MDM4U: Online Resources by Unit, and Plans for Probability

Happy long weekend!

So far I’ve really been enjoying my 2 classes of Grade 12 Data Management (MDM4U in Ontario). We’ve done several fun activities that involved critical thinking and rich learning. One of the goals I’ve had this year is to really work on making sure my lessons are not only engaging because they’re fun, but also provide good learning opportunities. I’d rather have a less “fun” lesson that involves a lot of rich learning than a super engaging lesson that has very little learning and critical thinking. Some of the lesson activities I’ve done so far:

Combinations and Permutations:

  • for nPr and factorial problems (order matters): Dan Meyer’s Door Lock
  • for combinations “some of” or “up to” problems: my take on Robert Kaplinsky’s Coke Freestyle lesson
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Noticings and wonderings from the Coke Freestyle video.

One-variable Statistics:

  • for measures of central tendency: Crazy Math Lady’s mean, median, mode
  • for sampling techniques: Mr. Waddall’s take on the Jelly Blubbers Colony experiment
  •  for measurement bias: Bob Lochel’s opener on the effect of a leading question.
    I did this as a Google Form: I assigned half the class a Google Form with one of the questions to fill out, and the other half of the class the other question (I split the class in half by their student numbers). I did the demo in real-time, which was terrifying, but it more or less worked! (I showed my class Bob Lochel’s data as well.)
  • for standard deviation: John Scammell’s celebrity guessing game. Here is my celebrity slide deck (as of March 9, 2018)
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Celebrity guessing game!

Two-variable Statistics:

  • for linear correlation: Bob Lochel’s Friendship Compatibility Test.
    I loved this one. I wrote a Python program to match students up randomly (I try to get my students to get to know each other outside of their chosen table groups). This lesson was scaffolded really well and it went smoothly.
  • for least-squares regression: I roughly based my lesson on Fawn Nguyen’s Vroom Vroom and Jon Orr’s take, Vroom. I modified it to teach Least Squares Regression to find a good line of best fit for the linear data.
    Comment from one of my students about this lesson: “Miss, class was so fun today! I mean, it wasn’t that fun because we had to do math, but it was still kinda fun.”
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Collecting data from the pullback cars in “Vroom Vroom”.

As usual, all the credit goes to the incredible teachers who take the time to share their resources on the internet FOR FREE! Thanks to all of you, me and my students both win.

Now we have reached what I consider to be “my least favourite unit”: Probability.
But why?! Probability is so fun! I agree. Probability is fun. We get to play with dice and cards and spinners. When I taught the unit last year, students had a lot of fun. My problem with the Probability unit is that, although students were engaged, I didn’t feel like the critical thinking aspect was very strong. Even if we have to skip out on some of the fun, this year I am determined to make sure that a lot of deep thinking happens and that my students remember the learning and not just the fun.

Here is my tentative plan for the unit. This is a work in progress and I am still looking for ideas. If you have interesting inquiry-based lesson ideas, please comment or message me and I will happily add them and give you credit! Here goes:

Probability:

  • DAY 1: Intro to Probability: I’m actually going to be away that day, so my plan is to leave students with a handout of probability definitions, including introducing the idea of “odds”, and some practice questions. (Boring, I know, but I won’t be there so I don’t want to leave anything too complicated.)
  • DAY 2: consolidate intro to probability and odds:
    Warm up: jumbled note review of the definitions from the previous day.
    Lesson: play Bob Lochel’s Jolly Ranchers game. Tie in connections to probability, sample space, favourable outcomes, and odds.
  • DAY 3: review of permutations and combinations:
    Warm up: ticket (formative quiz) on previous two days’ material.
    Lesson: we will review permutations and combinations as prior knowledge for probability with counting techniques, coming up tomorrow. I’m still not sure what I’m going to do for this lesson yet, so I’m open to ideas. I’d like to do something involving a lot of problem solving on whiteboards.
  • DAY 4: probability with counting techniques:
    Warm up: one of these from Would You Rather Math.
    Lesson: going to tweak Dan Meyer’s Starburst 3-act math to be about counting techniques. Maybe change the problem around a few times to address various concepts of the permutations/combinations unit.
  • DAY 5: independent and dependent events:
    Warm up:
    this.
    Lesson: play Skunk Redux. Key takeaway: no matter how many times you roll the dice and do not roll a 1, the probability of rolling a 1 on the next roll is still 11/36.
  • DAY 6: conditional probability:
    Warm up:
    not sure yet. Maybe a formative quiz.
    Lesson: Bob Lochel’s Egg Roulette lesson. Focus on tie-ins to conditional probability. Might come back to this for the hypergeometric distribution in the next unit.
  • DAY 7: mutually exclusive and non-mutually exclusive events:
    Not sure about this one yet. Maybe something with John Scammell’s free throws for the win.
  • DAY 8: wrap-ups:
    Warm up: the famous Monty Hall problem.
    Lesson: tie up loose ends, start test review.
  • DAY 9: test review
  • DAY 10: unit test

That’s pretty much all I have for now. After this is my favourite unit, Probability Distributions. I love this unit because there are many interesting problems that involve higher-level thinking and are also really fun! I will hopefully find time to post about that later on. In the meantime, I’m turning the floor over to you:

What lesson ideas and activities do you have for Probability?
What would you add to my unit plan?
What would changes would you make to my unit plan?

Write me in the comments!


I’m on Twitter! Come say hi! #mtbos

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Reviewing Angle Theorems in Grade 10

As a new teacher, two things that I don’t feel the most comfortable with in my teaching are:

  • teaching theorems by name. For example, opposite angle theorem (OAT), corresponding angles, etc. I know how they work, but I’m not very good at remembering the names.
  • review. I am still fairly new to teaching, and it’s been difficult figuring out exactly how much detail I need and how fast I should be going when I review material from previous years. I’m always a bit anxious and eager to start the new material (in this case, one of my favourite units, trigonometry.) Usually I end up doing too much or too little. This is something that will hopefully get easier for me with time.

On this particular day, I ended up doing both of those things.

Personally, I don’t think it’s even really necessary to teach all of the angle theorems along with all of their names. You really only need 1 or 2 rules. The rest can be derived from the first 2 to solve for any missing angle. But because my class was one of seven Grade 10 academic math classes running that semester, I thought it was important for consistency that they learn the names. We also have the same tests for all 7 classes on the same day, so I needed to make sure that if knowing theorems by name was on the test, students would know the names.

Based on what other teachers had done in the past, I began with a warm up review of some common terminology that students would be using later on in the trig unit:

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The students didn’t seem to have too much trouble with it, and we were able to take it up quickly.

We did a bit more practice with ratios and other odds and ends:

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(If none of this seems like it really goes together, please forgive me. New teacher syndrome.)

Then we got to the main part of the lesson: the angle theorems. Instead of going over each rule individually (all 9 of them! So many names!), I wanted to see if my students could derive the theorems themselves. So I put up this diagram and told my students that all 9 angle rules appear in the picture:

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We did the first one together:

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I then gave the students some time to work with a partner and told them to find all 8 other rules:

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When we took it up, my students got all 9 rules on their own! Some of them remembered the names of the rules, the others they told me which angles made the rule and I helped them with the names (I may or may not have had the names written on a sticky note on my laptop to remind me of what each theorem was called). I took a picture of the board and posted it on our Google Classroom as a summary of what we learned:

(Usually I have another column for who came up with the rule, but I cropped it out for the sake of my students’ anonymity online.)

The rest of the lesson we spent doing practice questions.

This was one of my favourite lessons of the year: student-focused and student-driven. Bring on the trig!