A "Random" Post?

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?

Materials:

• Google Slides - Student Notes (1 per student)
• Google Sheet - Student Notes (1 per student)
• Google Doc - Federalist Paper word breakdown (1 for all classes)
• Padlet - create a padlet using the "Wall"style.
• Forensic Linguistic Article (link)
• Simple Random Sample Site (link)

Lesson Outline:

1. 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.
2. 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.
3. Students gather all the class data on the Google Sheet. Each student creates a graphical display of the data.
4. 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.
   
5. 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. 
   
6. 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. 
7. 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?
8. 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?!