, have some students share what they've written, but keep it casual and short. Have them keep that paper and use the rest of it for their Evaluate activity.

Explore

Pass out a cut out set of the Card Sort to each student. In each card sort are numbers, variables, exponents, and addition operations. Also, pass out the data collection sheet. Allow students some quiet thinking time to use the cards to construct equations, and then input their equations into a graphing calculator, or other graphing software. Have them record their equations, along with a sketch of their graph and any observations, on their data sheet.

Explain

Once the students have investigated enough to fill out the data sheet completely, start the Inverted Pyramid process. Have students find an elbow partner, and share the relationships between the equation, graph shape, and any other general trends.

After the partner share happens, have the partners create a group of four, and share their findings. Finally, have students share to the whole group. During the sharing, write the observations on the board and explain why those observations are true, or why they aren't.

Extend

When the inverted pyramid is done, pass out the Always, Sometimes, Never True workpage. Allow students to work in their pairs, and have them evaluate the statements and determine the "truthiness" of each statement.

Evaluate

Have students look back on their 2-minute paper from the Engage. Post the following words for the students to see:

  • Polynomial

  • Degree

  • X- and Y-Intercepts

  • Maximum and Minimum

  • End Behavior

  • Turning Points

Have students participate in a Word Splash with these words. On the same piece of paper from Engage, they will write a paragraph using all of the words listed. Have the students share out their paragraphs if they wish, but have everyone turn their paragraphs in when done.

Resources