Friday, June 15, 2012


Today I was called in to supply for a grade 8 class for the afternoon.  When I arrived the teacher was still there and we talked for a few minutes about what my afternoon would be like.  She started off by telling me I would be rotating between her class and the grade 7 class for math.  I was really excited by this, as it would give me more experience for this class.  She started going through the lesson she was going to teach and from what I saw it was going to be really good.  Then she said its a little complicated so you can just watch a movie for both classes.  I told her I was capable to teach the lesson and that I was upgrading to my intermediate in math.  However that did not persuade her and she closed up her notes, handed me the movie and left.  I am really sick and tired of teachers thinking just because I am a supply teacher that I don't know what I'm doing.  Sorry for ranting, just wanted to blow off a little steam.

Three Act Plan

Three Act Lesson

Act 1
After being shared by one of our colleges, I couldn’t resist discussing this photo and its mathematical relationships. You could pose questions like, “What does the equation of the parabola have to be so that the walkway has symmetry?” “What is the equation of the parabola’s seen in this photo?”
You could ask similar questions for the half pipe photo below.

I started thinking of all the different day to day things that would really excite students without them even considering math. They would be so excited to discuss the walkway that the last thing they would think about is its relation to math. As soon as you mention that you’re incorporating it into math, they’d be hooked.
Just as the water walkway, this half pipe from the X Games could really grab the students’ attention. I thought that watching a portion of the X Games would give the students opportunities to see different portions of parabolic curves.

Act 2

Students could then take time to research necessary measurements to determine the appropriate quadratics for these photos. This could be done in a variety of different ways depending on the amount of time the educator wants to spend on this specific topic. The following are a number of expectations you could cover after introducing these ideas.
-          Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology, or from secondary sources
-          Identify the key features of a graph of a parabola, and use the appropriate terminology to describe them
-          Explain the roles of a, h, and k in y = a(x-h)2 + k,  using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry
-          Solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology

You could ask questions like, “How fast does the water have to flow in order to clear the walkway?”
“How fast does a skateboarder have to move in order to make it up the other side of the pipe?”

Act 3
In the end, students will determine the answers to questions like the ones posed above. They can apply their knowledge to real-life situations, like skateboarding, playing catch, kicking a soccer ball, or creating a neat fountain that brings tourists from miles and miles just so they can experience it.

Thursday, June 14, 2012

Cool Math

It's absolutely amazing what some people can do with the internet. This website has so many resources. Everyone definitely needs to check it out. I know it's kind of lame, but I was playing this math "Pac Man" game that dealt with Order of Operations while playing. Pretty neat idea.

Assignment 5 - 3 Part Lesson

Unit #:Measurement Day #:1 Estimating Area and Area of a Circle
Grade 8

60 min
Math Learning Goals
Curriculum Expectations: By the end of Grade 8, students will:
·   Determine the relationships among units and measurable attributes, including the area of a circle and the volume of a cylinder.

Specific Expectations:
The students will:
Measurement Relationships
·   Measure the circumference, radius, and diameter of circular objects, using concrete materials
·   Determine, through investigation using a variety of tools and strategies, the relationships for calculating the circumference and the area of a circle, and generalize to develop the formulas
·  Smart Board
·  text book
·  circle cut-outs
·  grid chart paper
·  area of a circle video
·  Smart Notebook file

Begin with a quick refresher of the formula for calculating area of a square. Also, a reminder on how to calculate the area of a parallelogram should be explained.

Use grid chart paper and circle cut-outs with the class to determine an area when cutting out the circle to form a parallelogram.

What variables are identifiable on the parallelogram that are also on a circle?
What information do we need to determine area? What variable do we need so that we can identify the area?

Minds On…

Discuss the links between the area of a parallelogram and area of a circle.
-         What do you noticed about the radius in when it is used to build the parallelogram? What about the circumference? Can we determine a formula for the area of a circle based on this information?
Based on their knowledge of calculating circumference, guide students to identifying possible equations for area of a circle.

Show video clip   that will help identify steps in calculating area.
As a class, work together to solve some circle area problems.
As completed, take them up step-by-step to model the procedure and solidify it for the class.

Be sure to address all methods of determining area that will be necessary to complete the assessment.
-         What equation would we use for each question? What information does the question provide us with? Can we figure out the other variables? How?




 Recap the lesson by discussing the relationships between the area of a parallelogram and the area of a circle

Consolidate Debrief



Skill Drill



Home Activity or Further Classroom Consolidation
Assign questions from the text for the students to gain a firm grasp of the formula for area of a circle.

As the students work at their seats, walk the room and address any difficulties with the questions. If a question appears to be causing difficulty for numerous individuals, take it up with the class.

Continue along with more area of a circle. Focus on the different ways of manipulating the formula.


As a class, they will be directed to form a circle in the centre of the classroom after my instructions. During the instruction I will inform the students that each tile on the floor is about one foot long and one foot wide. From here, the students will estimate the radius, diameter, circumference and the area of the circle they have formed.
How can we estimate the radius? How can we estimate the diameter? Explain.   How do we estimate the area?Explain.  
Can we be more accurate if we measure?
Helps provide a visual for students who are having difficulty thinking of the concept in an abstract fashion.

Math Games

During my time volunteering I occasionally find myself in the computer lab working with a particular classroom. After utilizing much of the time to complete a particular class, the teacher often allows for free time where students are able to access other educational resources. When students are provided with this opportunity I find that many gravitate toward the games that are offered either on the school computer, or websites that the students frequent. I sit back and watch, and I wonder to myself if these games serve any purpose at all. I don't want to sound like a pessimist but many of the games seem to be played without much thought behind them. For instance, a stick person swinging from a line (where the line is adjustable) and they must grab a second line to get to the platform on the other side of the screen. With math in mind, a student should be able to figure out relatively quickly whether they need to lengthen or shorten the line. I don't think that this is necessarily the case.

Since it is identified as free time, I wonder if young learners take this as a moment to free their minds from the stresses of school. Instead of thinking of whether a particular decision makes sense to attain a particular outcome, is it easier to be thought free and just take the time for what it is; free?

Wednesday, June 13, 2012

A first for everything...

Over the last couple of months, my life has been a little busier than usual. Between work, volunteering, school, and everyday life, I've hardly found time for sleep. This course has definitely been a unique experience. I don't think that I've ever had more exposure to technology than I have in the last two months. Between learning new programs while volunteering, and everything that I've taken from this course, I find that I am slightly overwhelmed. I hope that I will retain something because their is so much useful information being thrown about within the course.

I want to thank everyone for their contributions and their patience. I know it can be tough especially when everyone works at a different curve. I guess most of us are familiar with this because its part of what makes us who we are. I think that it is important to remember where you came from and what you hope to attain during your entire career. Doing so will allow you to appreciate every moment you interact with someone. Every interaction is a learning experience and it is important to always keep your listening ears open.

Tuesday, June 12, 2012

My First AQ Course

I thought I would take this last opportunity before the course ends to reflect on my experience in this course. 

This was a heavy course and with it being my first ever course of this type I was overwhelmed from the first day.  After just finishing school I found it very difficult to manage my time and finish all that was expected from us (especially with the gorgeous weather we have been having).  I enjoyed some assignments better than others and I wish I would have had more time to focus on them.

Although there was a lot of work, I do appreciate all the resources that were presented.  These were all great tools that should be used in the classroom and I would enhance them a great deal. 

My favourite part would have to be the Assignment 6 where we were to send our work to other people and have them give feedback.  The timing aspect was difficult because everyone was on different paces, but I love receiving feedback and am open to any suggestions that can be given.  This is a tool that should also be brought to the classroom because too often school becomes a competition instead of a safe working environment.  Now, some competition is always welcomed because it encourages learning but it can also turn students off to learning (in math especially).

Overall, it was a pleasure sharing this experience with all of you and maybe we will meet in our future teaching careers!

Math Examples Matching Students Interests Lead to Greater Success.

A few weeks ago I had the opportunity to supply in a kidslink classroom.  It was a grade 5 class with 6 boys.  Upon my arrival I saw a note on the desk from the teacher explaining what to expect from my day.  The one note on their said the boys love the math project that they are working on.  Kids loving math? You don't hear this statement too often so it really peeked my interest.  The students were working on a baseball project, where they would pick one baseball team and they would follow it.  They would have to figure out players batting averages, on base percentage, balls and strike ratios and many more.  When it came time for math I was pretty excited to see this project in action.  I told the students it was time for math and I was met with some groans and boos.  I thought to myself that this was strange considering the teachers note.  I said to the students "Your teacher told me that you loved math, is this not true?" They responded with their hatred for the subject. I thought to myself, oh well the day must go on.  I asked the students to take out their baseball projects and they looked confused.  One student asked "I thought you said we were going to work on math? Our baseball project aren't math."  I then realized that the students did not see these project as learning projects, they were just having fun keeping stats on their favourite baseball teams.  The teacher had made learning fractions, ratios, multiplication and division fun for her students by connecting her lesson to the students interest.

This made me think back to an experience with one of my relatives.  He really struggled with math all through elementary and secondary school.  It got to the point where he almost did not make it into the college program he wanted because of his math marks.  He was able to get into the program and that's where he math grades made a dramatic turn around.  He ended up having one of the top math marks in his class.  I asked him what the difference was between his college program and high school.  He told me the biggest change was that the examples given related to his field which he was really interested in and which he understood well.  I thought to myself, that can't be the only change.  Being interested in the examples could not have that big of an impact.

My experience in the teaching profession has told me that this is really the case.  If the student is interested and engaged with the examples given they will have greater success.  We as educators need to be able to pick up on our students interests and incorporate them as much as we can into our classrooms.
As we are in the last week of the course, I would like to wish everyone the best of luck in getting everything done.  We can do it!

"You will succeed.  Yes, you will indeed. It's 98 and 3/4% guaranteed!"
-Dr. Seuss

Integrating Math

As I was working in the Grade 4 classroom a few weeks ago, my eye was drawn to three large castles that were sitting on the floor.  These castles were part of a medieval unit that the students were completing.  They all took on a different form, though they contained the same components.  They were made of boxes and tubes and paper and tape (lots of tape) and were painted all sorts of colours.

Now you may be wondering what this has to do with Math so I will explain.

When I was looking at the castles I could not help but think how math could be integrated into the unit.  The castles were made up of a collection of 3D shapes which could be measured for surface area and volume.  Details and decoration took the form of two dimensional shapes that could be measured.  There were patterns in the shape of flags.  I also thought that plans could be drawn ahead of the construction that required the use of ratio and geometry. This list goes on.

I thinking about these connections, I realized how often we teach math in isolation form other aspects of the curriculum.  Although we connect it to "real world" applications, it is not often that math is integrated into other subjects.  There are only so many hours in a school day and a lot to cover.  Why not combine some subjects?  Integration of math into other subjects also provides students with different entry points into topics.  Although the measurement of 3D objects may be overwhelming on its own for one student, she may get right into building the castle and not realize until later that she has been measuring 3D shapes through the process.

I admit that I am working from a P/J perspective on this, but as intermediate classes are moving towards a homeroom model for all subjects I think it would be possible for more integration even at this level.  There is no right way to integrate, and it may not always work, but I think it is worth a try.

Thanks for reading!


Friday, June 8, 2012

Game Shows

I got some inspiration while reading the post on board games, because something that can also be used in the classroom as examples of using mathematic skills are game shows.

Let's see:

The Price is Right - there are many different mini-games in the price is right that involves probability, estimating, pricing items out, and logical reasoning out a problem.
Deal or No Deal - probability at it's finest. You could go through the whole game and simulate how probability changes (increases) as you eliminate each briefcase.

Wheel of Fortune - what is the letter that is most likely to make you money? what are some strategies to approaching each category/words being guessed? Look at the wheel, what is the probability of landing on bankrupt or $1 Million? And, considering the final spin, where they give you the 5 most common letters (RSTLNE)
Who Wants to Be a Millionaire - multiple choice questions - talking about probabilities
Bingo / Lottery - although maybe not age appropriate for younger kids (since they can't gamble) they have all probably played it before
Lingo - Lingo features two teams of two contestants who are given the first letter of a five-letter mystery word and five chances to identify it correctly. The team with the highest number of points earns the chance to correctly identify as many words as they can in two minutes (where in this picture: Red means the letter is correct, a yellow ball means that the letter is beside where they had placed it, and blue means wrong)

Shall we go a little bit older?
Let's Make a Deal - the infamous Monty Hall problem (which has already been discussed in this class)
Press Your Luck (also known as Whammy!) - where contestants collect "spins" by answering trivia, and then spin on the electronic board to win prizes or money, or could land on a whammy and lose everything. Three whammy's and you're out of the game (if I remember correctly)
Family Feud (although this is still one of the most popular game shows still around, I put it in the older category because of it's roots with Richard Dawson as its host) - the show surveys 100 people with questions and reports its findings - families battle to answer questions for points, and the final round has two people from one family answering questions and giving the best possible answer within 60 seconds (2nd person cannot repeat).
Card Sharks - using one deck of card, contestants decide if the next card is higher or lower (there's more to it, but that would be the probability aspect of it!)
Match Game - A panel of celebrities would answer a "fill in the blank" statement and a contestant would fill it in, hoping that celebrities might have used the same answer. For each match, one point was earned. In the second round, only those that did not match in the first round would answer (therefore, someone who was behind in the first round could catch up). Winner went on to the final round.

And many more....

So while some of these are more trivia related, you can bring in the concept of mathematics through the chances participants have in actually winning and different stages of the different games. I have always been infatuated with games shows (especially GSN) and whenever I got the chance (cable at the cottage and at my father's house included the channel GSN!!!!), I would be sitting there enjoying the risks people were taking in order to win or get more money (greedy greedy!).

Oh the fun memories I have. Using game shows in the classroom would also increase engagement, because everyone likes to have fun! However, make sure it is not too competitive and that your students know it is just for fun!

Thursday, June 7, 2012

Technology...How Far is Too Far?

I am new to this blogging thing, but I kind of like getting to read what others are saying and maybe people will be interested in what I have to say as well!

I felt I could take this opportunity to talk about my BIGGEST pet-peeve when teaching math.

THE CALCULATOR! .. (and now the dreaded smart phone with a built in calculator)

Calculators were not invented so that all people could shut off their brains.  They are a useful tool that should be used to enhance math, not remove all logic from people's brains.  I had students in grade 6 that could not subtract 10-1 without asking to use a calculator ....

Most simple math problems can be solved using logic and a variety of tools we have been taught in our lives.  When I was growing up I had a teacher that did not allow calculators in her classroom.  If there was division that needed to be done, you did old fashioned longg division or you tried to think of a way to simplify the problem to make it easier to figure out.  Now, I know this sounds extreme but this has helped me soooo much in my life.  I am able to add, subtract, multiply, and divide numbers quickly when I am given a problem, calculate tax on a price when I am at the store, break up large problems into smaller ones, I never get too much or too little pizza because that teacher made me a wiz with fractions, and I never get the wrong change at a store because I can easily work it out just as fast (usually faster) than the lady can punch in the numbers.

Monday, June 4, 2012

Let's play math board games!

Last night my boys asked us to play Monopoly game.(By the way, I don't like the name of the game because it looks like the purpose of play is to earn more money then the other guy). Before the game, my husband asked them to give some details about the game again. My 13year son said: there are 32 houses 12 hotels. The more you buy, the less we can buy. And you have to know the odds like when you are in “jail”(name used in the game) it's possible to get out immediately by paying $50 our using a free card. If it's early in the game is best to get out as soon as possible, so you can have more opportunities to buy property. Later in the game it's best to stay in “jail” as long as possible to avoid landing on our properties.” and so on....
I have always thought that Math board games are fun. They are a nice change from rote memorization and a good way to increase interest of math as a fun and interesting subject. Teaching a group of children right after school is a reason why I use the board games very often and math board games as well such as, monopoly, jenga, apples to apples, chess, uno cards etc,

I picked those since they have mathematics involved in their structure, practical strategies or analysis of the game results.

What I would like to point out in this blog is that even though they are games we can bring our professional knowledge by asking them to reason. Every time when they play the games I am there only to ask them to explain their choices or open discussions so they can verbalize their strategies or listen to others' strategies that they might have never heard of before. After that, a couple of children start to ask their friends about the strategies as well but a day after they tend to forget. But we know that practice and repetition strengthen their understanding. So, I keep repeating the questions and sometime I stop them in the middle of the game using “freeze” game and ask them what they think is going to happen, is there a reason why Ben put nr. 9 down (Playing cards), which way is shorter to climb up that ladder, how many times are you going to throw the dice so you can reach the top of the tree (Chutes and ladders), what are the options for Zack to land on your property, why do you use large or small bills to change a $ 25 bill (Monopoly)and so on.

The children love it because is fun, they are socializing with friends, they have time to think, the conversation and sometimes the debate is natural that makes them reflect on their own thinking.

I know that there are cons about board games such as, too competitive or I had a parent who said "playing cards teaches them how to gamble" or “my kid doesn't learn anything in school because all he does is play games” and I have my own cons as I mentioned in the beginning about Monopoly game. However, these cons and more are the reasons why those games should be played at home and school more often, so, the parents and the teachers are there to provide and create environments that make children think, solve problems,increase their arithmetic skills,calculate, challenge their understanding and have fun other than exposing them with the negative sides of the board games.

Here I have this paragraph from Paul Bryn Davies which I have it displayed on the wall all the time and also, I keep extra copies so I can give it to the parents(if they ask) to read about the benefits of the games.

                Benefits of Using Games in the Classroom

In the article “The Role of Games in Mathematics” Bryn Davies summarizes the advantages of using games in the math classroom. (Davies, 1995)

  • Meaningful situations - The application of mathematical skills are created by games.
  • Motivation - Children freely choose to participate in games and enjoy playing.
  • Positive attitude - Games provide opportunities for building self-concept and developing positive attitudes towards mathematics, through reducing the fear of failure and error.
  • Increased learning - In comparison to more formal activities, greater learning can occur through games due to the increased interaction between children, opportunities to test intuitive ideas and problem solving strategies.
  • Different levels - Games can allow children to operate at different levels of thinking and to learn from each other. In a group of children playing a game, one child might be encountering a concept for the first time, another may be developing his/her understanding of the concept, a third consolidating previously learned concepts.
  • Assessment - Children's thinking often becomes apparent through the actions and decisions they make during a game, so the teacher has the opportunity to carry out diagnosis and assessment of learning in a non-threatening situation.
  • Home and school - Games provide 'hands-on' interactive tasks for both school and home.
  • Independence - Children can work independently of the teacher. The rules of the game and the children's motivation usually keep them on task.
  • Few language barriers - an additional benefit becomes evident when children from non-English-speaking backgrounds are involved. The basic structures of some games are common to many cultures, and the procedures of simple games can be quickly learned through observation. Children who are reluctant to participate in other mathematical activities because of language barriers will often join in a game, and so gain access to the mathematical learning as well as engage in structured social interaction.
So, let's play because I love math board games, too!


Mathematics and Marathons

Achievement in higher level mathematics and completing a marathon are very similar. Both are done by few people. Most think that they are too hard or that you need to have natural ability to complete them. If you are successful at either (or both), naysayers will say it’s because you are born with that ability or that you are CRAZY! The fact is, both are essentially easy. They only take hard work, dedication, commitment, a belief that you can do anything you set your mind to.  There is a tremendous sense of satisfaction in completing or being successful at them. (I cannot decide which I am personally more proud of-getting an A in university level calculus or completing my first half marathon). Ultimately they are both solitary endeavors to which you alone accomplish albeit with a lot of support and encouragement from like minded individuals. You need not compete against others; the satisfaction comes from simply doing what others feel is too hard to do. Training for a marathon is a lot like learning the skills necessary to be successful in mathematics. Let’s look at the seven process expectations for mathematics as is found in the Ontario Curriculum documents.
Connecting-In math, students are expected to make connections among mathematical concepts, procedures and relate ideas to situations or phenomena drawn from other contexts.  Long distance runners are always making connections: I ate something different before my run today and now have a terrible cramp in my stomach only 5kms into the run; the bottom of my feet are sore, I’m in need of new shoes. Runners and mathematicians alike make connections between different things every day.
Selecting Tools-students select and use a variety of concrete, visual and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems. Runners select many types of tools for their running, from running shoes to athletic wear to what I consider to be the best gadget out there for runners, the GPS running watch. This electronic tool does countless computations for you, everything from how far you have run, to how fast you ran, the change in your pace in relation to the change in elevation,  how many miles you ran this week, this month, this year. Like a calculator in math, the newest running watches do all the mind numbing computations for you.
Reflecting-students will be able to demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem. Runners routinely reflect on their runs and training. Runners reflect on and monitor everything they do and how it affects their running. There is a constant drive for improvement and how to achieve that. Reflection is the only way to do that.
Communicating-students communicate mathematical thinking orally, visually and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions. Runners use their own vocabulary (to communicate what they are doing and how they are training to others). Runners even use programs like to communicate these things visually to other runners. Runners have their own vocabulary. For example, if a runner were to say “I just ran a half”, other runners would know exactly the distance they are referring to, non runners may ask “half of what?”

Representing-students create a variety of representations of mathematical ideas, connect and compare them, and select and apply the appropriate representations to solve problems. Runners represent themselves, rather than their ideas. Runners represent themselves with numbers, usually in the form of their bib numbers or with items signifying how far they can run. The only bumper sticker I have ever had (and possibly will ever have) on my car is a 13.1 sticker. I do not share my political beliefs or my religious beliefs with very many people, but my running, I shout out to the world “See me; this is what I can do!” This, along with a photo of my bib posted as my profile picture on facebook for weeks, are how I represent myself to the world. I am a private person, but this is what  I allow anyone and everyone to know about me.

Problem Solving-Problem solving is as important for runners as it is for mathematicians. Runners must sometimes figure out what is causing the aches and pains they are feeling when they run.  Is it bad form, shoes that are tied to tight, shoes that are too old etc? Runners must also sometimes experiment with different strategies/methods to determine what works best for them (just as mathematicians must sometimes try different strategies to solve problems to see if a solution is easier). I personally also find running to be the ultimate place to solve problems. When running for hours alone, one must distract oneself from focusing on the time or distance and must think of something else. I have found this time to be my best for solving the problems of my life. Your head is clear and focused on something completely different. Perspective changes and things that previously seemed difficult are suddenly simple and clear. I think in solving math problems, this is sometimes necessary too. You must walk away from the problem, clear your head and focus on something else in order for the solution to become clearer in your mind.
Reasoning and Proving-students develop and apply reasoning skills to make mathematical conjectures, assess conjectures and justify conclusion, and plan and construct organized mathematical arguments. At the beginning of training for the first time, runners make the conjecture that they will be able to do something that they have no experience doing. That is they have no proof that they will be able to do it. They simply have the idea in their head that they can. Runners assess their goal and then plan and construct the training plan that they will believe will help them prove they are correct and can reach their goal. Their final proof comes only on race day, when they run what others thought impossible. They have justified all the long hours and hard work by reaching the elusive goal.
I hope you have been able to see how math and marathons are alike. My wish is that this has encouraged all those mathematicians who think they cannot run, and all the runners who think that they cannot do math, to go out and try something new. You never know, it might have more in common with what you already know than you think.