Fast Fractions

In an earlier post, I talked about fast math. We used the difference from 10 or 100 to multiply larger numbers quickly. We can also talk about fast fractions…

Adding fractions that do not have a common denominator is not always easy. Traditionally, we are tasked with finding the LCD and then we convert both fractions to equivalent fractions with that LCD and FINALLY, we can add them. Fast Fractions takes out a step and a half.

Let’s start with 2/3 + 3/5.

Multiply the denominator of the first fraction by the numerator of the second, then do the same with the denominator of the second and the numerator of the first. Multiply both of the denominators.

2       ₊    3   =        (5 x 2) + (3 x 3)   =    10+9  =   19

3             5                        15                     15         15

(I apologize for the sloppy fractions…I couldn’t get them to display vertically any other way.)

Simplify your answer, if needed, and Viola! You have added your fractions.

Myths

I was recently reading an alumni magazine when I came across an article by a professor that was enumerating the common math myths and I thought it would be good to pass along…

Myth 1 – Men are better at math than women

There has been no research that proves this to be true. It is true that the mathematical sciences are filled with men, no question. The real question is why aren’t there more women there? There are so many theories out there; Nature vs. Nurture, The math classes are boy centric, the list goes on. The bottom line is: get the girls out there!

Myth 2 – Math is not creative

Math IS creative. You need to have a creative, problem solving mind to attack a lot of the math problems you encounter in the real world.

Myth 3 - There is one way to solve a problem.

There is no one “right way” to solve any problem, there are multiple ways to get the right answer. Think about planning a party, there are many ways to decide how much cake everyone will get.

Myth 4 –  You need to memorize a lot of facts, rules and formulas to be good at math.

Memorization is not nearly as effective as understanding the concepts. Think about the multiplication facts that most of us memorized as kids. We know from memorization that 4x4 is 16, but we also know conceptually that his also represents 4 groups of 4.

Polly Gone Crackers

So, you need to remember all of the polygon prefixes by 8 AM tomorrow, but you can’t remember the difference between a pentagon and a heptagon. Bummer.  What’s a kid to do? Have you tried MNEMONICS? No, not Satan worship…that another blog all together! I am talking using a form of word association to connect those pesky prefixes to the numbers they represent.  Most students will know how many sides a TRIangle has. But how many sides does a nonagon have? The nonagon has NINE sides. To help you remember that Nona means nine, make up a story about nona…Nona could be your crazy Aunt Nona who has nine fingers or, you could use the fact that Nona and Nine both start with N. The point is, find a story that you can remember that will firmly associate the prefix and the number.

Here are some of my favorite associations if you get stuck….

Triangle : Tri=3 : Tricycle, Trident has 3 points (think Little Mermaid)

Quadrangle: Quad=4: Quad at a school has 4 walls, there is an ATV called a Quad with 4 wheels.

Pentagon: Penta=5: There are 5 letters in Penta, there are 5 points on a star named Penta.

Hexagon: Hex=6:  SIX and HEX both end in X, both have 3 letters

Heptagon: Hepta=7:

Octagon: Oct=8 – octopus…

Nonagon: Nona=9: see story above

Decagon: Deca=10 : a ‘deck of’ 10 cards

Undecagon: Undeca=11: Think UN is like 1 and DECA is 10 so  10+1=11

Dodecagon: Dodeca=12:  DOS (Spanish 2) + DECA (10)=12

Money Makes the World Go 'round (Part 2)

For the middle schoolers and high schoolers everywhere. Cell phone roulette....

Did you know that, according to GeekSugar.com, teens are typically sending around 3000 texts per month?!! This frightens me. It should frighten everyone.

We've all heard the cries of our teens.."But MOM, everyone else has a cell phone, I HAVE to have one now!" Granted, the social stigma of tecnological inferiority is daunting, but those crazy kids have no idea what it means to a household budget! There are so many plans out there, all claiming the best service and the lowest prices.  If your kid is clamoring to raise thire social status with a new smartphone, have them do the math. Start by having them research phone plans.  Use the rate of 3000 texts per month as a baseline. Don't forget to have them look at the talk time.... Have them poll friends on their talk time usage. (You should poll your friends too on the kids usage in other households…) Every house has their own budget, adn the student needs to find a plan that will fit in without taking food off of the table for everyone else.

Did someone say fractions?

The lament of students and parents alike….Ugh, fractions. Why do we need them? They are very helpful in describing quantities in relationship to each other….”Only give Suzy half the box of frosted yum-yums dear, we don’t want to make her hyper…” This concept is usually a pretty easy one to grasp, especially when dealing with easy fractions like halfs, quarters, and thirds. It gets a little trickier when dealing in fifths, sixths and tenths.

A more difficult concept to grasp is comparing fractions…which is more 2/3 or ¾? 3/5 or 5/6? There are graphical ways to look at this and there are mathematical ways to look at this. If your child is more of a visual learner, I suggest making fraction bars from different colored pieces of paper (or white…you can use colored pencils to give them color – I don’t really recommend using markers for this – it gets really messy very quickly.) The most important thing is each piece of paper needs to be THE EXACT SAME SIZE! You need one piece of paper for each denominator that you want to compare. So, for example, say we want to compare halves, thirds, fourths, fifths and tenths; we would need 5 sheets of paper that are the exact same size. We are going to use folds to separate our pieces of paper (the whole) into its parts. For ½ - just fold the paper in half. Place the short ends together and make a nice crease down the middle. Next make the fourths. Once again, with a new piece of paper, place the short ends together and make a nice crease. Then, do it again. You should end up with four equal sections.  For the thirds and the fifths, help your child by marking the measurements for the thirds and fifths and having them fold the paper along the lines, accordion style. Make 2 sets for the fifths and fold one of the fifths in half again to get the 10ths. You now have 5 wholes separated into different parts. You can now compare fractions….what does 8/10 look like? Compare it to 2/3. Which is more of the whole? Can you find fractions that are equivalent? That have the exact same part of the whole?

You can play fraction top-it if you have 2 or 3 decks of cards you don’t mind blending…make a pile of numerators and a pile of denominators. The numerators be the 1, 2 , and 3’s , the denominators should be the 4, 5, 6, 8, 10. (you should have fraction strips to match each denominator for fact checking…)Each person makes a fraction; the person with the largest fraction (biggest part of the whole) wins the cards. If there is a challenge as to whose is bigger, go to the fraction strips. If the challenger wins, the challenged has to give them 2 extra cards.

As always…practice, practice, practice.

Puzzling

What can be better on a rainy summer Sunday that whiling away the hours flexing your math brain? “What?” you say..”The only math brain I am flexing on a summer Sunday is figuring out if I can cram 3 whole pancakes in my mouth at one time.” But, I am willing to bet you have been doing mental calisthenics without even thinking about it. Of course, I am talking about jigsaw puzzles.  On a recent weekend, I was lolling about with the kids, when the 8 year old grabbed a puzzle and quietly retreated to the game room. One by one, every member of my family was lost to the power of the puzzle. Jigsaw puzzles are not only great rainy day entertainment, they work that summer-slackened brain. Keeping it  thinking logically (No that piece can’t go there…not the right color red) thinking spatially (this little piggy goes somewhere over here…) and methodically (Start with the edges…work your way in.) You don’t have to get the 5000 piece circular puzzle to reap the benefits, start with 100 pieces and work your way up!

The End of Pi?

Did everyone hear about the fight to stop using pi and start using tau? No? Seriously? Every June 28^th for the last 10 years, there has been a call to stop using Pi in favor of using Tau. Granted, the call is from a small rogue band of mathematicians and physicist, but the call makes it to national news outlets. (Think yahoo news and NPR, not CBS nightly..) There is no argument against the value of Pi or the important role it plays in the circle, the argument is that Pi isn’t very useful in most of the calculations we need to do with circles. Tau is no mystery number; it is equal to 2 π.  So, for example, when teaching students about radians, you could say a ½ circle= ½Tau radians. There’s more parity. Yeah, yeah…I get it, but seriously, do we need to upset the apple cart here? No.

Why Not? Because there is no humor in Tau. Right now, there is a dearth of math humor for the middle school set; we need to keep the giggles going here. On March 14^th of every year (Pi day…) middle schoolers everywhere bake pies in the shape of Pi. What would they do for Tau day? (Not that they are in school at that time….) Would they make towels in the shape of Tau? Boooo-ring.  What about the t-shirt business?

i 8 sum pi...hahahaha!                                           Chicken Pot Pi

                       You just can't do this with tau......

Practice, practice, practice

Homework. The word is dreaded by students. Parents have a love/hate relationship with it. But, what’s the point? School systems are moving away from homework being a large part of one’s grade, so why do we subject the kids to it?  Practice.  Seriously. We don’t get better at anything without practice. In math it is especially true. Practice makes basic math facts automatic and allows us to see the patterns lurking right before us. What’s a parent to do? I have a list of favorite sites that help my own kids and my students bone up on their math minutes,

http://www.helpingwithmath.com/resources/tab_multiplication_tables.htm  This site is great for multiplication drill practice.

http://www.math-drills.com/  This site is my favorite all-around site for math. It has elementary to high school practice sheets. Addition, fractions, geometry.

http://nces.ed.gov/nceskids/createagraph/default.aspx?ID=f8529ab2e6e24a7694fba30b5b178d9d  This is a site sponsored by the National Center for Educational Statistics. It is a nice graphing interface.

Practice, practice, practice.

CSS for Class

I have a love/hate with the HTML and CSS. None of the background colors that I really liked seemed to want to cooperate, nor would my favorite fonts. I did manage to get things to go where I wanted them to, which kept me from throwing the laptop across the room. So, in summation, I am sure it is just operator error, but I am still a bit frustrated.


My Site:http://ceweb.uml.edu/tmoul28868/index.html

The Ancient Calculator

While I was researching math topics for a video web page, I encountered the abacus. Granted I know what an abacus is, my daughter, on the other hand, did not. I was surpised by this, but should I be really? Well, no. It is an outdated, outmoded tool. But it's also still used today in many countries. I can't help but think that  understanding how to use this tool, con only bolster one's basic math grasp.

Watch the video...see if you're as surprised as I was.

Wow..there's more than one kind of abacus? It's useful in counting systems other than base 10! (ie: hexadecimal) I also learned that abaci, in one form or another, have been around since 500 BC! Dating back to writings from Ovid!

Amazing!

Fast Math

Recently, one of my neighbors was asking me about this infomercial she had seen. A man claimed he could teach kids to multiply large numbers in their head. I managed to catch a short piece of it on TV and I, too was captivated by the thought of it. Wouldn't it be nice if it were true? I would love it if my students could escape the drudgery of long multiplication and really focus on the lesson at hand, because sometimes students get hung up. They encounter a problem that requires that they do a bit of long multiplication and they lose sight of the larger problem. I was intrigued. Naturally, I went searching for possible sources for this amazing method. What I found: Vedic Maths.

What is Vedic Maths?

According to VedicMaths.org:

"Vedic Mathematics is the name given to the ancient system of Indian Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). According to his research all of mathematics is based on sixteen Sutras, or word-formulae. For example, 'Vertically and Crosswise` is one of these Sutras. These formulae describe the way the mind naturally works and are therefore a great help in directing the student to the appropriate method of solution."

I looked around the site and I found that these methods were really neat and REALLY fast! 

Let’s start with multiplying single digits…

                A relatively simple example is 6 x 7. Set up traditionally, but also write in each difference from 10

                                6         4

                    X         8         2

Working from left to right, choose either cross difference…in the example, you could choose 6-2 or 8-4, either way, the difference is 4. This is your 10’s place. Now, multiply the 2 and the 4 to get 8. This is your one’s place, the answer is 48.

For multiplying double digit numbers, it’s very much the same, except, you work out of 100.

                Let’s work with 81 and 92.

                            89           11

                 X         92           8

Choose either cross difference, 89-8 or 92-11. In either case, the difference is 81. These are the first digits of your answer. Now multiply the 8 and the 11 to get 88 and these are the last 2 numbers. The answer is 8188.

Neither of these examples had “carries” where the multiplied digits were greater than 1 digit for the singles and 2 digits for the doubles. If they had, it would be very similar to what you do now, you would carry the extra digit over.

Well…that was my explanation of how that guy got those kids to be multiplication wizards in minutes. Try it yourself at home, make up a few problems and you, too will be a human calculator!

I have said it before, I will say it again..patterns are the key to successfully mastering more advanced math topics, like algebra. In my experience in the classroom, I have found that the student who have mastered their math facts have a significant advantage over those who do not. What’s a parent to do? A simple answer is: math games. A complicated answer is: make math important in your daily life.

In previous posts I have described a few of the Everyday Math games that foster basic math fact awareness. Games like Top-It for addition, subtraction and multiplication really  get students (and parents) thinking about their basic skills. But, it’s one thing to be able to know that 11+25 is 36, it’s another thing altogether to recognize that there are many ways to make 36. (2x18, 3x12, 4x9, 6x6 or all of the addition/subtraction facts that go along with that particular number.) To this end, there are a few games and puzzles that you can play or do that will foster recognition.

My favorite flexible math game for thinking forward/backwards and sideways about math is Target Practice. This is a game where you have to “make” the target number from the cards you have been given. In easier versions you only use addition and subtraction of positive numbers. This is ideal for kids who are in K-2^nd grade. As they learn about integers, you can start using numbers below zero. After they learn multiplication and division facts you can incorporate those into the game as well.

If your child is more of a visual thinker, you can introduce Ken-Ken as a way to promote pattern seeking thought. Ken-ken  is a soduko like puzzle that uses addition, subtraction and multiplication.

Each "block" is defined by a number and an operation. The number is the total for that block and the operation is the only operation used in that block. )if the operation is multiplication, all the numbers are multiplied to get the total.) The catch is, the number of blocks across the whole puzzle defines the numbers in the puzzle. In this example, there are four block across, thus the mumbers used in the puzzle are 1 thru 4. No numbers can be repeated in a row or column.

If you'd like to try it on-line go to http://www.kenken.com/index.html for puzzles and tips.

Happy mathing!

Tracey M

Money Makes the World go 'Round (part 1)

Money and math go hand in hand. We use money every day, it is a critical part of our everyday existence. When should we start talking money to our kids? Yesterday. Today. Tomorrow. Keep it going. But how? You guessed it…my favorite way to keep the math going at home. Games!

For the K-2^nd grade set.

Penny Exchange. Grab that piggy bank and raid it for pennies, nickels, dimes and quarters! This game helps the kiddos learn the value of our different coins and that 5 pennies is the same as a nickel.

You need:

1 die

A pile of pennies (at least 15 per person)

A pile of nickels (5 per person)

A Pile of dimes (3 per person)

A pile of quarters (4 per person)

The first player rolls the die and collects the number of pennies equal to the number of the roll. The player then gets to “exchange” their pennies (or other coins) for coins of higher rank. For example, if the first roll was a 6, the player would collect their 6 pennies, then exchange 5 of them for a nickel. Play then goes to the next player, who does the same thing…roll, exchange, pass on. The first person to get to a (quarter, dollar, 5 dollars) is the winner.

For the 3rd-5th group.

Monopoly.  Just do it. I know, the game goes for DAYS, but it can be a great tool for understanding how to use money..For example, can you really afford Park Place right now? Saving until you can afford to put up a house. Don’t go to jail. All valuable lessons.

Another game to play is “Budget.”  I give my daughter a “budget” of 5 dollars at the food store for her favorite snacks for the week. She can choose anything that is NOT candy but she has to stay under the 5 dollars. (I am going to spend it anyway, so I let her do the decision making. ) Fruits and vegetables are free.

Money is very important. The sooner we get kids comfortable with money, the better. Happy Mathing!

(If you need money direction for middlers and high schoolers, tune in next week!)

Introductions

Hello, my name is Tracey Moulaison and I have created this blog for my class "Exploring the Internet." I am working diligently towards a degree in Math and Education, with high hopes of becoming a middle or high school math teacher. "But WHY???" you cry in fear and desperation. "Math is awful, boring and painful. Add that to middle school drama and you are OUT of YOUR MIND!!!"  Yes, I know. I have heard this rant from friends, family, strangers on a bus...My response to all is this: I have had such great experiences working with kids from elementary to high school, that I know I have found what I am meant to do.

In the meantime, I am working at a textbook publishing firm. I spend my days working out problems, checking solutions and crafting guided solution processes for middle school math texts. The work is satisfying and, dare I say it, fun. I didn't think I would like it as much as I do. You see, this has been an extreme change for me, as I came from a long term substitute position at a middle school. I was used to a lot of movement and noise in my day. Coming to the quiet (so very quiet) world of publishing was a bit of a shocker. If it was quiet at the middle school, I got suspicious! But, I am getting used to it.

I am also mom to 2 bright and beautiful girls, wife to one sweet and generous man, and caretaker of far too many furry and finned beings.