One of the biggest topics in a secondary mathematics class is function transformations (horizontal/vertical shift, compressions, stretches, etc.) Usually students will memorize the rules rather than understand the reasoning. I needed a way to enhance the lesson to allow students room to investigate these concepts and draw their own connections and conclusions - time to spice things up with technology!
Topic: Intro to Transformations
Essential Question: How can I transform ANY function?
Materials:
Desmos Activity - Make a copy if you'd like to make some adjustments! (link)
Student Notes - Google Slides(link) Click [Use Template] to make your own copy in your Google Drive.
1 device per 2 students - I recommend a Chromebook/computer.
Recommendation: a Google Classroom to share the notes with each student.
Student Notes (Google Slides) Preview
Teacher Notes:
Assign the notes in Google Classroom where each student gets a copy.
Go to teacher.desmos.com. If you don't have one, create an account! I recommend with a Google Account to make the sign-in easier.
Open the Desmos Activity (Intro to Transformations) above.
Click on the teal [Create Class Code]. This will need to be copied on Slide 1 in the Google Slides. This is how students will access the activity.
Desmos Activity (Preview)
Students will partner up and bring their computer/Chromebook. Each student can login so that everyone answers the activity questions and can take screenshots to add to their Google Slides for their notes.
Encourage students to take their time exploring each transformation carefully. They may struggle understanding shifting left and right. I related it back to the distance formula - (x - 3) moves RIGHT 3, not LEFT.
The Exit Ticket/Reflection piece is on Flipgrid. Create a TOPIC in Flipgrid where students can respond.
TIP: I created a topic for EACH UNIT in my class so that students could see how their questions and reasoning improved as the unit continued.
My Reflection:
Since the remaining of the year (and future mathematics courses) depended on this lesson, I felt strongly about student exploring it on their own. I tried teaching the rules one year and it only set them up for failure later.
I'm currently reading Shake Up Learning by the infamous Kasey Bell of Texas. In her first couple of chapters, she stresses the importance of integrating 21st century skills into as many lessons as possible - hence, shake things up! Students will be asked to analyze critically and shoving rules in their faces wasn't accomplishing this and was NOT preparing my students for their future careers. Careers where thinking on their own and creating their own connections would be a requirement.
One of my biggest fears with "shaking up their learning" is that my students won't learn the concepts "correctly". What if they misunderstand and I don't catch it?! In my mind, technology allows me to assess formatively more often, therefore I can check understanding frequently. When my concern of "learning incorrectly" snuck in to my mind, I forced myself to remember Jo Boaler - making mistakes is a learning opportunity. Even more so, making mistakes will make their brains grow.
What is "random?" What does it mean mathematically to be "random"? Ask any person to pick a "random" number, and you'd most likely discover a pattern...wait, what?!
In Statistics and Probability units, students think they understand how random events work. They think they are sincerely selecting random numbers when asked. Funnily enough, this concept can be quite vague. In a previous post, I shared a lesson to help students understand the Law of Large Numbers.
In this one, I want to share a lesson where students understand when they pick a "random" number, it truly is NOT random. My goal with this lesson was for students to discover this definition by using inquiry. Students discover patterns and come to the conclusion that we don't actually pick "random" numbers - quite hilarious when you watch their eyes enlarge at the end of the activity.
Why I used technology:
Students are engaged by using their own sense of intuition and curiosity.
Google Sheets allows them to quickly graph the the class information and find averages without the hassle of too many steps.
Students log their observations on Google Slides, which they can reference later.
All links and materials students will need are in one location - Google Classroom on the Slides.
Students choose which graph they want to use and explain their choice.
Teacher can access all students Slides in Google Classroom and provide comments to students work without taking extra materials home.
Students create their own examples instead of being handed them. To me, this allows the learning to be their responsibility.
By sharing out definitions on a Padlet, students can share their thinking using various methods (text, picture, GIF, voice note, hand-drawn picture).
Students vote on their favorite definitions to develop the best one.
Ultimately, this enabled the lesson to be student-centered!!
Topic: Simple Random Samples
Essential Question: How can I create a sample of items that is truly random?
Warm Up: Students read a quick article about forensic linguistics using the link on Slide 1. They write what was surprising to them and how math was helpful in discovering the truth.
Activity: What is your Pseudonym? Students investigate the Federalist Papers to show how finding the average word length can determine authors. In this activity, students select their OWN 5 words they believe would best help them find the true average word length of the passage.
Students gather all the class data on the Google Sheet. Each student creates a graphical display of the data.
Now students use their calculator to select the 5 random words and calculate the average word length. Similarly, students gather all the class data and begin to compare the two rounds.
Expand: Students expand on their knowledge by investigating what a "simple random" sample is and create their own definitions to share on a class Padlet.
Encourage students to vote on the definitions they believe are the best. Ask students to find pictures online as well or draw something they can take a picture of and post.
IDEA: Have students grab a partner and submit one answer per team. If you want to keep their names, the definition that the class likes the most could win some prize?
Exit Ticket: As a closer, students fill out a Frayer Model with the formal definition, a picture, an example, and a non-example.
Take-Aways:
When students developed their own definition, they could remember the concept at a deeper level throughout all the units following.
Gather their examples (from Google Classroom) for the next day as a practice activity. Have the students organize the examples into 2 categories (Good/Bad) to see what they've learned. Discuss examples that students had difficulty classifying.
Introduce other sampling methods as a follow-up activity. Students can compare and contrast the various methods and when to use each one.
Students can find articles where simple random sampling has been used or why it was not used.
Check out the Mythbusters clip below where they check if yawning is actually contagious! Did Adam and Jaime use a Simple Random for their experiment?!
