Here's an example of long division, as will be shown in my kids book for math

Word problems are the most difficult for many students to master. What I try to do with all word problems is write an equation to the problem as I am reading it, if at all possible. Look for key words such as "sum" "more than" "difference" "times" "of" "is equal". Each one of them tells you a certain mathematical operation that goes in an equation

Difference  "minus"
More than, sum "plus"
Of "multiplication"
Is equal "equals sign"
Product "multiplication'
Quotient "division"
Square of "to the second power"


Look for these key words to help you set up your equations to your word problems more easily.

Here's a three by two multiplication problem that I illustrate in my new book that I plan to write. The idea is to provide easy step by step instructions to students just learning multiplcation.

I'm in the midst of writing a math book for kids. Here's a sample of how I explain a subtraction problem involving borrowing.

2 by 2 multiplication illustrated

No lattice multiplication here, this is simple, traditional, 2 by 2 multiplication explained with an illustration.

Suppose you had an arithmetic sequence such as 1, 4, 7, 10, 13, .....    and you wish to find the sum of the first 50 terms of the sequence. You could take all 50 terms and add them together, but that is time consuming. There are some simple formulas you can use to get the answer.

Sn (sum of the first n terms) is the average of the first and last term multiplied by the number of terms. Written as a formula this is Sn = n[(a1 + an)/2] where a1 is the first term and an is the last term.

To find the 50th term we use the formula

an = a1 + (n-1)d, where d is the common difference between the terms. You can clearly see that common difference is 3.

so the 50th term is 1 + (50-1)(3) = 148

Now to get the sum, we get Sn = 50(1 + 148)/2 = 25(149) = 3,725

Understanding Betting Odds and Potential Payouts

Although not exactly a math article, this does relate somewhat to math.

With football season approaching, many fans will start engaging in their fantasy football leagues and betting on games. Fans will check the numbers for point spreads, over/under and moneylines, to name a few. For the novice, this is all very confusing, not only to understand what the numbers mean, but also potential payouts and losses. I am not a gambler and am not taking a stand on whether or not someone should gamble, but have a strong statistical and overall mathematical background and can explain these betting concepts. So without any further disclaimers, call this "understanding betting odds 101."

The first popular betting line is called the "moneyline", which is a bet to who will win the game without a point spread or other variable. These lines are typically displayed first. When betting on the moneyline, the favorite will have a negative sign (-) in front of the number and the underdog will have a positive sign (+) next to the number. So suppose the Altanta Falcons are playing the Jacksonville Jaguars. Next to the Falcons you see -300 and next to the Jaguars you see +150. This means that you have to bet $3 on the Falcons for a profit of $1. If you bet $300 on the Falcons and the Falcons win, your payout if $400, for a profit of $100. So basically, it's a dollar profit for every three dollars you bet. If you bet on the Jaguars, you pocket $1.50 for every $1 you bet. Betting on strictly the winner of the game using the moneyline is typically called a "pick em" game.


The most common type of bet is the "point spread", which allows people to bet on the difference in score between the two teams. Once again, the team that is favorite will have a negative sign in front of the number, while the underdog has a positive sign next to the number. For example, suppose the Pittsburgh Steelers are playing the Dallas Cowboys and the Steelers are -6 on the point spread and the Cowboys are +6. That means the Steelers are a six point favorite, so if you bet on the Steelers using the point spread, they have to win by at least seven for you to win. If the Steelers win by six, there is a push and you get your money back. Any win of less than six or a loss and you lose the money you wagered.

Sometimes you will see a 1/2 or a .5 with the point spread. What is the significance of this? For example, you might see a game with the San Francisco 49ers against the Green Bay Packers and the Packers are -3.5 or -3 1/2. That means there is no chance for a push and some bettors may shy away from such a game. if you bet the Packers, they must win by at least four or you lose. There is no chance of getting your money back and breaking even when there is a 1/2 or .5 involved in the spread.

There is also the total score or the over/under, which lets you bet on whether or not the total score for both teams exceeds or fails to meet the predetermined amount. The over/under can also be for specific players total yards, touchdowns, teams combined yards, team wins for a season, etc. For example, suppose the Philadelphia Eagles are hosting the New York Giants and the over/under for the game is 48. If you bet "over", the teams have to score more then 48 points for you to win the bet. If they score exactly 48, there is a push and you get your money back. Again, if there is a 1/2 or .5, there is no chance for a push.

Typically, the moneyline given on the spread are -110 unless otherwise noted. If one side is receiving a lot of bets, the odds makers may adjust the lines accordingly in an effort to balance the action. Remember that you can also bet on a point spread on a whole game, part of the game, just look to see what kind of bets are being offered.

This guide is useful for those betting for money and even those who are picking games with their buddies without money involved, just for bragging rights. There are other more complex types of bets, but the one's listed above are the most common.

Enjoy the games, have fun and good luck with your bets!