Learning the concepts of mathematical equations is not easy for everyone.  Math is a subject that I struggled with during my years in elementary, junior high and high school.  It wasn’t until I had to take three Statistics classes in college that I finally realized why I struggled in math; it was the only subject for me that required me to think harder and to be honest, I didn’t feel like thinking that hard.  It was not because I was lazy, because I was good in all of the other subjects and did the work.  It was because, I just didn’t "get" math. I didn’t understand why I needed to learn how to solve equations like this, 23 divided by 149  = 0.15436.  In math class, all I could think about was, is this necessary to learn in real life?.  I didn't think it was, so I didn’t take learning math seriously.  Why?  I don’t know.  Addition, subtraction and multiplication was all that I thought we needed to be able to apply math in real world situations.  As I began to learn how to solve math problems, I realized that most, if not all math problems involved some form of subtraction and addition.  At first, I understood math better when I saw a math problem written in a basic format that I was used to, but when the problem was written in a different format, it was difficult for me to assimilate.  I even struggled with math even when I obtained a math tutor, unless she presented a math problem in the manner in which I was used to seeing it written in the classroom.   For example:  If she asked me to solve a word problem like, It takes the G bus 10 minutes to arrive at the corner of each bus stop.  The G bus arrives at Colorado Street at 12:00pm and you are getting off at Brown Street, which is 15 stops after Colorado Street, (my brain already shut down at this point in the question), what time was it when the G Bus arrived at Brown Street? Instead of just solving the problem as is, I want to know, how many traffic lights are there from Brown to Colorado Street, because this could impact time.  To me, that’s logical reasoning.  Yeah, I know, I think too much.  I realized later to just answer the question as is, without adding to the equation or taking away from the equation. My thought process was, but, where are the word cues in that word problem, that I am used to like, less than, that helps me know that I need to subtract?  Well, not all math problems are written in a simple format.  This is where the logical reasoning begins….If you know that Colorado Street is 15 stops before (the cue is before) Brown Street and you are trying to solve for: “What time was it when the G bus arrives at Brown Street?”  Then you understand that you need to start at what time was it when the bus arrived at Colorado Street, which is 12:00pm.  You also need to understand that for each bus stop, it takes the driver 10 minutes to arrive at each stop. All of this information is given in the word problem example above.   You also need to understand that Brown Street is 15 stops after Colorado Street.  Solving this problem may be easy for some, however, below is how my mind works to help me solve the word problem.  I immediately break things down the long way, in the way that makes sense to me.  Keep this in mind when you are explaining to your children how to solve math problems. Give them practice questions and ask them to show how they reached the answer, this way you can get an idea of their thought process and how to explain math to them in a way that they will understand it. 

Example:
Colorado St.

12:00 PM

 

1st stop after Colorado

12:10

add 10 minutes for each stop

2nd stop after Colorado

12:20

add 10

3rd stop after Colorado

12:30

add 10

4th "

12:40

add 10

5th "

12:50

add 10

6th "

1:00

add 10

7th "

1:10

add 10

8th "

1:20

add 10

9th "

1:30

add 10

10th "

1:40

add 10

11th "

1:50

add 10

12th "

2:00

add 10

13th "

2:10

add 10

14th "

2:20

add 10

15th stop after Colorado

2:30 PM

​

 

The answer would be, you would arrive at Brown Street at 2:30pm.  Others could answer the question by immediately starting from 12:00pm and counting down 10 minutes for each block until you get to the 15th blocks to get to the answer, but I am a visual learner, so I have to paint the picture, which takes much longer.   Your learning style preference is the way in which you learn best.  If you are visual learners, you learn by pictures and visual illustrations.  If you are a kinesthetic learner, you learn best by doing real world simulations and hands on activities.  If you are an auditory learner, you learn best by listening to auditory sounds.  Figuring out what your learning style preference is can help you figure out a way to break down concepts in a manner that you understand it.  To be able to solve math problems accurately, you have to know the rules of math.  You also have to have reading comprehension skills as well, to make sure that you know the question that you are asked, so that you will know when to add, subtract, divide or multiply.  The rule of addition is to increase by counting forward/upward by a specified number.  For example:  If the math problem is 25+7 = ?  You will have to increase the number 25 by counting forward by adding 7, starting at the number AFTER 25. 

Example:
        1     2    3      4     5     6     7  (these numbers are put here as a visual guide)
25, 26, 27, 28, 29, 30, 31, 32 .  The answer is 25+7 = 32.  Which can also be written as such and is the same thing:

1

25

+7

32

When the math problem is written in the latter format, you solve the problem from the right column 5+7, because the answer is 12, which is a two digit number, you have to put the right number at the bottom, and place the left number at the top above the number to the left, which means put the 2 at the bottom, and then place the 1 at the top above the left number.  Then, you have to add the numbers in the left column together, 2+1 = 3 place that number at the bottom left.  So, you should still have the answer, 32.

The rule of subtraction is to decrease by counting backwards/downward by a specified number.  If the math problem is 28–10 = ?   You have to count backwards 10 numbers downward starting with the number that comes before 28, which is 27. 

       1    2     3      4     5     6     7    8     9    10 (these numbers are put here as a visual guide)

28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18

Which means that 28-10=18

If adding is easier for you, you can test the accuracy of your answer by adding the last two numbers together to see if you come up with 28.  Example: 10+? = 28    10+18=28

If the problem is written out as such, you will still come up with the same answer:

  28

-10

18

Start with the right column and then the left column.

In a subtraction problem where the bottom number is larger than (more than/a higher number) the top number, you have to know the rules for borrowing from the next number and the rules for carrying over a number.  For example:  If the equation was this:

                   0

   13            1 13

    -9              -9

Because, the 3 is less than 9, you would borrow from the 1 in the left column, reducing the number 1 by 1 number less than the number given (the number given is 1),  the number less than 1 is 0.  Cross out the 1, place a zero (0) over top of the crossed out 1 and then place a 1 in front of the 3,  making the 3 a 13.  So, now you are solving the equation 13-9 = ?  To subtract, you would count backwards 9 numbers from the number that comes before 13.

         1   2   3   4  5  6  7  8  9 (these numbers are put here as a visual guide) 

13, 12, 11, 10, 9, 8, 7, 6, 5, 4

13-9 = 4                If you are better at addition, you can check your answer by adding the last two numbers  9+? = 13            9+4 = 13  

The rules of multiplication is to increase/add (yes, add), by a specified number provided.  For example:  The problem 6x6 is asking you to count upwards from the number 6, 6 different times.  Multiplication can also be a form of grouping.  So, for this problem, you can make 6 groups of 6 people and then count the total number of people in each group to get to your answer.

Example:

1st Group                   2nd Group         3rd Group                 4th Group          5 Group            6 Group

111111                       111111             111111                     111111           111111              111111

 

Count the numbers in each group, which will give you the answer of 36.  6x6=36

You can also write the problem as such and you will get the same answer.

   6

X 6                                                 1   2     3     4    5   6 (These numbers are here as a visual guide)

Its adding the number 6, 6 times   6 + 6 + 6 + 6 + 6+6 = 36

 

The rules of division is also like grouping, it’s dividing/splitting up into portions.  It is also like multiplication.  How many times does a specified number go into another specified number is what division is asking.   The most common division problem is dividing up a pizza which has 8 slices, between two people.

If you know you have 8 slices, and there are two people who want to split the pizza evenly for two people, you will have to split the pizza in half and count the number of slices given to each person to determine the answer.
Example:

​

1st person      2nd person

When you cut a pizza in half, there are 4 slides on each side, which means that to divide the 8 slices evenly between two people, each person would get 4 slices.   8 divided by 2 = 4.   Which you can also check your answer by using multiplication; multiplying the last two numbers 2x4 = 8       or
2 groups of 4 will give you the same answer, 8.    Count the total lines in each group.

Group 1               Group 2

1111                   1111

These are the basic concepts of math that are extremely important to understand as the foundation for solving mathematical equations.  Understand the rules of math first.  Learn the basics, so that you can begin to understand the more advanced math that involves percentages, fractions, multiple numbers, statistics, etc. concepts.  As you get older, you realize that money involves math.  So, yes, some math is necessary, so it is good to learn the basic concepts, because you will need to know them for real world situations involving money.  Understanding math is about learning what the rules are for each math problem.  When you know the rules, it makes math easier to learn, even when you don’t fully understand it’s logic.  So when teaching and learning math, do some math practice questions first to determine how you and/or your children or students process information and problem solve, learn how to assimilate and don't be afraid to ask questions to get clarity.  When constructing math problems, make sure that the questions are not confusing and that they are clear on what is being asked.  This will also help them solve the problem accurately.​  Learning is by design.

By Lynnette Clement