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Fraction Action


In my July 1, 2011 posting entitled Fractions for the Confused and Bewildered, I introduced you to an alternate method for adding fractions called Cross Over, but sometimes students may have to add more than two fractions.  What happens then?  Let’s suppose we have the following problem.

Start out by multiplying the numerator of the first fraction by the denominators of the other two fractions as shown above.  (1 × 5 × 3 = 15)

Do the exact same thing with the second fraction and then add that product to the first.

Now repeat this process using the last numerator of 2 and add that to 33.
  

The result is the numerator of the answer.  To find the denominator, just multiply all the denominators together just as we do in the Cross Over strategy.
 
 

As usual, you may need to reduce to lowest terms or change an improper fraction to a mixed number.  In this example, the improper fraction becomes a mixed number.
For many of us, this may seem like a lengthy and complicated process but for my mathphobic students who have difficulty finding the lowest common denominator, they view this as easy and stress free.  The key is that they have a strategy that works for them.
If you are interested in other alternate ways to teach fractions, check out the resource 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.
 
3)      Finished: If you are done early go back over your answers. Make sure that you did what the question asked and check your answers for clarity.

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. 
It is a free download.  Just click under the above cartoon.
 
 
 

 

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.
 
 

I Need Math Study Skills?

This semester, I am teaching a new class called Math Study Skills.  We are finding that many of our students who do not qualify for college algebra in reality do not know how to study math.  When you think about it, math is different than other subjects in that it continues to build.  You might do well on the test over Chapter #1, not so hot on Chapter #2, but for sure, you will not succeed on the test over chapter #3.  I am putting together lots of supplemental materials for the class which I hope to share with you on this blog. 

In our next class I am going to ask the students to determine if the following statements about math are true or false.  See what you think.
Math Profile Sheet

  1. In math, there is only one way to get the answer.
  2. To be good at math, you have to be good at calculating.
  3. If you are good at math, you skip steps and do all of the work in your head.
  4. Men are much better at math than women.
  5. There is a "best" way to complete a math problem.
  6. You have to have a mathematical mind to understand math.
Believe it or not, all of these are false statements! I think my students will be surprised as well. But of course the best study skill I can give them is depicted in the cartoon!


Are you interested in a Math Profile Sheet that will help you to measure the mathematical success of your students?  Check it out by clicking under the cartoon.

Anno's Counting Book


Anno’s Counting Book by Mitsumasa Anno is one of the best math picture books for children that I have used with kindergartners and first graders.  This wordless counting book shows a changing countryside through various times of the day and seasons.  It introduces counting and number values from one to twelve. On each page, you can find several groups of items representing the illustrated number, such as 4 fish, 4 trees, and so on. The number is also represented by stacked cubes at the side of the illustration.  The book contains one-to-one correspondence, groups and sets, and many other mathematical relationships.  I purchased the Big Book version so that the entire class could easily see each picture.

Here are a couple of activities that you might try with the book.

1)      “Read” the book to the children and discuss what is happening.  The following questions will help the children to connect what is occurring in the book:

a)      What time of year is it when the story begins?  Ends?  How do you know?

b)     What are the seasons that you see throughout the book?

c)      How is the village changing?

d)     What kinds of transportation do you see?

e)      Compare and contrast what the children are doing in each scene.


2)      Discuss what happens to the trees as the season change in the book.  Are there different kinds of trees in the book?  How do you know? (color of leaves, size, etc.)

a)      Have the students fold a 9” x 12” sheet of paper into fourths.

b)     Have them write the name of a season in each section. (summer, fall winter, spring)

c)      Have them draw the same tree in each section, but show how it looks in summer, fall, winter and spring.

Happy Reading!




Patterns and Problem Solving

In my last two posts, I have presented some patterns for you to look at with the hopes that you would try to dissect them and be able to answer a few questions.  Are you ready for two more?  Here is the first one that I call Consecutive Number Series.

What counting pattern do you see in this sequence?  How would you describe the sequence of numbers that are being added?  What pattern do you see in the answers?  Can you figure out the pattern for 8 × 8 and 9 × 9?  Notice this pattern made a triangle.  Do you know what kind it is?

My next pattern I call The Eights, and you will readily see why. It, too, forms a triangle, but a different kind. Do you recognize the triangle as isosceles?  If you take a ruler, you will find that the base is 4" while the sides are both 3".


What do you think will happen if we take this same pattern and add a 0?  Notice that this pattern does not begin with adding an eight.  Can you figure out why?

I use this type of patterns with my remedial math college students because I consider it important to do some problem solving while recognizing and describing patterns.  After all, problem solving is a part of life.  It doesn't occur in a vacuum. Because students must reason about some specific content, I think patterns are a great place to begin.  Problem solving also helps students to make connections to other parts of mathematics and find some relevance to what they are learning.  And did you know, that problem solvers are typically better test takers?  So take the patterns from my last three postings, and create some of your own questions for your students.  Use them in a journal or as a small group activity.  But whatever you do, have fun learning and discovering patterns in math.

A Little Math Humor

I just love to laugh in math class.  When I do, my students are surprised because they believe math is no laughing matter.  I like to have a small, humorous snippet on my tests or a cartoon hanging in my room.  Here are a couple I found on Pinterest which I absolutely love!

Apparently, x is lost!

------------------------------------------------------------------------------------------------------
Thank goodness, x has been found!
P.S.  Do you know the value of x in the above problem?

Ironing Coffee Filters; No Starch Needed!

What I should be doing!
When I teach angles or the properties of circles, I find that most children have difficulty cutting out a true circle (even with a blackline).  I have resorted to purchasing cheap coffee filters (not the cone shaped ones) and ironing them flat....much to my chagrin as sometimes these take precedence over my ironing husband's shirts. You can iron several filters at one time, and once they are ironed, they form excellent ready-made circles. Here are some of the ways you can teach angles using these circles.

1) Introduce the fact that each and every circle contains 360 degrees.

2) Have the students fold their coffee filter in half. Discuss that this is a straight angle. Ask, “How many degrees does it contain if it is one-half of a circle?” (180 degrees)

3) Have the students fold the coffee filter one more time, into fourths. Talk about this angle being called a right angle and that it contains 90 degrees. Ask, "What fractional part of a circle is this?"

4) Have the students use this fourth of a circle to locate places in the classroom where it will fit (e.g. the corner of their desk, a corner of a book, a corner of the board).

5) Explain that these corners are right angles and without right angles, we would live in a crooked world. Nothing would be straight!

Linking Math and Literature for Older Students

Read Sir Cumference and the First Round Table (A Math Adventure) by Cindy Neuschwander. This is a story about a clever knight of King Arthur’s named Sir Cumference. By using ideas offered by the knight’s wife, Lady Di of Ameter, and his son, Radius, King Arthur finds
Angles Resource
the perfect shape for his table. Basic geometric vocabulary involving circles (circumference, radius, and diameter) is introduced. Her book can be found on my bookshelf at the bottom of this blog page. Click on the book for more information.

Want more hands-on ideas for teaching angles? Check out Angles: Hands-On Geometry Activities.