Pop goes the Corn?

Modeling real-world data is an extremely beneficial skill for students to embrace in any math course, whether they're in elementary or secondary school. I'm a firm believer in the 5E Lesson model for mathematics. Through my years in the classroom, I've found success in students exploring math through patterns and making connections themselves - especially when you involve food of any kind.

In Algebra 2, I was able to introduce Quadratic Functions with the help of the activity below. For me, students have the hardest time answering the most simple question in math...

When will I ever use this in real life?!

Although popcorn may not be able to answer the question to the fullest extent, I found this to be an engaging lesson where students were surprised about this particular quadratic application.

Topic: Introduction to Quadratic Functions

Essential Question: What are the characteristics of Quadratic Functions?

Materials:

• Padlet
• Student Notes link - 1 per Student
• Mini-Bag of Popcorn - 1 per Student
• TI-84 Calculator Steps link - 1 per Group
• 1 device per group (Chromebook, iPad, phone)
• Graphing Calculator - 1 per student (recommended)
• Desmos Online Calculator link - teacher only

Teacher Notes (using the 5E Model)

DAY BEFORE LESSON: Distribute one mini-bag of popcorn per student. Assign each student a different time interval and tell them to only pop their corn for this length: 0 sec, 20 sec, 40 sec, 60, 80, 100, 120, 140, 160. (Yes, you'll have multiple students with the same time.)

Engage: 

1. Break students into groups of 3-4 using any method you'd like, and distribute one Calculator Steps sheet to each group so they can follow along.
2. Have students go to the Padlet and answer the "Entrance Ticket" question before you begin.
3. Encourage each group to explain their answer before beginning.

• Why do you think...
• Could you expand on...
• Defend your choice of function...

Explore:

1. Open the Desmos Calculator and ask students to share their delicious data from the previous night. (Click on the [Best Fit Folder] to create the best-fit quadratic)
2. Students go back to the Padlet and answer Check #1 with their team. Have a team captain share their group's answer.
3. The Class Data may not show a relationship yet. Encourage students to brainstorm why the scatterplot may not have a pattern yet. (Sample answer: different microwaves strengths/watts)

Explain:

1. Hand out "Student Notes" sheet to each student. Ask each student to create a scatterplot based on the data. 
2. Discuss why a quadratic would make the most sense for this situation.
3. Have students enter in the data in their graphing calculator using the "Calculator Steps" hand out for support.
4. Have students create the best-fit Quadratic model for their data and write the equation on their paper.
5. As a team, have them make a prediction about how many kernels will be popped after 72 seconds. 
6. Walk students through finding the optimal time and amount of good kernels using their calculator. Ask them to interpret the maximum in the context of this situation. 
7. Students go back to the Padlet and answer Check #2 as a team. Each group can share out after.
8. Stress that students utilize the vocabulary when sharing out their thinking: maximum, vertex, minimum, concave down, symmetry, etc.

Elaborate:

1. Have each team answer Example 1 together and respond on their Padlet for their final conclusion.
2. Ask students what other situations could involve quadratics. (Bonus points if it's food related...haha)

Evaluate:

1. Post a question on your screen and have EVERY students put their answer on the Padlet as a conclusion.