### Math Hacks: Equivalent Fractions

Fractions are so hard!  I know!  My kids really struggle with fractions.  When I introduce equivalent fractions, I begin by asking the kids, "What's my name?"  They look at me like I'm crazy and someone finally will say, "Ms. Banks."  I say, "I have other names.  What do my daughters call me?  What does my husband call me?"  I tell the kids, "Different people call me different names.  Mom, Karla, Ms. Banks.  That doesn't change who I am."  I explain that fractions are the same.  They may have many different names, but they are the same value.  We change the fraction to make it easier for us to add or subtract.  Then, I show the kids a multiplication chart.  A multiplication chart is actually a fraction chart showing equivalent fractions.  I know that just blew your mind!  Right?!

Look at this multiplication chart.  Look at the first two lines.  Look at the first line as the numerator in a fraction and the second line as the denominator of the same fraction.  1/2  If you follow the rows across, you will find several fractions that are equivalent fractions to 1/2.  2/4= 3/6= 4/8= 5/10 and so on.  Crazy!

Here's a second example.  1/4= 2/8= 3/12= 4/16= 5/20 and so on.

When kids struggle to find equivalent fractions, I have them use their (laminated) multiplication chart.  For the problem: 2/5=    /15

First, have them highlight the two rows that the problem is asking about.  In this case, 2 and 5.  Then I have them look to see if the problem gives them the numerator or denominator.  In this case, the denominator is given.  Students go across the denominator line (5) and look for 15.  Then they trace their finger straight up to the numerator line which is 6.  2/5=6/15
Once kids get the pattern, they can usually drop off using the multiplication chart and just multiply to find the missing numerator or denominator. 