Drowning in Formulas

     I feel like I should go out and plant a forest of trees after all of the paper that I have used to write notes this semester.  One unit that probably took up the most space in my notebook was the unit on area.  Each shape has a different formula, so each shape that I came across, I would start a new section in the notebook.  It got to the point where I was flipping through half of my notebook just to find the correct formula. 

     In order to make my notes more efficient, I went back and re-wrote all of the formulas on one sheet so I wouldn't have to search for them.  This gave me an idea for an activity for my future students.  Instead of just giving them all of the formulas, they could make up their own cheat sheet of formulas.  They could draw or cut out and paste the shapes and then write in the formulas. The following is a very linear example of the chart, the work of the students would not look exactly like this, but it shows a general example.

                                                      source

By having students make their own chart, the are able to take ownership of the resource as well as helping them cement into their memory all of the different formulas that they will need for the assignments.  I always believe it is better to get students working hands-on with the material than just giving them the information are expecting them to remember is all.  This is just not a realistic expectation and it setting both the students as well as the teacher up for frustration.

For more practice finding area, visit this website for an interactive game for students:

                               Area and Perimeter Game

Know Your Place

     When a difficult concept is put to a song or another mnemonic device, it seems to stick with the students so much longer.  I am reminded of my seventh grade science class.  Our teacher was teaching us about place values to the right of the decimal.  He then told us about a mnemonic device that I still remember to this day.  Tom Hardy Took Ted's Happy Meal.  The beginning letter of each word stands for a place value.  I created the following cartoon using ToonDoo in order to illustrate the concept:

Then I started thinking that I did not have a fun trick to teach my future students about place values to the left of the decimal.  I never have to think about it, it is just an automatic thing for me.  I started searching the Internet and came across a song from Mr. R. about place values from ones to hundreds.  Since I found this video, I have not been able to get this song out of my head, which I suppose is the purpose.  It is a catchy song like this that students will be singing every time they need to remember the place values.



It just makes me realize how many resources there are on the Internet and all around us.  There isn't any reason that students should be bored with their learning as long as teachers are willing to think outside of the box and find these fun little activities and presentations that will catch the attention of their students as well as give them tools in order to help them remember all of the information that is presented to them each year in school.  I still see my seventh grade science teacher from time to time and he laughs when I tell him about his silly little sentence that I am still using for my classes this many years later.

For some place value lesson plans, please visit:

                        Understanding Decimal Place Value

                        Ten More and Ten Less

                        Nine Digit Place Value Chart

                        Exploring Additional Patterns





In my PRIME

     It is few and far between when I can open up the assignment for the week and actually know how to do the homework without looking up examples.  This week we were asked to learn about prime numbers.  My elementary math teachers must have done a good job about hammering this definition into my head because the first thing I thought  was "A prime number is a whole number greater than one and is only divisible by one and itself."  I couldn't help but wonder where that little math voice was coming from; I wish it would show up more often.  As I started going through the numbers in my head I felt like I had a relatively strong grip on the concept.  I felt this way until they started shooting larger and larger numbers at us in the homework section.

     I started to think about ways I could double check if a number was a prime number without punching every number from zero to the given number in my calculator.  I started thinking about ways that I know it would not work out to be a prime number.  The most helpful was any even number other than two is not a prime number.  I started thinking of other rules that would work and ended up having to write down all of my wonderful "rules" because I kept forgetting them.  In the end, I realized it was not a practical tool for finding prime numbers since I could not remember a majority of my rules.  I decided to turn to the Internet to simplify the process and came across this website with different helpful ways to figure out prime numbers.  I liked the 2,3,4,5 rule and found this video to spell it out for me.  With these two tools, I could tackle any number my homework through at me.

     Once you get really good at figuring out prime numbers, you can take a peek at this Prime Number Chart to speed up the process.  I would not recommend jumping to this step until you figure out how to actually do the leg work.  If you rely on this chart and never learn the steps, you might as well not even know what a prime number is.  I always believe you have to be able to do things without the assistance of the Internet even though it is such a accessible convenience to many people.

Mental Math

           

           There are so many things I have learned in school that I thought, “When am I ever going to use this information?”  The one lesson that I have never had second thoughts about was mental math.  I use mental math every day without fail.  Until I took these math courses, I never really knew just how often I use it.  It isn’t very often that I walk into a store that I don’t have to figure out a sale price or fill up with gas without first estimating how much it is going to cost me.  I just don’t understand why people rely on their phone calculator for so many things it would be easier to figure out themselves.

Thanks to my love of shopping, my percentage figuring skills are honed to near perfection.  I bet I could figure out a sale price faster than someone having to dig out their cell phone and type in the numbers.  When I see people in the store trying to figure out how much their shirt is going to cost with the 20% off sign looming over their head I just want to go over and explain just how easy it can be.  I always figure out what ten percent is and then adjust accordingly.  You have a $35.00 shirt for 20% off?  Ten percent of this would be $3.50 so 20% would be $7.00.  Your lovely new duds cost you a measly $28.00.  Voilà, it is just that easy.

Another place that I have been able to use this trick is when I am out to eat.  Who needs a tip calculator?  Once again, figure out ten percent and be a good patron and double it leaving my waiter a 20% tip for their hard work.  I have heard of another even faster trick that will allow you to leave a tip between 15-20% every time.  For bills under $100, take the first number of the total bill and double it.  For example, a $48.00 bill would have a tip of $8.00 which is roughly 16.5%.  Either way works just fine and is a faster way of supporting the wait staff.

What is the World is Lattice Multiplication?

There is nothing that makes me feel older than when I hear my method of doing math being called the "old way."  This is especially true to multiplication.  When I was in elementary school, we learned the multiplication tables and had weekly timed tests.  I loved taking these tests and always felt like a rock star when I was able to beat my previous week's time.  As I progressed in grades, I learned what I am going to call the traditional method to doing multiplication (which sounds better than the "old way"). 

This week I was asked to learn a new way to solve a multiplication problem using the Lattice Approach to Multiplication.  I was stuck in my ways and resistant at first.  After solving the problem, I would check it using my preferred method to be sure I did it right.  After a week of letting it sink it, I now see how this would be an easier approach for students.  They are not only asked to find the correct answer, but also are asked to mind their place values.  Who can argue with this two for one approach?  I am finding it harder to do so, even if I continue to do the "traditional" approach myself.  What can I say?  Old habits die hard.

For all of you out there reading this, I have to let you in on a secret.  The Lattice Method has been around since the 13th century, so which method is the old one now?  Either way, I see the value in both.  I feel that my way is faster, but the Lattice Method is a better visual for students to see why they came up with the answer that they did. 

The following is a video explaining how the Lattice Method works.

                                        

                                                    

If you would like to know the history of this method, please visit this website on Lattice Multiplication.

Just remember, you youngsters, before you call someone old, that both ways come up with the same answer!

Walk a Mile in Their Shoes

               I sat down to do my homework this week and I see that it is about place values.  The first thought that comes to mind is this is going to be one of those ten minute assignments.  I could not have been more wrong.  Sure I understand the standard place value system that we were taught all those years ago.  What we were asked to learn however was so much more complex than that.   We had to learn how to use three different number systems.  They were the:

         Babylonian Numerals

http://www.mathsisgoodforyou.com/numerals/babylonian.htm

    
    Mayan Numerals

http://frontiers-of-anthropology.blogspot.com/2011_05_01_archive.html

                                        
    Roman Numerals

                                       http://www.mathatube.com/tables-charts-roman-numeral-chart-html.html


 Not only did I have to learn the place value difference, I had to learn the number system and then apply all of this knowledge.  I could clearly see that this was not going to be the ten minute assignment of my dreams.

                As I was going through and writing all of the symbols out and then trying to remember how to translate it back into our system I could not help by wonder why we would need to know this.  Then it hit me.  This is how students feel when they are asked to figure out place values in the first place.  They have not yet been trained to simply look at the number 16 and know that the one really means ten.  They just finished learning that that funny symbol means one and now all of the sudden it is supposed to mean ten?  I can see how this would be confusing.

 The feelings that I was having are similar to what my future students might feel when they are being presented with this strange new concept.  I now can sympathize with them and help them to work through it before frustration sets in.  Not only this, but I know I will never look at the number 16 or any other number the same again.  I have been taking the system for granted and through this activity I was forced to step back and truly learn why the place value system is set up the way that it is.

For an example of difference numeral systems, check out the following websites:

          Place Value System of Numeration

 Fact Monster

 IXL Learning