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by Josh Rappaport
Homeschoolers, do you have a child taking algebra who is pulling out her hairs? Are your hairs starting to come out as a result?
If so, you’re not alone. Many students wrestle with this subject. And many parents feel at a loss because they have forgotten the dreaded algebra.
I know because I’m a math tutor and the author of two books on algebra. I’ve seen firsthand just how difficult this subject can be both for children and parents.
The goods news, though, is that even if you don’t remember (or care to remember) algebra, you can help your kids by using a few key tips. And these tips are actually fun to put into practice.
What I’ll describe are the warning signs that your child is struggling with algebra, what the signs mean, and what you can do to turn the situation around.
1. WHAT YOU HEAR: “Yuck! Why are there letters in my math assignment?”
THE ISSUE: Your child does not grasp the concept of a variable.
SOLUTION: Tell your child that variables are just there to stand for an unknown number.
Here’s one way to put it. At the end of a murder mystery, the detective says: “Aha, so the killer was Mrs. Jones!”
At the end of an algebra problem (many algebra problems, at least), the student says, “Aha, the variable (often the letter ‘x’) stands for 7!”
Solving for a variable is just like solving for a mysterious criminal. You use the clues that you have (the terms in the equation) to lead you to the answer.
You can go even further to demystify the idea of a variable by using the word “what” in place of the variable. So the problem 3x = 18 can be thought of as: Three times “what” equals 18.
Any kid who knows his times tables knows that x, in this case, must be 6. And that’s a great first step toward mastery over algebra.
Once your child has that idea in place, try slightly more complicated equations, like: 3x + 2 = 17
Translation: three times “what” plus 2 equals 11. Or, phrased differently: I’m thinking of a number. If you multiply this number by 3, then add 2, you get 17 (that’s easier, isn’t it?). What’s the number? Most kids can get the answer, 5, mentally, just by playing around a bit.
2. WHAT YOU HEAR: “Don’t worry, mom. I totally get positive and negative numbers.”
THE ISSUE: Your child has no clue how to work with positive and negative numbers. (This problem is so common it is seriously not funny.)
SOLUTION: Tell your child that s/he can use money
(ka-ching) stories to make sense of those positive and negative numbers.
Your child just needs to think about positive numbers as representing money she HAS or GETS. (They love this part.) Then they can think of negative numbers as money they OWE. (They will change this to money you owe them.)
Anyhow, with these new concepts in place, they can translate problems into situations they understand.
Ex. 1: ¬ - 3 – 5 Here’s the situation. You OWE one friend $3, and you OWE another friend $5. What’s your bottom line? O.K., this is so easy that everyone gets it: you OWE a total of $8. That means the answer is – 8. It’s that simple.
Ex. 2: + 3 + 5 Here’s the situation. You GET $3 from your rich Aunt Harriet, and you GET $5 from your rich Uncle Bert. What’s your bottom line? Again, this is easy as pie. You end up GETTING a total of $8, so the answer is + 8.
Ex. 3: - 3 + 5 Here’s where your kids need to start thinking. They OWE their friend $3, but they HAVE $5. In the world of algebra, you always have to pay people off as much as you owe them. So you pay your creditor $3, and you’re still HAVE $2. So the answer is + 2.
The answer is always how YOU end up in these stories.
Ex. 4: - 5 + 3 is the situation. This is just the opposite of the situation right above. Now you OWE your friend $5, but you HAVE $3. You give their friend the $3 you have, but darn, you still OWE $2, so the answer is – 2.
Practice these ideas by giving each other situations, turning them into math problems, and solving them. I guarantee that if you develop a story foundation for problems involving positive and negative numbers, children will gain an understanding that lets them reason out the answer.
3. WHAT YOU HEAR: “All I have left are a couple of easy word problems. I’ll do them as soon as I come back from skateboarding.”
THE ISSUE: Your child’s fear of word problems is exceeded only by his fear of acne.
SOLUTION: Tell your child that he can actually do word problems, and that three tips will help a lot:
a) Restate.
b) Look for the question.
c) Change the numbers.
a) Restating the problem. This just means having your child read the problem, one sentence at a time, and put it into her own words. This allows your child to “digest” the problem. When kids do this, it’s remarkable how they suddenly grasp the situation, and then begin making progress.
Here’s an example of a word problem and its restatement. Note: I’m using a fairly simple problem, to get the idea across, but you can use this same technique no matter how difficult the problem.
THE PROBLEM: If Hilbert runs 323 feet in 17 seconds, how many feet can he run in 29 seconds?
YOUR CHILD’S RESTATEMENT: “O.K, there’s this guy named Hilbert (weird name, huh?). Anyhow, he’s running around, and he finds out that he can run 323 feet in 17 seconds. (Don’t ask me why he’s timing this!) Now he wants to know how many feet he can run in 29 seconds.”
b) Look for the question. In the example we just gave, you would have your child underline (or highlight) the part of the problem that asks the question, the phrase: how far can he run in 29 seconds? This helps children realize what they are trying to figure out. That helps them orient themselves toward finding the solution.
c) “Change the numbers”: If your child is like many children, she may feel stumped by this problem about Hilbert. It turns out that even though kids will say, “I have no idea what to do,” what’s often happening is that they are just getting intimidated by the big, unfriendly numbers in a problem, not the problem itself.
My third trick, “changing the numbers” helps kids over this intimidation hurdle.
Say the problem again, maintaining the wording, but changing the numbers to EASY numbers (usually round numbers, or multiples of 10).
The problem after “changing the numbers” : If Hilbert can run 200 feet in 10 seconds, how far can he run in 30 seconds?
After this change, your child might suddenly see that he can figure out Hilbert’s rate by dividing 200 by 10, for a rate of 20 feet per second. After that, he may just see that he just multiplies that rate, 20 feet per second, by the new number of seconds, 30, to get the answer: 600 feet.
Hold on, you say. What good is that? It’s not the actual problem!
True, but it DOES help because now your child knows the method for solving the actual problem. He knows to divide the number of feet by the number of seconds to get the rate. Then to multiply he rate by the number of seconds to get the distance, which is the answer.
So now your child can go back to the original problem and solve, like this:
323 feet ÷ 17 seconds = 19 feet/second
19 feet/second x 29 seconds = 551 feet in 29 seconds.
The once-intimidating problem has been slayed.
4. WHAT YOU HEAR: “Problem 9: Let’s see. I think I’ll do this one later. Problem 10: Um, probably do this later, too. Problem 11: … Hmmm, maybe I should work on my English now.”
THE ISSUE: Your child is freaking out about all the rules of algebra. There are so many rules, and they all look so similar, and they’re all insanely abstract. Result: these rules have turned your child’s brain to spaghetti — temporarily, of course.
SOLUTION: Sit down with your child and make FLASHCARDS for the rules that are driving your child crazy (usually the rules in the lesson your child is working on, and often a few rules before that, too).
Then have you child start memorizing these rules by going through the flash cards, just as earlier he memorized the multiplication tables. The rules of algebra need just as much attention. You might even set up some system of rewards for getting the rules memorized. Even teenagers enjoy rewards.
Here’s an example. Suppose your child is losing his cool on a section that deals with the rules for exponents. Remember that exponents are those teeny numbers that sit on the upper right shoulder of normal-sized numbers or variables.
Here are two of the rules for which you’d want to make flash cards because kids are forever mixing them up.
Same-Base Product Rule: (a^y) (a^z) = a^(y + z)
and
Exponent-to-Exponent Rule: (a^y)^z = a^(y x z) (that’s not an “x” in parentheses; it’s the times sign)
When making flash cards for these rules, don’t put the whole rule on one side. Instead, make it a game. Put the name of the rule and the problem on one side of the flashcard. And put the answer on the other side.
So for the first rule, your flash card will look like this:
[Side 1:] Same-Base Product Rule —
(a^y) (a^z) =
[Side 2:]
= a^(y + z)
That’s it! To give your child even more practice, though, I suggest making one more flash card for each rule. For this other flash card, keep the bases as numbers but make the exponents actual numbers.
So the format for thee other flash cards would be:
Same-Base Product Rule: (x^3) (x^5) = x^(3 + 5) = x^8
and
Exponent-to-Exponent Rule: (x^3) (^5) = x^(3 x 5) = x^15
Giving students actual numbers to work with allows them to grasp the rule in a more concrete way. This is very helpful, as they will mostly be working with these rules in a concrete way in their curriculum. You might be wondering: what about all of the other rules. How do I figure out how to make flash cards for them?
Simple. Just find out where your child is having trouble. Go to that section of the book and look for all of the rules. Textbooks usually set off rules in shadow boxes. Take each rule and make a dual-sided flash card for it.
By the way, since you’re making dual-sided flash cards, you’re getting two for the price of one. In other words, children can not only use the flash cards from front to back, they can also use them from back to front.
Example for the Same-Base Product Rule (above), children could begin by looking at the Side 2 with:
= a^(y + z)
Then she could challenge herself to figure out what is on the Side 1, namely:
(a^y) (a^z) =
Quiz your child with the flash cards, or just watch them go through their set of flash cards. I guarantee that as their knowledge of algebra’s rules solidifies, so will their understanding and grades.
5. WHAT YOU HEAR: “My stupid points won’t stay on the line. What’s their problem?!”
THE ISSUE: This is a coordinate plane issue. Remember the x-y coordinate plane, with its grid lines running vertically and horizontally? For some reason a lot of kids today do their coordinate plane work without using graph paper, by making their own coordinate planes (Don’t ask me why!) As a result they often plot their points inaccurately, and as a result they don’t necessarily know if their points really lie on a straight line (they need to know this for loads of Algebra 1 problems).
SOLUTION: Too easy to be true. Just buy graph paper from any office supply store, like Staples, Office Depot, or better yet, a locally owned one. (Or make graph paper yourself in a page layout program like InDesign®). Then make sure your child uses the graph paper, along with a 6-inch ruler to draw her lines.
Most textbooks today show students how to set up their work on graph paper. If your child uses graph paper, she’ll reap these rewards:
a) It will be easier to set up each graph. She just needs to trace over lines, instead of creating a whole new graph for every problem. Less stress leads to better attitudes leads to better performance at math.
b) Your child will find it easier to plot points. The points will all (or almost all) lie at the intersections of lines on the graph paper, like the point (3, 5). That makes them easy to find and plot.
c) With points plotted accurately, your child will be able to see the lines connecting the points she plots. And in later algebra, the curves she plots, like parabolas will also look better, more symmetrical.
So it’s a win-win-win to go with graph paper.
6.WHAT YOU HEAR: “These answers in the back of the book have gotta be wrong. I’ve worked on this stupid problem for half an hour, and this answer has a totally different denominator!”
THE ISSUE: Fractions, fractions, fractions.
SOLUTION: Buy a fraction calculator, like the Casio fx260 Solar ($10), or the Texas Instruments 30x ($10 - $30, depending on how complex it is).
These calculators have a special little feature that we parents could only have dreamed about (if we weren’t dreaming of other things) during our adolescence. They do fractions!
That’s right. You can input a problem like 1/5 + 2/7, and the little gizmo will brilliantly display the answer: 17/35
Multiplication and division too:
Input 15/27 x 18/45, and it will spit out: 2/9 (note that the answer it gives is in simplified form, too). Input 7/13 ÷ 28/26, and it will give you the answer that might take many kids a minute or so: ?
But not to stop there … this calculator will also simplify fractions to lowest terms. Suppose your child gets an answer of 72/96. Just punch that into the calculator, press the = key, and it correctly reduces it to lowest terms: ?
Not only do these calculators handle fractions, they also handle mixed numbers, like 4 7/11. Try entering 4 7/11 + 3 5/13. There’s a problem that would take many good math students at least a minute. The calculator immediately zings out the answer: 8 3/143
Now I can already hear the screams of parents who believe students today already have too much reliance on calculators. Such parents often believe (with good reason) that students should learn to do all math calculations using paper and pencil, just as we had to do back in the day.
To those parents I have two replies.
First, I agree, it’s always best if students learn how to do all operations in their heads or with paper and pencil. That leads to much greater understanding. But … if a student is now doing algebra and he’s still struggling with fractions, and that struggle is keeping him from keeping up, and if you don’t have the time to go back and teach fractions right now, a fraction calculator is a great crutch.
Also, there are some students who simply struggle with fractions — no matter how well the concepts are taught (manipuatives, visuals, lots of practice) — and you don’t want these kids to miss out on the gatekeeper higher math courses because of a problem with fractions. These kids may need to use a fraction calculator for the rest of their lives. And that’s o.k.
Secondly, if you do wish to re-teach your child all the essential concepts and skills for fractions, I have a suggestion: Key Curriculum Press’ Keys to Fraction series (four great workbooks, along with pre- and post-tests, and final tests, too). I use it a great deal as a tutor, and it works wonders. Plus it is self-paced, so it requires minimal parental involvement.
So in short, helping your child with algebra does not necessarily require you to relearn the subject completely. With these tips, you’ll be able to help your child a lot, and who knows, you may start remembering the stuff at the same time.
About the author:
Josh Rappaport is a homeschooling father and author of the Algebra Survival Guide: a Conversational Handbook for the Thoroughly Befuddled, and the Algebra Survival Guide Workbook, available in bookstores nationwide and at SingingTurtle.com. Josh has been teaching and tutoring algebra (and other math subjects) for the past 18 years.
Josh also authors a free ezine in which he answers math questions. Feel free to sign up and send in your questions or comments by visiting www.singingturtle.com/pages/turtle_talk.html
Email him: josh@SingingTurtle.com
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