Don't Flip!

My college students in remedial math just finished the chapter on fractions.  Talk about mathphobia.  Dividing fractions was the most confusing for them because it requires finding the reciprocal of the second fraction, changing the division sign to a multiplication sign, and then multiplying the numerator times the numerator and the denominator times the denominator.

Let me introduce a new method entitled Just Cross.

1)      First and foremost, you must understand what division is.  The statement 8 ÷ 4 means 8 divided into 4 equal sets, OR how many fours are in eight, OR how many times can we subtract 4 from 8?  (Yes, division is repeated subtraction.)
2)      Let me explain this using a hands-on visual.  Let’s assume the fraction problem is:

The question being asked is, How many ¼’s are in ½?”

First, fold a piece of paper in half.  The figure on the left represents ½.  Next, fold the same sheet of paper in half again to make fourths as seen in the illustration on the right.  When you unfold the paper, you will notice a total of four sections.  So answering the original question: How many ¼’s are in ½”, you can see that the half sheet of paper contains two parts; therefore:

3)      Using the same example, to work the problem, the fraction 1/4 would have to be flipped to 4/1  nd then 1/2 would have to multiplied by 4/1 to get the correct answer of 2.  That is why the division of fractions requires that the second fraction be inverted and the division sign be changed to a multiplication sign.

Let’s use the same fraction problem, but let’s utilize a different method entitled Just Cross.

1)  Cross your arms as a hands-on way of remembering the process.
2)  Now multiply the denominator of 4 by 1 and the denominator of 2 by1 as seen below.  (We do nothing with the denominators.)  Notice we always start on the left side and then we go to the right side.  I often tell my students it is, "Left, right; left, right"  as if we are marching.  If it is done the opposite way, the answer will be incorrect.

3)      Now simply divide 4 by 2 to get the answer of 2.

No flipping; no reciprocal, no changing the division sign to a multiplication sign.
Just Cross and divide.  Amazingly, it works every time.

I have a resource that features different ways to teach fractions using hands-on strategies similar to the one above.  Just go to Fractions for the Confused and Bewildered.

What You Need to Know to Study Math

Math is hard work, but you can't let that prevent you from being successful.  Anyone who has succeeded in anything has put in "tons" of hard work.  Think about the Olympians and all the practice that is required to even make a local team.  How about anyone who is good at athletics?  Do football players say, "Learning all of those plays is just too hard.  I think I'll quit!"  I don't think so.  The same holds true for learning a subject, any subject whether you like it or not. Below are eleven things to know and think about before you study math or take that next math class.

1)    Remember, an extra step is required to pass math. You must use the information you have learned to correctly solve new math problems.

2)    You must be able to do four things....

a)      Understand the material
b)     Process the material
c)      Apply what you have learned to correctly solve a problem
d)     Remember what you have learned and apply to new material
3)     Math has a sequential learning pattern; material learned one day is used the next day and the next, etc.  All of the building blocks must be included to be successful.

4)     Math classes should be taken each semester with no breaks to enhance the probability of remembering previous material.

5)      Math is similar to a foreign language; practice it or you will forget it.

6)     Math is a skill subject.   You have to actively practice the skills involved to master it – like learning to play a musical instrument, a sport, or using auto mechanic skills.

7)     Math is a fast-paced subject.  You must learn a lot of information in each class so you are ready to move on to the next class.

8)      Society doesn’t help students.   It says it is OK to hate math, to not be able to do it. You will often hear from parents, "I was never any good at math either."

9)    A bad attitude shouldn't prevent you from doing well in math if you decide you are going to do well. You may not like history or English either, but you have to take the required classes and do well in them if you plan on passing/graduating.

10)  Math is objective, and you will receive the grade you earn. There is no talking a teacher into a better grade BECAUSE you must know the material before you can move forward, or you will fail.

11)  Study to make an A on the first test in any math class. It is probably the easiest test, but it counts the same as all of the others. An A shows you know the basics you need to succeed. An A is a good motivator to do well on future tests. An A on the first test improves your confidence that you can do well.

Ten More Tips So You Won't Forget!

 Math Study Tips You Won't Forget
I know Moses only gave the Israelites Ten Commandments, but remember, these study tips are not commandments; they are suggestions. Keep in mind, math courses are not like other courses. To pass most other subjects, a student must read, understand, and recall the subject matter. However, to pass math, an extra step is required: a student must use and apply the information they have learned to solve math problems correctly. Special math study skills are needed to help the student learn more and to get better grades. Below are my last ten of twenty Math Study Tips.

1)      What You Know:  Answer what you know first.  That way, you will be more relaxed when you get to the more difficult questions.

2)      Read: Read the questions.  Look for words like explain, define, select, give an example, etc.  Look at the points attributed to each question and do what you are asked.

4)      Jot It Down! Write items down such as formulas (or what they are used for) or items you are afraid you will forget somewhere on the test as soon as you receive it. Now you can relax and concentrate just on the test.

5)      Show: Show all of your work; it may be worth points.

6)      Clarity: Reread your work for clarity.  You may know what you mean, but if the teacher cannot make heads or tails of it, you will not earn the points.

7)      Dress Appropriately: Ask yourself, “Is the classroom normally cold? Hot?”  You do not want to be uncomfortable during the assessment.

8)      Books/Materials: Bring all books and supplemental materials that can be used on the test.

9)      Time and Date: Know the time and date of your test.  Set an alarm, and do what you need to do to be on time for class.

10)  Be Persistent:  After taking 19 steps towards success, you are going to do great!

The entire list of Math Study Tips is now available on Teachers Pay Teachers.

Study Skills - The First Ten

Most of us are familiar with the Ten Commandments.  I am NOT Moses, but I do have ten good study tips for when it comes to studying mathematics.  Read them over carefully as some of them might surprise you.  Feel free to copy these and hand them out to your students before the next big math test.  That's what I did with my remedial math college students, and I was surprised at how positively they responded.

1)      Notes: Organize them and make sure you are not missing anything.

2)      Instructor: What did your teacher tell you to study?

3)      You: Study in a way that works best for you (ex. place and times).

4)      Friends: If you stay on track, studying with friends can help.  Quiz each other, and everyone can explain what they know.
5)      Tricks: Use methods such as mnemonic to help memorize blocks of information.

6)      Do It Now: No one wants to fail, go to summer school or take the class again.  Work now so you do not have to pay later.

7)      Breaks: Take regular breaks while you study and do not stay up all night.  Lack of sleep will make it hard for you to focus and do your best.

8)      Eat: Eat a good breakfast or lunch before the test.  Not only will a growling stomach interfere with your concentration, but your brain will not function at its best ability when it needs energy.  (Note: Research has shown that eating peppermints will help you to remember what you study!)

9)      Avoid Caffeine: Coffee or coke may give you a quick alert boost, but you will rebound and lose steam.  Drink water; it keeps you hydrated.  (This is a hard one for me.  I am pretty wicked without my morning cup of Java!)

10)  Needs:  Take what you need to the exam or test.  Think ahead.  Do you need a ruler, a calculator, paper, etc.?

Now have your students go back and highlight the study tips they are already doing.  Then ask them to draw a star beside the one they want to work on before the next test.  If you have your students do this activity, I believe you'll find it to be a positive beginning on how to study math.