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
30007581_10155073302965989_1189857678_n

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)
29920334_10155073308570989_502273331_n

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.”
30019914_10155073302970989_35147398_n

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

Advertisements

Grade 10 Math – Resources by Course Expectation

Last year in second semester I taught 1 section of Grade 10 academic math (MPM2D), and 2 sections of Grade 12 data management (MDM4U). Grade 10 math was one of my favourite courses to teach as a student teacher, although I had only taught it at the applied level (MFM2P). The curriculum is so relatable, and it’s concrete enough to constantly have fun 3-act math and other similar activities that I could draw from or make in order to make the math come alive. My class was super eager and into it, and there were many “aha” moments. As a teacher, it was exciting to see my students experience math in a new way.

In order to keep myself organized, I use Google Sheets to keep track of the online resources I use for future reference and to pass on to other teachers looking for ideas.  I made one spreadsheet for each course, and within that, I have one sheet for general resources and information, and one sheet for warm up activities, blogs, and other things like spiralling resources, pedagogy and assessment ideas. I then added a new sheet for each unit: linear systems, analytic geometry, quadratics I, II and III, and trigonometry. I was not spiralling the curriculum this time, but someday I’d like to. Although I don’t like to see math as a bunch of isolated topics, this format helps keep me organized to make sure I am meeting all of the curriculum expectations.

nov9-1

Below are my Grade 10 math resources, organized by unit and topic. Some of the activities I did for one unit I ended up coming back to later in order to teach a different concept. In a spiralled course, these could be blended together over a few days. My resources are geared towards Grade 10 academic (MPM2D) but many can also be done in an applied class and adjusted to meet the expectations, many of which are similar or the same. All the credit goes to the original creators of each activity, lesson or idea. If I forgot to give anyone credit for something, my sincere apologies – email me or comment and I will add it in.

Note that this is not a comprehensive list. Some of the topics I didn’t use an online resource for or haven’t found one yet. I will update this post as I find new information.

Unit 1: Linear Systems

  • Review: slope and y-intercept. Lots of activities for this – here are a couple:
    -Jon Orr’s Reading Relationships
    -Mr. Hogg’s Fast Walker
  • Review: independent/dependent variables
  • Review: graphing linear equations – Jon Orr’s Crazy Taxi (4 representations)
  • Solving systems – substitution and elimination
    -Kyle Pearce pile ups
    -Alex Overwijk – solving systems with manipulatives
  • Solving systems – word problems
    -there are a few types. One is the distance/speed/time problems – I use Jon Orr’s Two Trains

Unit 2: Analytic Geometry

  • Distance formula: Jon Orr’s distance formula without the distance formula (love this one!)
    -review of Pythagorean Theorem – Andrew Stadel’s basketball travel 
    -consolidation: Desmos Zombie Apocalypse by Andrew Stadel
  •  Equation for a circle: no link, but developed my own lesson in a similar style to the “distance formula without the formula” lesson
  • midpoint: Dan Meyer’s best midpoint (similar lessons available for best ________, but I found that too many similar type lessons gets repetitive)
  • review of equation of a line: Kyle Pearce’s paper stacks 
  • equation of the median, altitude, perpendicular bisector
  • characteristics and properties of triangles
  • verifying characteristics and properties of quadrilaterals, circles, triangles, other shapes

Quadratics I: Factoring

  • expanding and simplifying expressions: box method (no link right now)
  • review of algebra tiles: warm up – #29 on Which One Doesn’t Belong
  • common factoring
  • factoring (simple): Jon Orr’s algebra tiles for factoring
  • difference of squares and perfect squares
  • factoring complex trinomials

Quadratics II: Zeros of Quadratics

  • difference between linear and non-linear: find the pattern/group similar things together (is there a Desmos activity for this?)
  • first and second differences: I used Tips4Math’s “Going Around the Curve” activities
  • solving quadratics by factoring: used a video from Legendary Shots with an estimated distance and equation (that factors perfectly) to solve – I will blog this eventually
  • quadratic formula: Dan Meyer’s will it hit the hoop?
  • read and non-real roots
  • problem solving (word problems)

Quadratics III: Transformations and Completing the Square

  • modelling quadratics: my own performance task – see my post here
  • transformations a, h and k: Laura Wheeler’s Desmos pattern finding
  • comparing y=x^2 and y=2^x: Mary Bourassa
  • graphing y =a(x-h)^2 + k
  • determine the equation of a parabola from the graph
  • transformations activity: Desmos Faceketball
  • transformations activity: Desmos Marbleslides (so much fun!)
  • vertex midvalue method
  • completing the square
    -mathcoachblog: the box method
    -completing the square visual representation
    -whenmathhappens: why completing the square works
  • max area given perimeter: Jon Orr perimeter jumble (tweaked to focus on the Grade 10 expectation)
    -a teacher at my school has his students do the max area given set perimeter by using toothpicks to make the biggest possible area – as a square, using only 3 sides, etc.
  • other max/min problems

Trigonometry

  • review – rates, ratios, proportions, angles, congruence/similarity
    -see my post on reviewing angles here
  • comparing congruent and similar triangles: Desmos card sort – congruent triangles
  • similar triangles word problems (shadows, reflection, etc.)
  • tangent – Jon Orr’s trig through slope (love this one)
  • primary trig ratios (SOH CAH TOA): see my tweet here
  • Sine Law: see my post here
  • Cosine Law (and Sine Law): I didn’t use this personally, but maybe you will be able to use some of these visuals
  • problem solving: Dan Meyer’s marine ramp makeover (one of my favourites)

 

That’s all I’ve got. If you know of any online resources that I missed, please comment and I’ll add it to the list! Happy Friday!

Mullets and Chocolate Milk

When I was a student teacher, one of my and my associate teacher’s favourite lessons that we did in our Grade 9 applied (MFM1P) class was the mullet ratio lesson. Quick recap: students learn the index of a ratio by determining who has the best mullet among hockey players, celebrities, and even students in our class and in the school. Some of the students actually had mullets and were happy to be part of the lesson. Students had many ideas about what makes the best mullet (“how long it is in the back”, “how much longer it is in the back than front”, “how greasy it is”). The idea that we were leading into is that the best mullet is one with the highest ratio of party:business (as the saying goes, a mullet is a hairstyle with “business in the front, party in the back”). Hence, the index of a ratio: one number that you can use to compare ratios.

The students loved it! It was something they could relate to since most of them were from rural areas where mullets and country music were very popular. Even the students who were normally completely un-engaged were excited. I couldn’t wait until I had my own class so I could teach it again.

Fast-forward one year: I’m teaching Grade 7 math at an all-girls private school in the suburbs of the Greater Toronto Area. We are starting rates and ratios – my favourite topic! I was excited to break out the mullets again when I realized something: these city girls are not going to be interested in learning about mullets. Some of them might not even know what a mullet is. I needed a different approach. That’s when I came up with the chocolate milk lesson.

We started off with a quick review of the previous day’s material:

ratios1

And then I posed the question:

ratios2

We talked about whose chocolate milk is more chocolatey and how you can tell.  Some students tried to guess. Some used similar reasoning to my Grade 9s with the mullet ratios: Sasha’s* has less milk, Kate’s has more chocolate powder. Some found equivalent ratios. I led into the idea of the ratio of chocolate powder to milk in each drink. We found the index of the ratio and determined that Sasha has the higher ratio, and therefore her drink was more chocolatey. We did some practice comparing other chocolate milk ratios:

ratios3

In that class we only ever talked about ratios in terms of chocolate milk. On the test, I decided to throw in a thinking question to check if my students really understood the concept. Instead of chocolate milk, I asked student whose drink was more lemony. Almost all of them were able to make the transition to thinking about the index of a ratio in a different context.

Sarah and Mia are making lemonade.

Sarah uses 3 scoops of lemonade mix and 8 cups of water. Mia uses 5 scoops of lemonade mix and 11 cups of water.
a) [K/U – 1 mark] What is Sarah’s ratio of lemonade mix to water?

b) [K/U – 1 mark] What is Mia’s ratio of lemonade mix to water?

c) [T – 3 marks] Whose lemonade is more lemony? Explain how you know. Show all of your work.

Take away: it’s all about context. Put math into a context that students can relate to and can understand. This will vary depending on the culture and background of your students.

Another example: when I was teaching data management, I included this communication question which I got from an assessment at the school where I was a student teacher:

The price of bread and the price of canola oil both increase sharply after a long period of no rain in the prairies.

Explain the type of causal relationship that most likely exists between the 2 variables. Assume that the first variable is the independent variable, and the second variable is the dependent variable.

When my students got to this section of the test, I got so many questions from students about what canola oil was made of! I didn’t even consider that my suburban students might not make the connection that students who grew up on or around farmland wouldn’t think twice about.

 

*Names changed.