Estimation ~ Guesstamation

I loved estimation in school.   This is something you use your entire life.   I always called it guess-ta-mation for fun.    Estimation is very crucial to learn.   If you don't you have to learn the hard and embarrassing way at the cash register in the grocery store because you bought too much and don't have enough money.    There are some key skills you need to know for estimation.

Now in order for students to catch onto estimation, the must fully understand place value.  If they don't  they will struggle to figure out what number to look at in order to find the estimated number.

First students will need to learn rounding. http://www.aaamath.com/est27ax2.htm. Here is an explanation, then if you scroll down there is a practice area.   You now will work through the place values of tens, hundreds and thousand.   Rounding decimals is next.See video here.

There is also front end rounding  shown here:click on "watch out"
http://studyjams.scholastic.com/studyjams/jams/math/addition-subtraction/estimate-sums-diffs.html
 There is also steps for estimating the difference and such.  Estimation also includes time.   Students need to learn how to tell time to the nearest hour, half hour and quarter hour.

Estimation is something we all use on a daily basis.   I think coming up with real life situations for this unit will be easy and you can make it fun too.    You could have students plan some kind of party where they have to estimate how many students there are then estimate how much each person would eat and drink.  Then for all their hard work and planning, you could cook or bring in that actual amount of their estimation to see if they are right.

Technology- Pros and Cons

Our society has many wonderful technologies that have improved our lifestyles.   IPads for instance are really cool.   I just started to learn how to use one in the school I work at.   They offer some really cool apps.   I sometimes wonder how our technology is advancing, if we will one day be like the cartoon "The Jetsons".  I don't think we will have hovering and flying cars or eat food from pills.  What I am referring to is having the ability to push a button and some gadget will think or do it for us.

I know I have gotten what I call "lazy brain," since I have had a cell phone.   I don't bother to memorize any one's phone number  because I have my contact list and I scroll to their name and push a button.  My phone is outdated to most peoples standards  because all the smart phones have voice activation, call  Joe.  No, dialing or buttons needed.    Don't get me wrong I think these are all cool and fun gadgets.  I just worry that we won't use our brains to the fullest.  I realize that students are learning on these new gadgets but I still wonder how much screen time is too much?

Let's look at the Pros:
http://www2.ed.gov/pubs/EdReformStudies/EdTech/effectsstudents.html
http://www.usnews.com/education/high-schools/articles/2011/07/14/study-emerging-technology-has-positive-impact-in-classroom



Let's look at some Cons:
http://www.huffingtonpost.com/cris-rowan/technology-children-negative-impact_b_3343245.html
http://www.edudemic.com/2013/05/the-4-negative-side-effects-of-technology/      

I will use technology in my classroom but I will also dance, art, boardgames and other interactive activities.  I do see how nice using IPads can be for certain subject but they will not be the only tool I use.

Integers

After having to review and work with integers for a college class, it got me wondering what the best approach would be to teach this topic.   This concept seems like it would be confusing at first to students.  Using a number line to initially show students where negative numbers are on the line is easy enough, but it is the rules of addition,subtraction, multiplication and division that gets confusing.    

Learning the rules for addition and subtraction would be a bit confusing at first to students because of the way you change the signs.   I found  a video with a song on this rule.   

  Here is a cool video I found that explains this wellhttp://youtu.be/5eLiz1rdhsk.  Now that I am older, I look at adding and subtracting integers like balancing a checkbook or a credit card bill.   For younger students I think it might be a little more challenging to come up with a real life situation for them.   

I have to admit when I first learned about integers it confused me how a negative number times a negative number equaled a positive number.   The rules for multiplying and dividing integers is a bit different.  I think it is relatively easier to grasp because you are not changing signs as much.  Here is a song on the rules http://youtu.be/QMst5BcgHhQ.    This video shows one way to explain the rules    

 I am sure there are many ways to teach this topic, I am  just on the look out for many methods  to teach in order to find one that is effective with my students.  Never hurts to have a lot of tools in the tool belt.

Musical Math

Like math, music is all around us everywhere.    From the birds singing, the roll of ocean waves to jingles on commercials and our favorite song on the radio.  Most people would not link these two subjects.  They have more in common then people think.  An article I read called "Music, Math, Patterns"  by Natasha Glydon gives some examples on how closely related they are.  Here's the site
http://mathcentral.uregina.ca/beyond/articles/music/music1.html.http://mathcentral.uregina.ca/beyond/articles/Music/music1.html  Studies have linked math and music all the way back to the ancient Greeks.    In the following article, Fibonacci sequence is mentioned.   This was discovered by Leonardo of Pisa(nicknamed Fibonacci), who lived from 1170-1230.    This sequence is found in nature all around us and I found a video that gives an interesting perspective on life.  

 Advertising companies have figured it out.   They make up jingles and songs for their products.  Why, because we remember songs and sing them in our heads throughout the day.   We even remember jingles of products we don't like.   This has been a strategy for years.   So why has it then taken us so long in the education field to put this strategy to good use?     Combining music and math will make learning not only fun but students are more likely to remember the math song and concept.   In recent years, more and more teachers are embracing this idea.     Here are some examples:http://youtu.be/n2kg4CcgUKg  here is an older gradehttp://youtu.be/2XEbU-s-VVs.  This are just of of the many examples out there.

http://www.questia.com/read/1G1-99618634/integrating-music-and-mathematics-in-the-elementary This site offers an article on the benefit of music with math.     By exploring new ways to teach math we as teachers will be able to tap into our students different abilities.   Gardner's theory of multiple intelligences encourages people to learn in all different ways.   By opening the many doors into our students minds will make learning fun and something they remember.  I think singing and dancing are something that all elementary children can relate too.  Relating a subject to the student makes it easier for them to understand and want to learn the subject.

Fractions Oh, Fractions

When I was growing up, I had a hard time with math.  Fractions seemed to be one of the concepts that I really struggled with.  I do not recall the exact grade I was in but in one of my elementary classes we made marionettes. This was during the time of  "The California Raisins".  So everyone made a raisin and had to perform a poem with it.    Most of my classmates were using Shel Silverstein books.  So, even though I loved his poems, I picked another poem book.   I chose "The New Kid on the Block" by Jack Prelutsky(very funny poems).   I chose the poem called "Homework Oh, Homework", the line that still resonates with me is "homework oh, homework, I hate you, you stink"!  Now mind you at that age I thought that was funny.   I then  related that saying to other unlikable subjects like fractions.  Thus, leading to the title of  my blog.

When I went to college, I had to take remedial math classes because I was so lousy at math.  Let me tell you having to take and pay for classes that do not count for your degree is not fun or cost effective for that matter.   Kids the lesson here is - don't be afraid to ask for help in school when you don't understand something.  Well I made it through to College Algebra.   I did learn a lot, but those darn fractions, I still didn't feel comfortable with them.

This past year at work, I changed from working with the younger students(K-3) to working with the older students(3-5).  This was a big change for me.  I found myself having to help teach fractions to students.   I felt very unsure of my ability to help with this subject.   I looked at the math book the students were using and walked myself through the steps.   After sitting down the first time with a student to work on fractions, I was finally starting to get fractions.  I think having to explain it to someone else reassured me that I did know what I was doing and fractions were finally clicking.
I had discussed my unease with my coworker and she too has always struggled with fractions.  So we came up with a plan for the student I had been working with.   Once I felt the student had a grasp of the concept, I had  my coworker ask the student for help.  She told him she really didn't understand and asked if he would teach her.   At first he was like yeah right, your just saying that.  We convinced him that it was true and I told him the troubles I had with them.   He did a great job explaining the concept.  It was an amazing interaction to watch.  I could tell how proud he felt inside for being able to teach the subject he just learned himself to someone(let alone an adult).  We were both so proud of the job he did.  The next day he said he didn't need any help.
 
I guess the moral of my story here is I know that math is not always easy but if you keep trying and don't give up you can learn it.   Have confidence in your own abilities.   When I have my own classroom I want to encourage students to believe in themselves and to always ask questions.   I want to create an environment that students will feel okay to say they don't understand.   I also want to have students teach each other and teach their parents.   I would like for my students as homework, to go home and teach their parent or an adult what they learned that day in math class.  I realize that adults already know this stuff but I would ask parents to sit with their children an listen to them teach the topic.  This way the children get to be the teachers and the adult is the student.  I would ask that the adult write about what their child taught them.   This will not only help the student understand more, but it encourages parents spending time with their children and some good conversations can come about from this interaction.  Fractions oh, Fractions you are okay. 

Multiple Multiplications

There are multiple ways to figure out a multiplication problem.   The problem is finding the one that makes sense to each student.

 This is the way we begin to learn about fractions.  Multiplication with
  Arrays.

We then move on to multiplying one-digit with a two-digit number. This Grid method is only one way to approach this.

There is also the standard method.  This is the way many of us were taught in school.

25
x6

You can also use the Area Method which you will need the Base 10 blocks to use for hands-on learning and a visual to figure the answer.

We will now get into two digits with two digit problems.   With this one can use some of the previous methods or try this: Lattice Method.

Now there is a method I had not heard of until this recently, which is the Russian Peasant Method.

Then we get to algebra and we add the F.O.I.L Method.

 There are so many multiple ways to do multiplication, what are the best to teach?  How many methods in a grade are too many?   One method may work for one student and confuse another.  I had never heard of the Russian Peasant Method before seeing it on youtube recently.  I found it very interesting.   As a future teacher I wonder in my classroom, do I teach multiple ways to solve the problems then let the students pick the one that makes the most sense to them to continue to use? Or, do I teach multiple ways to multiple and require them to use each method for a certain amount of time them test them on it?   I am not sure?  Is it more important for a student to have multiple tools to solve a problem or is it more important for them to choose which tool works best for them out of their options?    The problem is when students are learning to add, we teach a helpful method to use their fingers, then we tell them they have to stop using their fingers and do the math in their head or use a different method.   While with multiplication what if a student finds using multiplication with arrays helpful, they cannot use that method forever because when you get to multiplying bigger numbers it would become too labor intensive to be helpful.   So if we encourage students use a method that works for them, will we be hindering their education because a child may stop using other methods and not want to learn others?    Will giving the option allow students to see that yes, they do have options but chooses to use one verses the other and finds having options a good thing and seek out more ways to solve problems on their own?