Math and beautiful food

To continue on with how math can be used to create beautiful food, I discovered this amazing web site
(http://vihart.com/food/) that depicts how if strategically used, mathemeatical formulas can create art with food.

Candy Corn Sierpinski's Triangle

Sierpinski's Triangle is a neat fractal that can be made out of all sorts of materials. Candy corn, being roughly triangular themselves, make a lovely version! Sierpinski's original triangle is equilateral, but candy corn has more of an acute iscosoles shape that makes a nice elongated Sierpinski's triangle.
This is a perfect example of how mathematical formulas or theories can be used to create images from real life objects.  There are many more examples and pictures on the link above. Enjoy!

Why making cakes is mathematical!

The cake in this picture is a perfectly baked and structured cake.  It is not leaning and very sturdy which is a very planned out mathematical process.  As you will see in the later picture, things can go awry if exact measurements are not followed.

I would have to say that I am an amazing baker (not so much a cook though), so I realise the importance of using exact measurements.  There is no such thing as approximating or estimating numbers when baking a cake.  It just will not work-guaranteed. Not only are measurements important, but many people do not realise the significance of such factors as speed of mixing and the length of baking time.  All of these factors although they are pre-determined in most recipes are calculations that sometimes take years to perfect.With the first batch of cupcakes I ever made, I remember that I left the mixer on for too long and I had the wrong shaped paddle and the cupcakes as a result were not much denser than I would have preferred.  Same thing with the frosting. If you don't stop whipping and mixing at the exact moment required the entire consistency will be a flop!!! I actually attended a week long course on cake baking at The Bonnie Gordon School of Cake Decorating and that was one of the first things we learned.  Numbers, speed, mixing time and baking time must be exact.  One second can ruin an entire batch of cupcakes. Estimation is not allowed and creativity is only limited to decorating.  The following picture depicts what may happen if the angles and sizes of cakes with many tiers can be destroyed if they are not properly constructed.

Math and Beauty!

Many mathematical principles are based on ideals, and apply to an abstract, perfect world. This perfect world of mathematics is reflected in the imperfect physical world, such as in the approximate symmetry of a face divided by an axis along the nose. More symmetrical faces are generally regarded as more aesthetically pleasing.


This image that many women and men have about what the perfect face should look like is something that I see everyday in my job.  I work for a very reputable make-up company that may subliminally endorse this perfect ideal.  We have a face chart (blank template of a perfectly symmetrical face) that wer follow when we recreate make-up looks.  This gives many people the wrong impression or unrealistic ideal in which they beleive they must have the same face in order to have the perfect face.  The distance between their eye brows, the contours of their cheek bones, the length of their eye lashes, the shape of their lips are all math related!


The above picture is a template we use of the 'perfectly symmetrical face'.  Clients often refer to this template as a guideline to guide their desired symmetrical look throught the use of make-up.

Geometry and real life!

This week in my grade 4 I had the opportunity to teach art and math both in the same day, so I thought a cross-curricular activity would be beneficial.  For art class the specific expectations that I had for the students were learning how to use shapes and lines to draw pictures.  I found a great activity online in which the students are asked to draw and paint an old Victorian home, which was very fitting due to their many shapes and sizes.  They turned out amazing.  I was very impressed at the use of various shapes and sizes, and also the painting techniques.  The next class just happened to be math and we were starting a unit on geometry.  I used the classes house designs and asked the students to identify the various shapes and sizes in their Victorian homes.  They had a blast and they also realized how geometry can be related to real life.  It was an awesome transition, and the students will probably pay closer attention to shapes in homes as they observe the scenes in the back of their parents car on the way home.  Or better yet, for all the young aspiring architects in the class, they may have the desire to design their own future homes!

The Odds of Winning the Lottery

I just purchased my annual Heart & Stroke Lottery ticket that I will become a winner once again! My family members and friends often discuss their 6/49 tickets and Lottario, but for some reason I feel like I am wasting my money by purchasing the tickets every week.  One Heart and Stroke lottery ticket is $ 100.  In the past 10 years I have won 4 times!  Not huge prizes, but cool ones like a watch, $250.00, an ipod docking staion and even a toaster oven.  The fact that I win keeps my hopes high.  Why are these lotteries so attractive to me? For one thing, when I get my yearly flyer in the mail the first thing I notice is ODDS OF WINNING 1 in 3!!!  This always gets me.  And the fact that I have won so many times is my main motivation. I have never won the 649.  I dont know anyone that has ever won to be honest.  My biggest question would  be who decides what the odds are? Is there really a formula?  If there is a formula for the odds of winning, why is there not a formula for winning.  If only I could choose a very practical mathematical formula to create- that would be it!! I would love my math talents to help me win the lottery!

Teaching Math with Base 10 Blocks

Now that I am a pro at teaching math (3 days in) I can comment on how successful base 10 blocks can be when teaching math.  I did a grade 4 lesson today using the base 10 blocks.  I had the entire grade 4 class meet me on the carpet so I can explain to them how to subtract 3 digit numbers.  I honestly had so many aha moments even before I began to teach the lesson.  I practiced the problems at home before I began and the entire time I wished that I had learned it the same way when I was a student.  I had a lesson on mental math the day before and I noticed many of the students confused on how to subtract mentally.  It seemed as if they did not want to subtract anymore!  When I got them on the carpet and began to demonstrate how to trade blocks etc. I could almost see the light bulbs going off on their head.  The room was bright!  To physically see how to take away the blocks and get a remaining number made more sense to the students.  Next class I will attempt place value.  I can't wait!
Here is a great video that really helped me grasp the concept of subtracting with base 10 blocks
http://www.youtube.com/watch?v=o1CfyICcEfo&safety_mode=true&persist_safety_mode=1&safe=active

Teaching Mental Math

Today I taught a grade 4 class how to subtract mentally- it was quite the challenge.  Even with all the strategies listed in the text book I still had a difficult time understanding that it is even possible to teach someone how to do math in their head.  I do not remember learning such mental math strategies in my math classes as a young student-maybe I blocked it out.  However, I do use mental calculations on a daily basis in real life for so many situations, such as; calculating tips,making sure I received the correct change from a purchase, figuring out taxes, keeping score when I play golf, adding calories I eat throughout the day, and so on.  It's actually a math strategy I use constantly, but I didn't realize that it was actually a strategy that was in the curriculum.  I always thought i just had a natural talent for doing math in my head.  Teaching students to use mental math with definitely be something that will be helpful for them in many everyday situations.

Keeping students active durinig math class!

So, I am anticipating teaching my first math class next week (all week).  I am a bit nervous but I have had the opportunity to observe the teachers methods for the last 2 weeks.  It is very interesting to see the different techniques she uses to engage the students.  The lesson is done on the carpet, and then the students move to their desks.  Once this is done, each student that volunteers goes up to the board to demonstrate how why got answers from their homework the night before.  Then, the students sit at their desks to do text book questions independently.  So, I have observed that in the course of one period, the students have moved around the classroom and done various activities in order to keep their interest peeked.  At one point, the teacher even noticed a couple kids getting bored and asked the class to do 15 jumping jacks.  It worked!  It seems as though the children do not dread math class (like  I did when I was young).  Stimulation is the key to success! I am looking forward to seeing if I can keep them interested for a whole 50 minutes!!!

Mentally Preparing myself for my first math lesson

So, I feel it is important to note that getting up in front of the class the first 2 times in my placement has been exciting and wonderful.  I taught art and health. Two subject that I know a lot about and am extremely interested in. However, in the back of my mind I can't stop worrying about having to teach math next week.  I also find it interesting that my associate teacher reminds us everyday that we will not have to teach math the first week.  She wants us to get our feet wet in other subjects first.  That is scaring me even more!!!  I walked around the room the first day to help the kids with their questions and I remember the anxiety as I read the question and hoped I knew the answer.  It was very simple and I got it-but can I teach it?? I am anxious to start and see what happens.  I will let you know!  I feel as though the anxiety I get trying to solve math problems (banking, school etc.) may be transferred into the classroom and it will hinder my ability to teach.  Hopefully this will be a positive teaching experience. I will keep you posted.

sitting on the carpet during math is fun!

It's my first week practice teaching and I am still amazed at the methods being used by my associate teacher.  I also realized how important the seating arrangements are during the lesson.  I remember as a child sitting in rows in a very structured seating arrangement.  I also remember daydreaming a lot during our math lessons.  My realization is that it is very important that to get the children engaged they must be comfortable and feel as if they are a part of a group that is excited to learn.  When the teacher does the instructional part of her lesson, she moves the class to the carpet and has them sit facing her.  They love being on the carpet.  They are close to her, they are close to their classmates and I notice they feel more eager and involved in the lesson.  Of course this technique would vary depending on the grade level (I have grade 4), but this can be adjusted according to the grade level.  Doing any sort of activity in groups is enticing for students!  My aha moment this week was that not only is the technique of teaching math important but so is the physical comfort and arrangement of the classroom when conducting the lesson.

First day in the classroom!

Today was my first day in my grade 4 class!  I was pleasantly surprised to observe my associate teacher using blocks for her math lesson.  Her technique was very similar to the one used by Professor Antosz.  She would write a number on the board and asked students to come to the front of the class to show how the number would be arranged in blocks.  The part of the lesson that I found interesting was her use of the blocks to show the numbers as well.  For example, on the board, there would be a number such as 7,631, under each number a student would draw the shape of the blocks used that would correlate.  This was also used to assess the students at the end of the lesson.  It was great to see the interaction and involvement of all the students in the lesson.  It seemed as though the blocks were toys to them.  Math was now a game to be played instead of a tedious memorization of facts.  That was my biggest lesson of the day.  Math was fun!!  If students can carry on this excitement throught the grades, the subject will not be so intimidating as I and many other people find it!

Math and Exchange Rates

 

I realized today that I have be en applying my math skills in a wonderful way! I went on a little shopping spree in the United States this afternoon, and realized half way through that I was figuring out exchange rates all day. Living so close to the border (Detroit) has allowed me to exercise this throughout the years.  I do not travel outside Canada very often, however, I think it is important that children learn how to figure exchange rates, so they do not get confused with the use of various currencies throughout the world.  This could be done through the math curriculum as well.  After all, figuring out how to exchange currency does involve multiplication!  For example, here is an problem:
Pam is going on a trip to Texas and has $250 Canadian Dollars (CND) . If the exchange rate is 1 CND = .6733 USD how much American money will she be able to get?

a) Set up the equation

1 CND = .6733 USD

b) Multiply both sides by $250

1 CND (250) = .6733 USD (250)

$250 CND = $168.325 USD

Pam will have $168.33 American Dollars from her $250 Canadian Dollars

This is definitley a convenient skill to have weather you are travelling, or work in a bank etc.  I know I use it quite often!

Helping Kids Learn Math through Sports

So we are near the end of baseball season once again, and as I was listening (and watching) the Tiger game last night I couldn't help but notice that every once in a while the broadcaster revealed statistics about players, the game etc.  So, I thought in that moment that sports and math are interconnected in a big way.  Not only is statistics a large part of every sport (i.e. batting averages of players) but it is also used in creating strategies of play.  An example of this would be football.  Have you ever seen a picture of a coach's plan on the chalkboard in the locker room?  It looks like an algebra exam!  With this being said, it is important to note that kids love sports and it would be a great way to help them learn math.  Here are just  a couple examples that can be used in a classroom.


1. Jerry hit 32 home runs in one year and 43 the next year, and 54 the next year. If this pattern continues how many home runs will he hit next year?

2.   Casey had 63 baseballs. She gave 16 to her friend. Then she gave 27 to her brother. Then she bought 57. Now how much does she have?



Exercising the Brian through math

Math enhances your logic skills and exercises that part of your brain. So now when you have an issue in your life that doesn't involve numbers, you will understand how to make your own formulas and solve the issues.  I truly believe that the problem solving skills that in every subject area throughout my university career can be related back to trying to figure out how to do math.  It's not just the use of numbers that is important in math.  It does exercise the part of the brain that tries to 'figure things out'.  Just like the other side of the brain is creative and used in art classes.  The same principle applies.   For any students starting in the early stages of math, these skills can be transferred into other subjects.  For example,  problem solving skills can help develop and solve hypotheses in science, and the list goes on.

The connnection between math and music

Math and Music

The above diagram is an example of reading time signatures in music.  In music rhythm and pitch, two of the most important basic elements of music are best described using math concepts.  There is a strong relationship between math and music.  I noticed that the time signature looks a little like a fraction or arithmetic.  Filling up measures feels a little like finding equivalent fractions too.  In "four four time" for example there are four beats in a measure and a quarter note gets one beat.  So, four quarter notes would fill up one measure.  But so would any other combination of notes that equals four quarters: one whole, two halves, one half plus two quarters, and so on. 

So, I still do not have any musical talent, but if I continue to try to relate basic math to reading notes It will eventually become second nature and playing the recorder will be a true joy!!!

learning long division a new way

This week I learned a new way of doing long division.  I am going to be honest.  As the topic of division came up I thought I had all the basics covered as far as my knowledge went.  In my mind, there was only one way to do long division.  I was wrong once again.  Division was also a math subject that was easy to learn using objects (which I am still getting used to).  So, when the professor showed us his version of how to do it, I could not understand and I didn't want to understand.  I thought it was torture trying to figure it the first time and that I was not going to do it again!  Well then, I was told to forget my old way, and I started having chest pain.  I almost left the class without really grasping the concept.  Then another student asked the professor for help and I stayed and learned a lot.  I was impressed with his one-on-one teaching skills.  Honestly, if he wasn't so confident that his way was better I would have left.  I kept the paper the other student was practicing on and went home myself and tried it a few times.  It takes a bit longer but I can see how teaching someone with little math skills this technique would be more efficient.  I am determined to get rid of my old habits from now on!

calculating is constant

After my first math class, I really started to think about how often in a day I used math.  I soon came to realize that from the minute we wake up we are unconsciously using our math skills. It actually starts before we go to bed the night before when we are setting our alarm clock.  I need to calculate what time I need to get up in order to make it class on time for example. Then I have to figure out the order in which I will carry out my daily activities.  For example, if I wake up at 6 a.m. and I have to leave the house by 8a.m. how much time do I have to eat, take a shower, brush my teeth etc.  I basically have to divide my 2 hours accordingly.  And it can be broken down even further into every minuscule detail of my life.  For example, how many calories should be in my breakfast if I'm on a 1300 calorie a day diet? Once again I am using division.  The real-life examples of math in real life is endless. I will probably expand on many of my revelations in the upcoming days and weeks.

First Math Lesson

Today was an interesting day for me.  I walked into my first math class since I was a child, only to discover that if I had only learned it from Proffessor Antosz first,  I might not be so petrified to face it today!  I have always been afraid of math-literally!  Today I learned that math can be taught using blocks (or objects).  Although my classroom memories are fading with each passing day,  I do not recall such teaching strategies.  What I do remember is that the teacher stood in front of the class and wrote numbers and symbols on the chalk board, erased it and continued with a different set of numbers.  The class had to memorize everything. 
When I left the classroom, nothing I learned or did not learn was applied to my surroundings.  The classroom was a separate entity than my outside environment.

Today, I learned that we can explain and learn concepts in math through the use of blocks as a more effective method of teaching.  By effective, I mean that what I learn with the blocks can be applied to my real life.  I never associated math with the real life environment even though I do realize the significant correlation! I did have many "aha" moments when I was learning how to learn with blocks.

Now that I know that blocks are actually numbers I look forward to learning how to re-train my thinking (if at all possible) and attempt to consciously apply my knowledge through my environment daily.