October 2005, By Cheryl Feuer Gedzelman
Are you better at math or English? Most people can answer that question easily. For those of you who claim to despise math or just don’t understand it, don’t pass along this attitude to your children. The mystery of math can easily be deciphered. If you can master math facts, fractions, decimals and percents, estimation, and word problems, you have the basics to work with higher level math.
Facts – Math is logical and full of patterns. When first graders learn their math facts (one digit addition and subtraction), they learn patterns. 3+5=8, 5+3=8, 8-5=3, and 8-3=5. 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. My best way to teach children addition and subtraction facts uses four rules:
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.
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 are already using some of these strategies, and you may think they are obvious. However, for many children, direct instruction will increase their fluency with facts. If you have other strategies that have helped you learn facts, these may help your children as well.
Multiplication facts are more difficult to learn. 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, be sure to 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, order a multiplication fact song on CD, 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. The 6, 7 and 8 tables are the most difficult, but 9 has many shortcuts. My favorite is this: 9 X 5 = ? Subtract 1 from 5 to get the first digit, (5-1=4) and for the second digit, count up from there to get to 9. (4+5=9) So the answer is 45. Once multiplication facts are memorized, division facts are easy because they are opposites. Again, patterns are important.
Decimals and Fractions Made Easy – Decimals are easy to learn because at least at the beginning, they can be converted into money. 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%. 1/4=.25=25%. 1/10 = .1=10%. To review fractions, start with ½ a sandwich, 1/8 a pizza, or ¼ of an apple. Play a fraction game. I have one that I use with all ages if I suspect that a student does not really understand what a fraction is. It is called “Fractions are Easy as Pie” and can be ordered from sciencekit.com, item #1716203. For more options, search for “fraction game” at Amazon.com or explore hammett.com for math games and other teaching supplies.
Estimation Counts – 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, 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.
Practice Mental Math – Can your child easily compute 200 + 350? If so, 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 3000+4000, and how impressive! A second grader should be able to quickly add 20 + 18, and add 19 +18 by starting with 20 and then subtracting 1. 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.
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 money will it cost on gas for a family trip if gas costs $2.24 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 elementary school 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. You will be glad you did.