Dyslexia Strategies 3: Problems with Math
My first suggestion is that you learn math from the very beginning using www.KhanAcademy.org Do not start with calculus or algebra. Most math problems are due to problems you had learning elementary school math. Start with first grade math. It’s easy and you will move quickly to higher levels of math.
For other suggestions, start with the questions below.
If you have problems with math, (dyscalculia) begin by deciding if your problem involves
—–a. reading the problem
—–b. understanding the problem, knowing what to do next
—–c. doing the calculations
—–d. errors because of sloppy writing
You may, of course, have problems in several of these areas.
Read and Understanding the Problem:
If your problem is reading, you need to improve your reading skills. You also need someone to help you learn to read a math problem. You need to be able to separate different kinds of information. Do NOT find all the numbers in a problem and do something with them. It is important to know which numbers to use and what to do with them.
—– What is the given information?
—– What information you are really looking for?
Look for a question. Does the problem ask, how fast is the train going? How old is the boy? How much does one bottle of juice cost?
The question should be easy to find. It should be the only sentence ending in a question mark.
—– What other information you might need (usually information you should know)
—– Is there a picture you can draw to help you understand better?
—– Is this problem similar to others you have done?
—– Will drawing a diagram or picture help you solve the problem.
Let me give you a very difficult example:
All the animals in the farm are either pigs or chickens. There are 8 animal heads and 22 animal feet. How many chickens and how many pigs are in the farm?
The question? Actually there are two questions: How many pigs are there? and How many chickens are there?
What information do we know? We know there are 8 heads and 22 feet.
I hope you realize you won’t get the answers by adding 8+22, subtracting 22-8, multiplying 8×22, or dividing 22 divided by 8. They all give nonsense answers. Panic? What else can you do?
Read the question again. If they have 8 heads, what else do you know? There probably aren’t any animals on the farm with two heads. Eight heads means there must be a total of 8 animals. This is helpful.
It really might help to draw a picture. When drawing chickens you should realize they have only 2 legs, while pigs have 4 legs. This is important information not included in the problem because it is assumed that you know this.
If you can’t figure out what other information you need to know, you can always guess and check. What if there are 7 chickens and 7 pigs? Think about it. There are only 8 animals. 7+7 = 14 animals. Start again.
There could be 4 pigs and 4 chickens and there are several other possibilities. 0 and 8, 1 and 7, 2 and 6 ….
How many legs would there be?
4 pigs x 4 legs = 16 legs. 4 chickens x 2 legs = 8 legs.
16 pig legs + 8 chicken legs = 24 legs.
We are pretty close to 22 legs.
Look back at my work. I did NOT just manipulate some numbers. I was careful to define what each number meant. When you do this, you understand what you are doing.
You can continue to guess and check or you can use algebra.
Let us say that C is the number of chickens and P is the number of pigs. Notice that C and P are easier to understand than x and y.
We also can figure out that two legs times the number of chickens is 2C, the number of chicken legs.
four legs time the number of pigs is 4P, the number of pig legs.
When we add chicken legs and pig legs there will be 22 legs.
This means that 2C + 4P = 22 legs.
You should remember at that point that there are two ways to proceed when you have an equation with two unknowns: substitution method or simultaneous equations.
Substitution method: Since we have 8 animals, if we have C chickens, we must have 8-C pigs.
Add them up 2C + 4(8-C) = 22 Solve for C and then use 8-C to find P
P + C = 8 The number of pigs and chickens is 8
4P + 2C = 22 The number of pig legs and chicken legs is 22
Now we have dealt with reading and understanding a math problem. All you need to do is finish the calculation.
Check your Answer. When you get your answers, do not just write numbers. That doesn’t make sense. You need to say “There are 5 pigs and 3 chickens.”
Let’s see if that is right. 5 and 3 do make 8 animals. Good.
5 pigs x 4 legs makes 20 legs. 3 chickens x 2 legs makes 6 legs.
20 legs and 6 legs makes 26 legs. The problem says there are 22 legs. NOT GOOD. You need to find your mistake.
Another problem that confused students is this one: It is much easier. Just stop to think.
Jerry had 3 dollars. He buys 5 pieces of candy. Now has 2 dollars left. How much did he spend?
Write your answer. I’ll give the answer at the bottom of the page.
For the other math problems, you may need to find a good tutor, either from the office of learning disabilities, a math teacher, or a student who is good at math and very patient.
Problems with Simple Calculations: Add, Subtract, Multiply, and Divide.
—–A.Problems with calculations are sometimes due to sloppy writing. Some students find that graph paper helps them line up their numbers to add or subtract. Doing your problems very neatly can help you avoid many problems.
—–B. As I demonstrated above, it also helps to take your time and label your information.
—–C. Perhaps the problem is that you don’t know your basic math facts. Do you know all of your addition facts? What about 9+7 ? Do you know all of your multiplication facts? What is 7 x 8 ? If this is the problem, you might get permission to use a calculator in classes and on tests. This might be easier, now that you are in college. I would still recommend, when you have the time, to work on those basic facts. You need to be prepared if your calculator stops working in the middle of a test.
—–D. You might have the problem Tony had. He could never remember which way to borrow in subtraction and which side to carry in addition.
In both addition and subtraction, you start on the RIGHT side. If you are right-handed that could help. Otherwise think about starting the RIGHT way.
When you start on the right, you can only go one direction. You started on the right. Wha direction is left. You must always move to the Left. When you add, you carry to the left. When you subtract, you borrow from the left.
And if you can’t remember which way is right and which is left? I always wore a ring on my right hand. You could wear a watch or bracelet. You could wear a RED bracelet or watch band and remember RED and RIGHT. If you must wear something on the left side, there isn’t a color starting with an L. You could wear something green and call it “LEAF GREEN for LEFT.
It is also helpful to understand place value. Many students remember that the first numbers on the right are in the ONE’S place, and moving left are the TEN’S place, HUNDRED’S, etc. But this is related to carrying and borrowing.
Think about money. If you are counting money, you could take ten one dollar bills and trade it for a ten-dollar bill (10 in the one’s place is 1 in the tens place). This is what you do when you carry.
Now for borrowing. You have two ten-dollar bills and 3 ones. You buy something worth five dollars. You don’t have enough one dollar bills. You take one of your tens and trade it for ten ones. You now have one ten, and 13 ones. Now you can subtract. 13 ones – 5 = 8 ones. You end up with on ten and 8 ones.
Answer to the questions above: The question is how much Jerry spent. $3 – $2 = $1. He spent one dollar.
Many students insist on using all the numbers in the problem. Here you might have divided the dollar by 5 and found that the price of the candy bars was .20 each. True, but this isn’t the question that was asked.
Many students find it helps to underline the question if you have word problems on a test. Then, after you solve the problem, read the question again and see if your answer makes sense.
Many students have problems with fractions, decimals and percents. Just because you didn’t understand these in elementary school doesn’t mean you can’t learn now. You just need a patient teacher.
You might try using manipulatives. Some people find these more helpful that drawings. On the next page, I will give an example of understanding fractions using manipulatives. I will also give a method of using a toy train – or your pen – to understand the addition and subtraction of integers (positive and negative numbers).
The next page is Math Concepts