Non-science STEM courses may find some difficulties in starting labs, but once real-life applications can be found, labs will develop more easily. For this example, we will use a 9th Grade Common Core Unit Plan. This plan is free, so if you teach math and would like to utilize this, feel free.
In this lab, students will be studying probability and statistics. Specifically, the following topics will be performed:
- Empirical Probability - Physically Testing Probabilities
- Theoretical Probability - The Actual Percentage of Getting a Specific Result After an Infinite Number of Experiments
- Combined Probability - The Probabilities of Combined Events Using AND or OR
- Compliment Probability - The Probability of Something NOT Happening
- Permutations and Combinations - Finding Every Possible Outcome with Combined Probability
- Analysis and Conclusions - Written Reflection
Day 1 - Empirical Probability
In this section, students will be given a video to watch that explains basic probabilities, both empirical and theoretical probabilities. Students will watch a homework assignment created or found by the teacher and watch the video for homework. Additional homework will include choosing two probability objects such as a die, coin or deck of cards, and perform a test multiple times.
Homework for the Night Before:
Video - Empirical and Theoretical Probability
Then, when finished, choose two of the following Probability Objects:
- A Coin
- A 6-sided Die
- A Spinner with 3 or more sections
- A Deck of Cards(Warning, this will take a LOT of time)
- Any other object that receives your teacher's approval
Once you choose your two objects, you will choose your desired outcome. This must be a specific outcome, meaning that you will choose an outcome that can only occur once( you cannot choose getting a Jack from a deck of cards, since there are 4 Jacks in the deck. Instead, choose a specific card such as Jack of Hearts. When you choose this desired outcome, perform your test 100 times at home, making sure to randomize the environment as best as you can. Record your results for the first class day.
In class, students will compare their results with other classmates. Ask students to put their two probability items on their desk. Have one half of the class take their results and talk to at least 4 different students with at least one common probability item and compare their results to arrive at conclusions. Once students have explored results with their peers, have them sit back down and discuss the results.
At this point, the teacher may have students use Google Drive Forms to have students enter the following information to be opened in a Spreadsheet for each probability object:
- Their Name
- Choose their probability Object from a dropdown (conditional processing based on this)
- The number of times their desired outcome happened out of 100
With this information, the teacher can import student answers and derive a "success percentage" and share the results with each student. This way, each student can see where his or her outcomes match up to fellow classmates with identical probability objects. This information would lead to students seeing similar trends in their empirical application.
For more information, check out Zone 3: Technology Use
Day 2 - Theoretical Probability
After day 1, students will have some key knowledge about probability.
Homework for the Night Before:
Video - Odds of Winning the Lottery and Video of Theoretical Probability
Note how this video is an outside resource. It gets students thinking.
Note how this video is a technical explanation. You, the teacher, could easily make a video like this. This video also gives "food for thought" for students to think about for the day. Note how personal and imperfect the video is. Students WILL appreciate the content.
Once students learn the initial knowledge, they will come in with the understanding of theoretical probability. In class, students will do the following:
- Derive their own theoretical probability
- Compare their theoretical probability with other classmates to ensure they got the correct answer
- Compare their Empirical Probability with their newly-derived Theoretical Probability
- Are the probabilities similar?
- Are they exact? Why or why not?
- Predict what would most-likely happen if they were to do their experiment 1000 times or 10000 times
Day 3 - Combined(Joint) Probability
Once students have an understanding of how probabilities work, it is time to explore combined probability. From their probability objects, students will explore the probabilities of both desired outcomes happening at the same time, and the probability of either event happening. Students will understand how the probabilities increase or decrease when performed under an AND or an OR joint probability.
Video - Finding Combined(Joint) Probability Pt. 1
Video - Finding Combined(Joint) Probability Pt. 2
Optional: Addign Fractions with Different Denominators
Students will come in knowing how joint probability can be calculated. In class, they will work with a partner to find the probability of both outcomes by multiplying both theoretical probabilities and discussing whether or not they think it feels accurate. Then, student swill switch partners and find the probability of either outcome happening in an experiment.
Once finished, students will practice calculating odds of every combination of two probability objects, creating a hierarchy of joint probabilities. Students can see how rare occurrences such as drawing the Jack of Hearts can "weigh down" the odds of flipping a coin and landing on heads when analyzing joint probability.
Day 4 - Complements of Probability
Next, students will learn about the complement of an event happening, or the probability of it NOT happening. Students will watch a video that teaches the initial skill and prepares them for what they will be doing in class.
Video - Complement Probability
Students will now find the complements of their desired outcomes, noting the method to find it. Once they find the compliments of their indiviudual desired outcomes, they will find the joint complement probability of their probability objects.
Day 5 - Permutations and Combinations
Next, students will learn about permutations and combinations of each probability object.
Video - Combinations
Students will find the number of combinations that could occur between their probability objects after 5 tries. Then, students will also find the number of combinations that can occur between both objects.
Day 6 - Analysis and Conclusions
At the end of this unit, students will write a small reflection discussing their findings. If students wrote a 1-3 sentence reflection detailing each part of their projects, the essay will flow smoothly. This provides cross-curricular learning, and also allows students to document their findings. Students can use Google Docs to create their reflections, and also provide a portfolio that shows each step of their process.