FRACTIONS: MATHEMATICAL “TOWERS OF TERROR” TAKE TWO

FRACTIONS: MATHEMATICAL “TOWERS OF TERROR”

TAKE TWO

In our last episode, we discussed recognizing fractions and the terror created by “stacking numbers” into numerators and denominators.  Most students understand “sharing” items to be shared evenly.   This sharing is simply dividing.  In the progression of mathematical learning, students learn to count, add, subtract, multiply, divide, and finally fractions.  This progression is natural.  Sharing with your friends is an idea in fairness and equity.  The difficulty becomes the actual numbers themselves.  

After teaching our students to look a “part of the whole”, we expect them to begin manipulating those strange numbers and perform our favorite operations upon them.  Students are now expected to add and subtract fractions, along with multiply and divide them.  While in the natural progression of numbers, multiplication and division come after addition and subtraction, these operations are the most difficult operations to perform with fractions.  The reason is three very scary words----“Least Common Denomination.”   Telling students that you can not add halves and quarters, because they don’t have the same denominator sends another wave of terror through the classroom.

  The students need a three-step combination to dispel the terror and crack the LCD code.  The first part of the combination is ensuring that we are clear in our instruction and all parties in the classroom are involved in the learning.  It is important for all parties involved in the classroom to work together to create a key to break the code–the code of adding and subtracting fractions.  The classroom should have a class-created and student-contributed anchor chart, which is in plain sight of all the students.  It is also a great idea for each student to have his or her own smaller version of this anchor chart close by to use as a reference.

The creation of the class-contributed anchor chart will allow the students to assist each other in their respective learning.  It gives the students more practice in supporting and critiquing each other’s work.  Only when the entire class works together, can the true learning begin for all.  Each student needs to know that they are contributing to their own education, as well as each others.  

The second number in the combination is ensuring that each student is knowledgeable in fraction equivalents.  Knowing that ½ = 2/4 = 3/6 = 4/8 = 5/10, along with some equivalents for 1/3, 1/5, 1/4.  These equivalents will give the students some beginnings for the addition and subtraction of fractions with different denominators.

The last number in the combination would be a strong grasp of their multiplication factions.  Factoring the denominators is an important step in computing the LCD, which makes knowing their basic factors a necessity.

Once the students have gathered all of the necessary numbers to enter the combination, they are ready to begin.  However, it is the process to the combination that is the major contributor to their learning.  Students need to see that they can do it, before they will begin they can.  This three numbered combination is key to it.