Fractions and Multiplication

Over half of my current Pre-Algebra class do not know their multiplication facts which is making it quite difficult to teach equivalent fractions.

If I ask them what number 8 and 4 can go into, their first response is 2.  They confuse factors with multiples.  I suspect it might have to do with lacking consistent mathematical instruction in their earlier years.

I finally found a method that works fairly well but is not anything I learned  when I took all my teacher prep classes.  Those classes were so long ago and expected students to be fluent with their multiplication tables by 9th grade.

Since they are not fluent in their multiplication, its hard to use prime factorization to find the lowest common denominator.  So instead. I have them list the multiples of the denominator such as

4, 8, 12, 16
8, 16.

It is obvious from the list that 8 is the lowest common denominator for 3/8 and 6/4.

Next I have the child count how many multiples from the first one to the common which for the first line is 2 and 1 for the second line.

So the student then multiplies both the numerator and denominator by that number.

3*1/8*1 = 3/8 and 6* 2/4*2 = 12/8

Therefore 3/8 + 12/8 = 15/8 or 1 7/8.

Another way, I've had them look at lowest common denominator is through the use of basic fraction strips.  On one problem, they had 1/5 and 3/20 so of course their first guess was that 1/5 < 3/20 because 20 is bigger than 5.  I had them look at the strip of fifths while I drew it on the board.  I asked them if you could divide the fifths into smaller units so you had 20 of them.

About half the students had to look at their multiplication tables or count on fingers but they said if I divided the 1/5 into 4 pieces I'd  have 4/20.  So I rewrote the 1/5 as 1*4/5*4 = 4/20 so the problem now looked like 4/20 > 3/20.

So the above two ways are the ones I'm using to help my students learn to do equivalent fractions for addition, subtraction and comparison of fractions.  Will it work?  I don't know but I'm hoping.  Let me know what you think, I'd love to hear.

I'm hoping by doing it this way, they will connect their multiplication facts with the process but its hard when about half the students just want to guess.