Probability Introduction

I started the topic of Probability with my Year 10 students yesterday and I was so happy with how the lesson ran and how engaged the students were, so I thought I’d share.

These kids didn’t see probability at all last year, so even though they’re a really strong group of mathematicians, I wasn’t confident with how much they remembered.

We started of by drawing mind maps of everything they could think of to do with probability – individually at first and then as a class on the whiteboard. Most of them were pretty blank. We ended up with words like chance, predictability, certain, impossible, likely, unlikely, 50/50. A few students also wrote that probability can be written as fractions, decimals and percentages so we had a chat about the probability number line.

Rather than start off with relative frequency calculations, I really wanted to get these kids thinking about the broader concepts in probability. I read out the statements below and as a class we talked about whether or not we agreed with it and, more importantly, why.

  • There are 26 letters in the English alphabet. Therefore the chance that someone’s name starts with the letter X is 1 in 26.
  • There are only 2 possible outcomes in a game of tennis – winning or losing. Therefore I have an even chance of wining a game.
  • I have flipped a coin 4 times and each time it has landed on tails. Therefore it is almost certain the next toss will be a tail.

These started some really great conversations about whether the outcomes were equally likely, whether events were independent of previous outcomes, etc. Now that their minds were warmed up and thinking about probability, I handed out these sheets for students to complete in pairs. I didn’t work through the whole activity as it’s described – instead I printed “Are They Correct?” and “Card Set: True, False or Unsure?” back to back and had students write a sentence about each statement.

After a while we came back as a class and spoke about a few of the statements that had caused a bit of debate or that identified an important concept.

To finish off the lesson we had a look at this problem from nrich. I had students stand around the edge of the room with a piece of paper and a pen. I asked them to write down a number between 1 and 225 and not let anyone else see it. Then I asked them what they thought the probability was that at least two people had chosen the same number. The general consensus was that since they had 225 numbers to choose from it was pretty unlikely. Then I had them read out their numbers one by one. The first time we did this there was laughter and playful mocking of the students who had the same numbers and it was largely written off as a coincidence. We repeated this about 5 more times with new numbers and every time there was a minimum of 2 people with the same number. It was beautiful watching my student’s faces as they became really curious about what was happening.

Next lesson we’re going to dive into the maths that explains why they were so likely to pick the same numbers.

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My Flipped Classroom

At the start of this year I decided to flip my year 10 classroom. It’s been a pretty steep learning curve and it’s taken a lot of time and effort but I’m so incredibly happy with the outcome. I feel like my time with this class is used so much more effectively and the feedback from my students has been overwhelmingly positive. I stand in my other classes waiting for students to copy down notes and can’t help feeling like we’re wasting each others time.

The flipped classroom is a broad concept that can look different in every classroom. So what does my flipped classroom look like?

  1. I make a video in Explain Everything (maximum 10 minutes) and upload it to a folder in Google Drive that all my students can view.
  2. My students watch the video at home before the lesson and take notes in their books.
  3. Students then answer three questions that check their basic understanding of the content. I set each quiz up as a Google form and email the link to my students. Students also have the option to ask any questions they might have through the video.
  4. Before the lesson I read through the responses and gauge how well the students have grasped the content.
  5. The class can start in one of three ways:
    • If everyone seems confident with the topic I’ll get them to start on the exercises or activity straight away.
    • If there were a few students with different questions raised in the quiz responses I can talk to them one-on-one while others get started.
    • If it seems like a number of students have the same question or if a common misunderstanding has been highlighted in the quiz results then we run through a few examples or have a class discussion about the concept before getting started.

We’ve been flipping for six months now so I decided to ask for feedback from the people who matter most. I’ve shared some of the questions and responses below:

What benefits have you noticed with the Flipped Classroom approach?

  • A benefit from the flipped classroom approach is that it can sometimes leave more time for people to complete questions in class. It also gives us stepped out videos on the skills we learnt which is valuable when we come to study.
  • When I get to the harder questions in class I have miss to help where as at home I don’t have that opportunity for the help, leaving questions till the next session.
  • There are several benefits in regards to the flipped classroom, these include: being able to catch up on any work if you’re away
; really easy for us to go back and check things that we may have forgotten
; more time in class to do the exercises
; less homework
; allows us to ask Miss more questions

How could the Flipped Classroom be improved?

  • If the teacher could go through 1 example when we get into class just to refresh what we’ve learnt in the video the night before.
  • I don’t believe it can be improved as I think it is highly effective and a much better way of learning as it is. 

What other comments do you have about the Flipped Classroom approach?

  • With the introduction of the flipped classroom also came summary books – this have contributed greatly to the learning experience and are extremely beneficial when study for exams.
  • Miss Davis’ videos are very clear and straight forward which makes it easy to understand at home
  • I hope it continues throughout the rest of the year because it has been beneficial for my learning.
  • We should keep having the flipped classroom. ◕‿◕

Excitement for the new year

This past week was a nice way to ease us all back into the teaching routine after the Christmas holidays. We started with the Australia Day public holiday followed by two staff development days with time allowed for planning, then on Thursday years 7, 11 and 12 started the school year and on Friday we were in full swing with years 8, 9 and 10 starting up too.

I’m pretty excided about a few things this year:

  1. Each year everyone in our staffroom moves desks. This year I’m seated next to my closest colleague and already we’ve had some amazing conversations that are made so much easier now that we can just spin in our chairs rather than walking the length of the staffroom. We’re helping to keep each other grounded – reminding each other to pick one thing in our classes to focus on and make amazing rather than trying to improve everything all at once.
  1. I’m working with Year 7 for the first time this year. I’m pretty excited to be teaching younger students and new content.
  1. I’m flipping my classroom! Last year I had a beautiful Year 9 class full of hardworking and enthusiastic students, and I asked (really nicely) to have them again this year. It was beautiful to have a student say “Miss I almost cried with happiness when I found out we have you again!”. Anyway, I feel like I know these kids and I think they trust me so I figure it’s a perfect time to try flipping my classroom. Last year all the teachers at my school were given iPads so in the holidays I played around and made some videos. I’m planning of flipping this first topic (rates) and then evaluating how the flipped classroom went and asking for feedback from my students. I’m using Google Drive to share all the videos with my class, and I’ve made a Google form where students need to answer 3 questions about the content and I get all the responses in a spreadsheet. That way I get a snapshot of their understanding and I can highlight any misconceptions I need to address with individuals at the start of the next lesson. I explained all this to the kids at the end of the first lesson and they seemed pretty impressed with the idea… “So we watch like a 5 minute video, take some notes and answer 3 questions – and that’s it for homework?!”. The only concern anyone raised was that they might not be able to watch videos if they had work or other commitments after school, but we talked about the fact that it should only take 15 minutes and that they would have the same problem if I gave then a page of questions to complete for homework. I really think this will be amazing if all goes to plan but I’m a little scared because really, how often do things go according to plan when teenagers are involved?

Nerves and Poetry

Not so long ago I wrote this post about how important I think it is be self-confident as a teacher.

Then yesterday I had a moment that had me almost as nervous as the first time I ever stood in front of a class.

I read an amazing poem by Ben Orlin a few weeks ago called Once There Weren’t Numbers and I loved it so much that I decided to read it to one of my classes.

At the end of a lesson I got them all to pack up a few minutes early and told them I was going to read them a poem – but get excited because it’s a maths poem! And then all of a sudden I got really nervous. Like the type of nerves I had when I stood in front of a class for the first time ever. I was thrown back to my high-school days of speech giving. I was actually shaking and I didn’t know why. I stand in front of these kids every day. I get along with all of them. I can joke with them and they engage really well with everything I give them. So why was I so nervous?

Reflecting on it now I think it might have been because I was revealing something of myself to them. Revealing my inner nerd and love for nerdy maths things to them (even more than I usually do) and maybe I was scared they would think it was stupid – that they’d reject it.

Turns out they loved it just as much as me – and I knew they would! That’s why I chose to read it to them in the first place so we could bask in its amazingness together.

If you haven’t already, you should read it so you can bask too.