My kids can : making math accessible to all learners, K–5

Keisha wrote that is bigger “because the denominator is a lot smaller and
you could get bigger pieces.”
Tara wrote that is bigger “because 6 is a larger number than 4 but since it is
6th it has smaller pieces and the 4th has bigger pieces.”
Ron wrote, “I would say because is bigger than .” (See Figure 8–1.)
Pete wrote, “You cut the pieces and you cut how many people there are so for
one you cut 4 and for the other you cut 6. Four is less but it is more.”
Jhali used a picture: She circled and wrote bigel(bigger) and then the word
smallerunder.
After looking at these responses, I saw that there were some elements of un-
derstanding of the numerator and denominator, but I worried that students’ un-
derstanding might still be fragile. I had several questions that I wanted to explore
further based on what I learned: Does Jhali realize that the wholes must be the
same size? Would Ron and Pete be able to justify their responses? Would Tara and
Keisha be able to apply their reasoning to fractions with like numerators that were
not unit fractions?
I decided that this small group of students was ready to compare three frac-
tions at a time, so I asked them to create models for , , and. I chose these par-
ticular fractions because I anticipated that the consecutive denominators would
provide a scaffold as the students ordered the fractions. It was also important that
they begin to view as a landmark fraction and use it as a basis for comparisons.
As we progressed through the work, they began to say things such as, “One-half
means you have 2 equal pieces. If you make more pieces than 2, you get more
pieces, but they are smaller.”

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LINKINGASSESSMENT ANDTEACHING

Figure 8–1.