Last year I was very proud of my fractions unit. This year our district cut back on the amount of time dedicated to fractions in
fourth grade. As a result, I had to make
some tough decisions on which lessons to cut, and which were
non-negotiable. And I believe if my
students only learn one thing, it has to be a true understanding of equivalent
fractions. So after introducing the idea of equal parts and equivalent fractions with 1/2
with paper folding just as we did last year, we continued on to finding other equivalents.

The next day, they brought their recorded observations with them to quiz
ME. I repeated the "how
did she do it" sessions as I modeled how to sort equivalent
fractions. As some students were able to
articulate the algorithm and demonstrated that they could apply it themselves,
I gave them extension questions such as comparing and ordering fractions (which
our curriculum cut this year). Those
kids who were able to find equivalents were, of course, able to add and
subtract fractions with ease. Those who
did not have the concept yet continued to use manipulatives with me until they
were able to draw their own conclusions about the algorithm. There were several ways I helped my remedial
group:
- We used fraction number lines as a tool for locating equivalents in order to add and subtract fractions. This way they could retain the understanding that equivalents were needed, as well as reinforce the idea of adding numerators for like fractions (not denominators).
- We explored online tools here and here to help us find equivalents at home.
- We played games online to practice visualizing, and then calculating equivalents.

Then we moved on to changing from improper fractions to
mixed numbers and back again. We started
with fraction number lines, since this is a common visual fourth graders are
expected to be able to interpret on MCAS.
I felt like Math in Focus didn't give quite enough direct practice on
using them, so I created several number
lines pages of my own (link to product) to break down the process. And that's when something amazing happened.
After using the number lines to count up using mixed numbers
and later improper fractions, most of my students found it simple to use
fraction circles to tell 11/3 equals 3 2/3.
With a few hints, some were even able to find the algorithm of dividing and
finding a remainder. But one of my
students said, "I have a different way to change a mixed number to an
improper fraction. Just draw 11 circles,
box them into groups of 3, and you have 2 as a remainder. The 3 groups is your whole number, the 2 is your numerator, and the denominator stays the same so it's 3."
She showed me a model she had drawn to prove her point (I tried to make it darker and in color so it would show up on camera).
But even better was the fact that many of the other kids
from that point on had become determined to find a method for the skills we
were learning because they wanted a method named after them too!


So despite a few disrupted weeks thanks to weather-induced
days off, and outside pressures to speed things along, fractions was once again
one of the highlights of our year. We
have today (Wednesday) off again for
snow, but I think they are ready for their test on Friday (in record
time).





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