~My Weekly Report and Reflection 12~

This week I and two of my peers presented on topics at the college and workplace levels.  I definitely appreciated the new approaches that my peers took and can definitely think of ways to integrate these new methods into my future teaching!

The first presenter focused on compound interest for a grade 11 college level class.  He started the lesson by first going over the formula for compound interest, indicating what each variable stood for and reminding us of certain ways things are added into the formula (ex. interest is in decimal form, time is in number of times per year, etc.)  He then applied the lesson to the real world by having the students look at different types of payment methods when purchasing a brand new $2000.00 TV.  Each table received a different method and had to calculate what the interest would be, any applicable fees, any benefits or cash back, and the total cost to buy the TV.  After some time to do calculations, everyone shared their answers and as a class we discussed the different benefits of each payment method.  I really enjoyed this presentation because although it was simple, it touched upon a subject that many students will enjoy learning about and will apply to their everyday life as they grow older.  There’s not much that I would change with this activity.  I would maybe try to incorporate technology and have students research the different credit card companies themselves, or allow them to select certain ones in class and research it together – this way students can investigate the different types of credit cards they are actually interested in and may have in the future.  A small concern was that when given to groups, not every person was a contributing member.  In our group there were 5 of us and only 1 or 2 people really wrote out the formula and did the calculations – there just wasn’t enough work to be spread around.  In the future I would maybe alter it to accommodate for that concern.

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The second presenter did an activity focusing on experimental and theoretical probabilities in a grade 12 workplace and everyday life level class.  She did this by using the card game Blackjack.  Each group was given a deck of cards.  The rules of blackjack were quickly explained – if you get an ace and any card with a value of 10 (10, J, Q, K), that is 21 points, or blackjack, and you win.  If you go over 21 points, you bust or lose and if you’re under 21, you still have a chance of winning, as long as your value is higher than the dealer’s.  For the first part of the activity, we simply had to see how easy it was to get a blackjack with only two cards.  For our table, this resulted in 0 blackjacks in 50 trials.  The highest a table got was 2 blackjacks in 50 trials.  This gave us our experimental probability.  We then checked our theoretical probability by calculating the probability of drawing an ace followed by drawing a value 10 card and multiplying it by 2 for symmetry.  This was cool because we could compare what we actually got to what we theoretically should have gotten.  Lastly, we got to play blackjack at our table (without gambling) and see if using probability actually increases your probability of winning!  I think that this was a great activity to use when teaching data management to young students.  Everyone loves card games and by incorporating this into a concept that can be very challenging for some makes the concept much less intimidating and much more fun.  The one thing I would change about this activity is the final portion of actually playing blackjack.  Although it was fun, some people at our table had experience and some did not so it took some time to fully explain the dynamics of the game to the new players.  Therefore, more time needed to be allotted to this part of the activity as we were only able to play a few rounds.  As well, some students were given the probability charts to see if they won more often, however, not much was discussed about the probability charts.  It may be biased because I’m so interest in the math behind things, but I think it could have been beneficial for students to hear the mathematics behind why the chart would tell them to do certain things.

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Overall, I really enjoyed the topics this week!  I can definitely see myself using these ideas in the future!

~My Weekly Report and Reflection 11~

This week we got to observe mini lessons on topics that could be used at each of the grade 12 classes (functions, calculus and vectors, and data management).  I definitely appreciated the different approaches that my peers took and can definitely think of ways to integrate these new methods into my future teaching!

            The first presenter focused on the topic of laws of logarithms for a grade 12 university level course.  She started the lesson off by having us investigate the characteristics of logs and what happens when we add or multiply different logs together.  After going over these concepts and practicing with a couple of questions, we got to play dominoes with logarithms!  This version played like a regular game of dominoes; however, instead of numbers on each tile, there were equations with logs.  In order to play your turn, you had to first calculate what each equation was using the log rules we had just learned.  If you were unable to play or took longer than 45 seconds, you had to pick up another tile.  I really enjoyed this activity!  It was a much more fun way of practicing log rules than simply answering drill questions out of a textbook.  However, there was one thing I would change if I were to do it again.  I understood the purpose of the 45 seconds or pick up rule, however, I felt as though that wasn’t enough time.  I struggled trying to figure out the math in time for my turn, and I’ve been using logarithms for years.  I imagine first time learners would definitely need more time or no time limit at all.

Retrieved from: http://weknowyourdreams.com/dominoes.html

            The final presenter led a lesson that focused on probability ratios from a grade 12 data management class.  To demonstrate the idea of changing probabilities, we got to play Deal or No Deal in small groups!  In each group, one person was the banker and the other the contestant (but ultimately everyone just worked together).  Similar to the rules of the game show, the contestant had to pick a case as their own and then open 6 cases.  After 6 cases were opened, the banker offered them a deal in exchange for their case.  It was then the contestant’s job to calculate the probability of winning a case with more money than what the banker had offered and to decide if it was worth the deal or not.  I had a lot of fun with this activity!  It felt just like playing the real game – however, I think that this may have been its one downfall.  As my group started playing, we got so involved in the cases and trying to win a million dollars, that we forgot all about calculating the actual probability – which was the main point of incorporating the game into the lesson.  If I were to do this in the future, I might instead consider doing it as a class.  That way, as the teacher, I could control the speed of the game and only move onto the next case when I believed that everyone had the correct answer.  Another thing I might change is finding or creating an online version.  In the system we used, once we ripped some of the cases off, they were really hard to put back on.  As well, some cases were see-through so we knew where the million dollar case right away.

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Overall, I really enjoyed the topics this week!  I can definitely see myself using these ideas in the future!

~My Weekly Report and Reflection 10~

This week we got to observe mini lessons on topics that could be used at in grade 11 classes.  I definitely appreciated the different approaches that my peers took and can definitely think of ways to integrate these new methods into my future teaching!

The first presentation was created for a grade 11 mixed class and focus on the concept of exponential functions.  Most presentations seen thus far have all focused on the action portion or the actual teaching of the lesson, however, this presenter chose to focus on the consolidation.  To consolidate student learning, we created math concept review booklets/folders/notes.  I’m not sure what you would technically call them but they’re really cool!  So once we had learned our topic, we each received three rectangle shaped papers.  We would fold the first one about a third of the way.  The next paper was folded a bit more than the previous rectangle, and the final paper was folded a little bit further than the second, but the same distance as between the first and second.  Once folded, we placed the folded rectangles inside of each other and stapled the sheets together so that it was like a flip chart with multiple tabs.  For each tab there was a different subject.  So for this case, the first tab was the title and topic.  The second tab was the domain and range, third was asymptotes, then x and y intercepts, exponential growth, and exponential decay.  When you would open the tab, space to fill in information about the topic was available right above the title.  I thought this was a great study tool for students!  Most reviews consist of students simply writing the information on a boring sheet of paper that is filled with a million other things to study.  In this case, everything about exponential functions can all be found on one sheet of paper.  I feel like students would really like the approach as it makes the concept less overwhelming and more appealing to study.  I can definitely see myself using this idea in the future!  If I were to change anything about it, I would have made the rectangles a tad bit bigger, just so that students have more room to write.  As well, I would have to think of a way to store these, as they’re the perfect size to get squished in the bottom of binders, bags, or lockers.

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The second presentation was created for a grade 11 university level class.  This presentation focused on the concept of creating triangles when only certain sides and angles are provided (SSS, SAS, SSA).  To help demonstrate this concept he made custom cut-outs of different side lengths on construction paper.  To indicate that we knew the length of the side, the line would end in a flat surface and to indicate that a side could be any length, it ended in a point.  As well, to indicate that we knew an angle, two lines were stapled together so that we could not change it.  To indicate that we didn’t know what the angle was, lines were held together by a paper fastener so that we could change the angle.  I really enjoyed this strategy!  In my experience, students have a difficult time understanding angles and lines, especially when they can’t physically manipulate the triangle.  By using this really simple manipulative, students can better grasp how a triangle can be made when only given SSS, SAS, or SSA.  I can definitely see myself using this in the future!

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The final presentation also focused on a grade 11 university level class, however, this presenter focused on the topic of exponentials.  Three stations were set up, each providing a real world example of exponentials.  The first station was about zombies infecting the Hamilton population.  Each zombie was represented by a red tile and could infect four other people a day.  The second station was about the infamous ice bucket challenge.  Each challenger was represented by a blue tile and could challenge three other people a day.  The third station had a piece of paper and students were to record how many sections a paper would be divided into after continuously folding it in half.  Again, I really enjoyed this activity!  As you get into higher years of mathematics, I find it gets harder and harder to find real world examples for students to relate to.  When thinking of exponentials, students might not think that a virus or an internet sensation can actually be represented by math – which is why I really appreciated this presentation!  It definitely gave me some real world application ideas that I will definitely use again the future!  If I were to change anything, the only precaution I would take is with the wording of instructions at each station.  In the third station, the instructions said to estimate after explaining what to do so our group forgot to estimate until halfway through folding.  In other stations, we were not quite sure what zombies/challengers were included in our daily counts.  By slightly changing these wordings, I think this activity would go off without a hitch!

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Overall, I really enjoyed the topics this week!  I can definitely see myself using these ideas in the future!

~My Weekly Report and Reflection 9~

This week’s blog will be slightly different as I was only present for half of last night’s class.  Instead I will discuss the topics that we talked about for the first hour of class and one of the presentations that I did get the opportunity to sit in on.

            We started the class off by talking about spiraling.  Spiraling is a method of teaching the curriculum that focuses on learning concepts over time and not in specific periods of time.  What I mean by that is instead of teaching the mathematics curriculum one section or unit at a time, you almost teach all units at once.  As explained by Amy Lin (2017), you first start by teaching a little bit of everything – but only the basics.  After going through every section of the curriculum, you complete a ‘cycle.’  You then repeat the process, going over more difficult concepts as the cycles get smaller and more focused.  I think this is a really cool way to teach mathematics!  When it comes to exam time, students are always forgetting what they learned in unit one.  By using spiraling, it eliminates this problem as students are consistently using what they’ve learned in every unit throughout the duration of the semester.  As well it creates a connection between different types of math.  By teaching this way, students are able to learn about not only these links between topics, but between mathematics and the real world.  As a very new teacher, this method is very intimidating to me.  I love the idea of it, and all of the benefits from its use makes me want to try it, however, I haven’t become comfortable with the entire curriculum yet.  I feel as though before I would even attempt spiraling in my own classroom, I would first need to teach the semester a couple of times in order to be comfortable enough with the curriculum to explore different methods of teaching.  This is definitely something that I’m going to remember in the future and I hope to give it a try one day!

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            I was also fortunate enough to see one presentation.  Last night’s presentations were at the grade ten level, so this lesson covered factoring trinomial quadratic equations.  When I learnt factoring in high school, we were to taught to find two numbers that multiplied to c and added to b in the equation y=ax^2+bx+c.  However, this presenter taught us how to do this factoring with algebra tiles – a method I’ve never seen before!  I thought it was such a cool tool to use, and it would have been so useful to me as a student when I was first learning how to factor.  To use algebra tiles to factor, you simply arrange all of the tiles that correspond to each expression in the equation to make a rectangle.  For example, if you had x^2+5x+6, you would have one large square for x^2, 5 rectangles for 5x, and 6 small squares.  When you arrange these tiles into a rectangle, the sides that don’t contain the x^2 tile will make up your factored equation (see diagram below).  For this example, the answer would be (x+2) (x+3).  I can’t reiterate enough how cool I think this is.  I will definitely take this with me and use it for my future students – if not for individual student use, at least to help demonstrate the concept with a visual.

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Overall, I really enjoyed the topics this week!  I can definitely see myself using these ideas in the future!