Flipping Out over Math!

With the dawn of virtual learning, it's been increasingly difficult to create engaging experiences for my students, especially in math. This year, I've taken on a dual role of digital coaching and instructing PreAP Algebra 2. What was I thinking?! 

I knew this year would offer challenges, not only in terms of rethinking instructional best practices, but also utilizing technology in a responsible way. I wanted to be "on the ground", so to speak, with the staff, but also find ways to help support them.

At our campus, we have shifted to a block schedule, with 90 minute class periods. That's a lot of Zoom, you might say! Isn't that too much for students?! 

While a 90 minutes block has it's challenges, especially for teachers with virtual learners, it also has the potential for deeper thinking. This year, I've decided to try something that I've only been reading about - flipping my instruction.

What can that look like?

1. 📽️Record and edit my content video using WeVideo. 
2. 💻Embed in Edpuzzle with questions to guide thinking and encourage predictions.
3. 💜Utilize the beginning of class as a "check in" using Google Forms (approx 10 min)
1. Instant data to provide quick feedback before diving deeper into content
2. A private space for students to share how they are doing
3. A fun space to get to know your students
4. Drop in a "this or that" to increase fun discussions
4. 📊Desmos Activities to expand thinking and build connections (approx 35 min)
1. Show videos and ask for predictions
2. Use sliders to build pattern recognition
3. Utilize multiple choice, but add "Explain your thinking" option.
4. Use Starter Screens as an exit ticket
5. ⏰Asynchronous Time with GoFormative (approx 45 minutes)
1. Students work on exercises at their own pace, seeking help when needed.
2. Provide students CHOICE: Stay on Zoom and treat like a Q&A, go to a virtual Breakout Room to work with a small group, or log off to de-Zoom, but still accomplish the task.
3. Give instantly feedback while students are working. Provide QUESTIONS not ANSWERS!

Samples:

• Google Form - Parabola Features
• Google Form - Applications of Quadratics
• Desmos Activity - Solving Quadratics
• Desmos Activity - Graphing Absolute Values
• Desmos Activity - Domain Restrictions

Navigating the Course

As I finished up Teach Like a Pirate by Dave Burgess, I found myself evaluating my previous lessons and how I used the hooks he mentioned and how I could improve the ones that needed what he calls "seasoning".

The lesson that I want to share is a topic in PreCalculus (used to be taught in Algebra 2) called Conic Sections. If you've ever taught it, you know it can be a beat down for students, causing (pun intended) circles to go around their head, which I find such a shame because it was my FAVORITE to teach.

All students love Play Doh!
(It really is the little things in life)

I loved how changing just a few numbers could affect the graph so drastically yet they were all related to each other in the smallest ways. I enjoyed that I could find all of them by simply slicing a cone differently at various angles. (The intro lesson I use for this unit involves students molding Play-Doh into a cone and using floss to make the various cross sections...yes, high school students go NUTS for Play-Doh!) The best part about this unit? It's usually BRAND NEW to students and I get to be the one who shares it! To watch them ask questions, and say "Oh don't you worry...that's tomorrow's adventure!" and "I love that you connected those ideas. Share that with your group, and if you'd like, with the whole class!" While the formulas can be a bit dull, it's the relationship between the equations that I find the most intriguing - and more importantly, the hidden applications they offer! One of the more interesting applications is to the medical field - whaaa?!?!

The lesson in particular that I enjoyed the most was about ellipses - the elongated circle if you will. I used a variety of Dave's hooks throughout and added some improvements so that teachers who were 1:1 could see how to integrate more technology! Although the hooks didn't really change the content, it made the presentation stronger and students were eager to learn - isn't that what we want?

Google Slides Exit Ticket

The "Hooks": Because the application I chose involved the medical field, all my hooks revolved around that!

• The Mozart Hook: As students were walking in, I had the theme song for Dr. House playing - "Teardrop" by Massive Attack
• The Picasso Hook: Students were given a half-sheet where they connected the intersection of the curves to make an "oval" shape. When they were finished, they measured various distances to discover the definition of an ellipse. You can also do this with wax paper using these directions.
• The Real World Hook: As an extension for that evening, students read up about one application of ellipses (lithotripsy - the process of dissolving kidney stones), solved the problem using the Chrome extension, and then had to find another application online. Curious about the application in further detail? Check out this site!
• The Costume Hook: A dressed up in purple (my school color) scrubs for the entire day.
• The Techno Whiz Hook (New Addition): As mentioned above in the "Real World" Hook, students solve a problem and did further investigating. Instead of doing this on paper and turning it in, they shared their thinking and solving on a collaborative Google Slides and their applications on a Flipgrid (WHICH IS FREE NOW!) 

The Challenge

Could there be even more hooks to include? Absolutely! I must say that when I was reading his book, I found some hooks were challenging for math, but had to ask myself, isn't that good?! I can re-imagine my lessons, re-think some strategies, and will encourage me to utilize the strengths of my team! How energizing, am I right?! Instead of teaching the same lesson, I get to "take the stage" with the content.

One of my favorite parts of his book was that it was content-neutral. He stresses that ANYONE with ANY CONTENT can teach using the P.I.R.A.T.E method if they just begin with an open-mind and a willingness to step outside of their comfort zone. He emphasizes that not every lesson will be success - some might even FAIL! And the biggest kicker - that it's OKAY! You get to try again the next day and even the day after that. I know I've had lessons that have fallen flat, and while discouraging at first, it lets my students see how I respond and how they too can respond when things don't work the first time. If it doesn't work, then it's feedback time! Isn't that a valuable lesson even if it's not content related?

"Transform" your Mind to "Transform" your Students

Algebra 2 can "stretch" the student's brains, because it truly extends what they've seen in new ways. I believe that this course has new topics that students haven't seen, but much can be built on their foundation from Algebra 1 with the help of inquiry-based strategies.

Transformed functions showcased in the Olympics

Transforming functions has a huge impact in the real world, because let's face it, how often do you see a Parent Function staring at you on a day-to-day basis? (Yes, it's okay if you said never...) However, once you transform them using a variety of operations, you've created something incredibly useful and underrated in classrooms today.

I wanted to share this lesson involving inquiry-based instruction that depends on student's to explore the various rules and see them in action using Desmos.

"Millions saw the apple fall, but Newton asked WHY!" -Bernard Baruch

Check out this Desmos Teacher Activity that I created! If you haven't used Desmos before, I highly recommend it! It allows students to explore various cases in mathematics within seconds. Students can make connections instantly and feel free to investigate freely.

In the Desmos Teacher Activities, you can:

Teacher Options

1. Select your own "Pacing." This is especially helpful for those courses where chunking is crucial to student success.
2. Select the "Pause" to make connections as a class and bring the group together for a quick formative assessment.
3. Select "Anonymize" to help students share their answers in a stress-free environment. 

Screenshot from a Statistics Desmos
Activity where they were asked
to create a line of best fit.

While you're running the activity, you can determine if students have answered all the questions and leaves you free to assist students as necessary. The grayed-boxes in the picture would help be assist students that are struggling and need additional support with questions or encourage them to work with their team to brainstorm.

I've included some screenshots of previous activities that I've run in my Statistics course as well. The picture below shows my students creating what they believe is the "best-fit" line before we discover how to actually determine the real best-fit.

I can't stress how important it is for students to make predictions first before revealing anything. I couldn't count how often my students surprised me with their intuition and mathematical connections before I shared the "real" answer.

Screenshot of Anonymized Students
and students' Progress

The hardest part of Inquiry-Based Instruction that I've found is allowing your students the freedom to explore and knowing that they WILL discover it on their own without you. I get very tempted to step in, show them the steps, and then have them practice. However, I PROMISE, they will have a firmer grasp if you give them the chance.

Inquiry Based Benefits: My Favorite 5!

1. Nurture students' passions and natural curiosity
2. Increases engagement by relating the content to them personally.
3. Teaches perseverance through tough problems
4. Encourages students to take responsibility for their own learning.
5. Allows students to ask deeper questions.

Interested in learning more about Inquiry-Based Instruction? Wanting to become a teacher?!

Consider the UTeach Program and its sister programs across the United Stated. I am an alumni of the Teach North Texas program at the University of North Texas.

Pieces of my Heart

Check out Desmos Art for more!

For my final post in the Mathematics Series, I want to share one of my favorite projects. (Don't worry...just taking a break from the math to begin a new series)

Piecewise functions can be drag and cause students to break into pieces themselves. To me, piecewise functions can be the most useful ones in all mathematics. I usually explain to students that these are thieves - stealing pieces of functions that it needs or finds useful.

"To me, mathematics, computer science, and the arts are insanely related. They're all creative expressions." ~Sebastian Thrun

One of the BEST projects that I've done for my students is creating a "piece" of art using only piecewise functions. Not only do I get to see my students creativity come to life, but I also can determine their level of understanding of this topic. The project requires...

• Knowledge of Parent Functions
• Knowledge of Domain and Range
• Knowledge of restrictions that apply to different functions
• How to utilize inequalities for shading

Instead of focusing on graphing these functions and writing their equations on a worksheet, students are practicing these skills digitally but also engaging in other digital skills. Students loved coming to class to create a picture using maths. They were constantly surprised about how maths could fit into the pictures they were creating. Students were driven to reach beyond functions we've seen and create new ones (circles, ellipses, and trigonometric function). At the end, students shared their work and voted on their favorites to be featured on our class Twitter page.

Project: Pieces of Art

Directions: 

1. Students work with a partner to complete the activity in Desmos. This will help them discover and learn Piecewise Functions. This activity walks them through how to create different functions using Desmos.
2. The last slide of the activity provides a link to the Desmos website for students to get started with their creation.
3. A rubric is included below that uses Google Docs (paperless we go!).

👍TIP: Have students create a Desmos Account! This way they can save their work each day and then email you the picture at the end of the project!

👍TIP: Use a Google Form for student submissions. Then you have all the links in one place and your email is less flooded!

Materials:

• Student Activity in Desmos (Click me!)
• Piecewise Art Rubric (Click me!) 
• Example of a Google Form for student submission (Click me!)

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.