Mastering the Mysteries of Math
By Cheryl Feuer Gedzelman
I love math because there is usually one answer to every problem. What else in life can give us so much certainty? Some people just don’t appreciate math, and often the reason is because they never mastered the basics. The mystery of math can easily be deciphered. If you can master math facts, fractions, decimals and percents, estimation, word problems, and basic algebra and geometry, you have the fundamentals to be literate in functional math and can comfortably ease into higher level math.
Math is logical and full of patterns. Most elementary schools use math manipulatives such as counters, so children can see exactly what they are doing. In order to advance to more complicated problems, children need to know their facts fluently and automatically. Many children learn them just from all the repetition on their worksheets, but others need more practice at home.
Addition and Subtraction:
- The Doubling Rule: Memorize all doubles, such as 6+6=12, and then it is easy to see that 6+7=13 and 6+8=14. This rule works well for addends that are close together. The same principle holds for subtraction. 12-6=6, so 12-7 must be 5.
- The Switch-Around: For addition, always start with the larger number, even if you have to switch the numbers around. For 3+8, switch to 8+3. This rule works well for addends that are far apart. Later, use math properties (commutative, associative and distributive) to manipulate numbers.
- Counting Backwards: For subtraction, when a small number is subtracted from a large number, just count backwards. 12-2=10.
- Counting Up: For subtraction, when numbers are close to each other, such as 9-7, counting up, from 7 to 9, works best.
Many adults use some of these strategies, and you may think they are obvious. However, for many children, direct instruction will increase their fluency with facts.
You cannot get away with just counting very fast in a pinch because this will slow you down tremendously and increase careless errors. Children who memorize multiplication facts by third grade will have a much easier time solving more complicated multiplication problems, division, proportions, algebra and more. While your child is learning multiplication facts in school, follow along and make sure he knows each number before going onto the next. To make the tables easier to learn, you can use computer software, make up silly rhymes, learn a multiplication fact song, or put flash cards of the difficult facts in your child’s room and review them several times a day. Short on time? The car is a great place for review. If you notice that your child does not know the multiplication tables, go through the flash cards and find out which ones he doesn’t know. It will probably be just a handful or two. Mastery will be manageable and achievable.
Once multiplication facts are memorized, division facts are easy because they are opposites. Patterns are important.
Decimals and Fractions
Decimals are easy to learn because, at least at the beginning, they can be converted into money, and children are usually motivated by money. It is imperative to understand that decimals are the same as fractions and percents, in a different format. Everyone needs to know certain basic relationships: ½ = .5 = 50%. ¼ =.25=25%. 1/10 = .1=10%. To review fractions, start with ½ a sandwich, 1/8 a pizza or ¼ of an apple. Later, children will discover that ratios and proportions are another way of looking at fractions.
Every elementary school textbook has a unit on estimation, but it is important to incorporate rounding and estimating when solving all problems. For example, if you compute the problem 500-250 and get 25, you can’t accept that answer because you know that the answer has to be in the hundreds. When reviewing homework with your child, teach him how to make sure the answers are logical choices based on estimation. A good practical exercise is to go grocery shopping and estimate the total by rounding the price of each item. Then see how close you came to the actual total.
Practice Mental Math
Can your child easily compute 200 + 350? How about 200 + 351? Mental math takes your knowledge of math facts and estimation further by generalizing to bigger numbers. Any first grader who can add 3+4 can also add 300 + 400 or 3,000+4,000. A second grader should be able to quickly add 20 + 18 and add 19 +18 by starting with 20 and then subtracting 1. This also works with multiplication. Mental math exercises keep your brain active and keep up math skills and math fluency. The car is a great place to challenge each other.
Many games incorporate logic and math and can improve math skills. These include Connect Four, Chess, Checkers, Sudoku, Go, Professor Layton Games, puzzles on the DS, and any game that involves planning moves ahead or logical deductive reasoning. Logic skills will become vital later on for standardized tests as well as geometric proofs and calculus.
Life is Full of Word Problems
Word problems do not have to be scary. The most important part of attacking a word problem is to understand what the question is asking. Then, make the problem more manageable by taking notes, writing down the problem, drawing a picture or creating a chart. If possible, plug in the answer at the end to see if it works. (Plugging in the answer is also a great strategy for algebra equations).
Finally, do not miss the opportunity to use math in everyday life. Word problems come up all the time – be sure to let your children help solve them. Challenge your children by making up word problems. For example, how much will it cost in gas for a family trip if gas costs $2.78 a gallon, the car gets 20 miles/gallon, and the trip is 220 miles each way? You can make up all sorts of problems and even make them fun and silly.
Most importantly, do not let your children fall behind in math because catching up is difficult. Every aspect of math is a stepping stone, and proficiency is necessary to succeed at the next steps. At the first signs of trouble, get your child extra help from a family member, teacher or tutor. Your child will appreciate it.