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......