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

A Double Dose of Math

But it’s clear that although she can use the words, she’s not yet able to com-

pare fractions with like numerators.

DIANE: Today we were looking at two fractions in a word problem and she

tried to say something about the bigger the number, the smaller the pieces.

But she got confused and started talking about the numerator.

MARTA: That’s what I have noticed as well. She starts off very confident

and seems to begin connecting what she has worked on previously, and then

she moves on to use a completely different and inefficient method for com-

paring the two fractions.

DIANE: I think part of this is her inability to stay focused. Even in our small

group every day, she jumps from one idea to another without finishing what

she had started to say. I think we should have her work with the same three

fractions for a few days, comparing those same ones each day and see if she

is consistent in how she explains her strategy.

MARTA: Would you be able to work on using different representations with

her for several days? Let’s stick with , , and. And then I can reinforce her

practice as the class moves on to other fraction comparisons. Let’s check

back later next week.

Implementing the Plans and Assessing Progress

Because I had planned the learning trajectory that our class would follow during our
work with fractions, I suggested the sequence of activities and assessments that Diane
would use to support Jhali in accessing the ideas that our whole class would be study-
ing. Diane was able to use individual interviews and formative assessments with Jhali
more frequently then I was. We agreed that these assessments would focus specifi-
cally on the individual goals we had set for Jhali, in particular, visualizing fractions
and identifying relationships between unit fractions. I would continue to offer sug-
gestions for subsequent activities and assessments that would meet Jhali’s needs.
Through repeated practice, we wanted her to connect representations to symbolic
notations of fractions, to verbalize her ideas before applying them as a consistent
strategy, and to connect the formal language of mathematics with her own ideas.
For the next two weeks, Diane had Jhali manipulate fraction bars and circles
and explain the images on the fraction cards we made in class. She also provided
Jhali time to practice explaining her reasoning when comparing the three frac-
tions. Because Diane had more time with Jhali than I did, she was able to listen
carefully to how Jhali was using the vocabulary and how she was developing an
understanding of the meaning of the words numeratoranddenominator. We espe-
cially wanted to assess if Jhali was moving away from viewing the numerator and
denominator as two separate whole numbers.

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