A Fraction of This…

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I’m sure by now that everyone has figured out that everything in my educational process tends to circle back to my children and this is still the case as I begin to examine teaching and learning about fractions.  Fractions can be a daunting task for some adults who basic math concepts should be second nature for.  Imagine being a youngster and trying to figure out the world of fractions and why they are important to learn.  I for one was a student who used to complain that I would “never use this in real life,” and so I wondered why on earth I was being forced to add, subtract, multiply and divide fractions on a worksheet.  I’m someone who needs to see how something will have a direct effect on my life before I am completely on board learning about it, so when I think about teaching my daughter about fractions I know that I will definitely begin by showing her where she will use them in real life.

ObviouImagesly, neither of my children (ages five and two, remember) are at the point of learning to use fractions.  We are still working on addition and subtraction of whole numbers, but I know that this will be headed our way eventually.  Together, my children and I like to cook and bake.  Baking is one of the best places to show children the value of learning fractions.  Have you ever baked chocolate chip cookies?  I assume the answer is yes, but hey what do I know? I was in a fourth grade classroom this spring where we took a field trip to the school kitchen and baked cookies in math class. (How I got to sub on that day is beyond me, but I was super pleased with my luck!). The day before I arrived to the class, the students were given this recipe for cookies. The teacher then ran through different scenarios with the students: “If I only have one egg, but wanted to bake cookies, what could I do?” (The answer is obviously to cut the recipe in half). or “Can I cut this recipe into fourths?” (No, because you cannot take half of an egg), etc.  When I got to the classroom, we multiplied the recipe ingredients to make a triple batch before leaving for the kitchen to see if our math was correct (the teacher instructed the students the day before that if the cookies turned out that their math must have been correct).  I thought this was a very fun way for the students to have a chance to see the value in what they were spending classroom time on.

As teachers, it is our job to not only teach that one half plus one half is one, but to show our students why they should learn these ideas.  As shown with the baking example above, there are many fun ways use fractions in the classroom.  I have also seen teachers create or use fun videos to show the value of learning fractions.  It is so important for us to create and use lesson plans that teach the facts, but also the reasoning behind learning it.  My daughter is only five, but she always wants to know why she needs to learn the things we work on.  Interestingly, I am also of the opinion that instead of focusing on the Common Core Standards that so many states have adapted (mine included), perhaps lesson plans should be proven valuable by giving real-life scenarios of when the information could be valuable.  This goes for every subject, but math in particular could be effected.  If you’re like me for example and want to rebuild your deck and you find out that your current deck is twenty two and one half feet by thirty and one fourth feet…there are a few ways to calculate the area (681 square feet once I rounded up), but you have to know a few things first!  I could convert it all into inches (which by the way, is what I did) multiply to get your answer and convert back to feet (rounding to the nearest whole foot).  I could have also simply
multiplied the fractions to get my answer and then of course rounded up. I can now use this information in a plethora of ways (I can round back down for an estimate of how much it will cost to rebuild my deck or I could round up to get a higher estimate just to be safe, etc.).  The entire point is to illustrate to students how to use fractions properly and show them where they will actually use them in their lives.

The Value of Money

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I have been workpiggybanking on a fun little
project lately that deals with teaching money values to students. Any grown individual can relate to the fact that money makes the world go round and the importance of knowing your money inside and out.  Money management cannot be achieved until money is understood in its most basic forms.  As always, everything I do comes back to the value (pun intended) it has to myself and my family. As I have mentioned in earlier posts, I have a five year old daughter who is learning about life and all that goes with it.

Within the last six months or so, we began explaining money values to our little girl.  We began with the penny and moved up from there to the nickel, dime, and quarter.  We then introduced the dollar.  I think it has helped her that she already knows how to tell time and that there are sixty seconds in a minute and sixty minutes in an hour (thus she understands that within one thing is another).  I used actual dollars and coins in the beginning and then we found a few fun money apps.  I also sing the “penny song” with her and play money bingo (which I’m not sure if I made up or not…I got the idea of money bingo from seeing a picture online, but didn’t bother to read the instructions and came up with my own method to play).  So, I’m not the first parent to play the game with her child, nor am I taking credit for being brilliant at inventing games.  This is how we play: I made bingo cards that have pictures of different coins and a one dollar bill as the “free space.”  I have a huge change jar and randomly draw coins out and she has to then place the coin on her playing card (if she has that coin available).   Whoever gets five across, diagonally, or vertically, first-wins.   After she got good at that game, I made new boards with the actual value in the place of pictures of the coins.  We played the same way, only she had to figure out what the value of each coin was.   This was a fun way for her to practice her money values! I try to incorporate learning into many aspects of our everyday lives.

Each summer we enjoy heading to farmers markets to purchase fresh produce.  This year I began giving my daughter a five or ten dollar bill when we arrive (what ever I have laying around in my wallet in cash).  I let her spend the money on whatever she wants at the market that day, but the catch is that she has to handle everything on her own (of course I’m there supervising and helping along the way).  Her first purchase is always easy (all she has to do is hand over the ten dollar bill), but the second and third (if she gets that far) are where she has to really start to think.  She gets to handle the exchange, count her money and make sure she is given the correct amount of change.  This has been an excellent source of education for our entire family.  My daughter sees why learning about money is so important and it also gives her a sense of pride when she gets to come home with a bag full of yummy goodies to show her dad!

Operating on a Level Playing Field

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As you all know by now (if not, check out my welcome post), I am taking an online course this summer. This week in math class was quite interesting for me.  My biggest issue with any kind of coursework is “what am I getting out of this?” or “How will this help me in the future?”  I like to know that what I’m doing is actually benefiting me in some way.  Busy work drives me absolutely bananas.  I’m pretty sure any parent out there can understand where I’m coming from with that statement (we all have enough things to do during the day without feeling like our time is being wasted on something that will not directly benefit us in the very near future).  The lessons from our text this week were completely valid.  I will admit that at first I thought it was going to be silly (I mean, why would we need to know what kind of numeration system ancient Egyptians used?!); however, about half way through the chapter, I decided that it was a great lesson for me to learn (maybe not the math itself, but the reasoning behind  the math.  Well-played, Chapter 3, well-played.

This week we worked on using the different math operations with different base numbers.  So, if our current numeral system works off a base ten (which it does), think about switching it up and trying to do addition or subtraction using a completely different base (ie: base 5 or base 2).  It took me a few tries to really wrap my brain around the concept.  The base ten system has been ingrained in my head for so long that I felt almost naked trying to operate off of a completely different system. A light bulb at this point went off and I realized that this is how students feel when we try to teach them something that is so natural to us.  This week I learned to put myself back in the shoes of my students and remember what it feels like for some of the concepts to not come quite so naturally.

I like to think about it as trying to explain to someone what exactly we’re doing when we’re chewing or swallowing food.  For most of us adults things like the number of minutes in an hour and the number of seconds in a minute are something we do not even need to think about anymore.  It’s natural –or at least it certainly should be for those of us even considering teaching America’s youth!  What if you had to explain to a child how to properly chew food?  Could you explain how to use your tongue to push the food around? When to know to swallow? How many times to chew? Which teeth to bite food off with versus which teeth should be used to grind the food up?  These are all things that come to us naturally at this point, but think about a six month old baby having her first experience with solid foods. Also think about having to explain it to someone for the very first time…it would be frustrating!  As a parent, do you hand the baby a grape and expect her to know exactly what to do with it? For your child’s sake, I certainly hope not!  We need to approach math with a similar thought process.  We need to ease our kids in and remember that this is all new for them.

I was surfing the net to see what kind of numeral systems are used around the world.  I was surprised that the whole concept of swapping base numbers is not just utilized in this course.  This is a very normal occurrence (similar to using a Fahrenheit / Celsius conversion…which if you have ever spent any time in Europe at all, you will know is something definitely worth knowing)!  It is an excellent example of taking ourselves out of our comfort zones to understand where our students are coming from.

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Real-Life Applications…

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Hello and welcome to mathisfunforeveryone.  As stated in the heading, this blog is for an online math course I am taking this summer which is aimed at teachers and future teachers.  This week we have been working on addition, subtraction, multiplication, and division of whole numbers.  I have to say that I enjoyed this week a lot more than the first, simply because I found a real-life application.

I have a little girl who is just beginning to learn about the concept of doing “math.”  We are obviously starting with addition, and this weeks readings, videos and homework has been fun for me mainly because I have been able to apply it to helping my daughter. A lot of what we worked on in the course (properties, models, sets, etc.) is much too advanced my little one; however, the main concept of showing students-through the use of manipulatives- how the math breaks down has been extremely helpful for us at home.

During my mini-lessons with my daughter, we have been using candy (something she definitely relates to and loves) to learn how to add small numbers.  I give her a handful of candy and we work on “If I have three pieces of candy and you give me 2 more, how many pieces of candy do I have now?”  She caught on very quickly and I was able to introduce equations and show her how they relate to the pieces of candy we had started out using. I picked up some fun worksheets here that really helped us along.  I was very pleased with seeing such quick results from such a fundamental concept through this week’s assignment.  I even decided to download a new math app on my phone and tablet that lets her practice her addition complete with music and an applause when she gets the answers correct.

In short, the thing I hope to gain most from this course is the real-life application of the concepts we’re learning.  Math is such an abstract form to so many people (truthfully, myself included), that I really hope to find a way to make it more user-friendly.  This week was a great start for this and I really hope that I will be able to continue with this! As any parent knows, things generally seem more worthwhile when you can find a way to use it to help your own kids out!Image