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

A Double Dose of Math

TEACHER: Which of these two do you think is the biggest, or? Before you

answer, think about what you just said about and.

JHALI: I don’t get it because they are the same because they have the same

number.

TEACHER: What number is the same?

JHALI: The numerator, the top number. So they are equal.

TEACHER: Look at the and. They have the same numerator but you told

me that the was larger. Why did you say it was larger?

JHALI: Because the pieces are bigger. But now the pieces are the same.

I could tell she was getting frustrated and I was not sure where to go next. I won-
dered what mental image she was creating for and.

TEACHER: Can you explain to me what picture you see in your mind for?

JHALI: 2 colored pieces and 2 not colored and for the other, 2 colored and

3 not colored.

TEACHER: Which has the bigger pieces?

JHALI: Oh, the is smaller because I had to cut the pieces skinnier to make

5 of them.

I was very pleased that Jhali was able to visualize and explain that the bigger de-
nominator signified “skinnier pieces.”

Planning Next Steps

Diane and I discussed my interview with Jhali and used that information to plan
the next set of activities: comparing fractions with like denominators and unlike
numerators ( , , ). My knowledge of where the class was headed with our work
in fractions and my observations of how other students in the class accessed the
ideas were critical to this planning decision. At the same time, I depended on
Diane’s expertise about how learning challenges can be supported with accom-
modations and her understanding of how Jhali’s language difficulties affected her
understanding. Because we knew that Jhali had comprehension problems and was
still building a listening vocabulary in English, it was important to make sure our
explanations made sense to her. We needed to listen carefully to how she de-
scribed her ideas to see if they indicated mathematical confusion or a limited
repertoire of vocabulary.
For the next two weeks, we made sure that Jhali was getting a “double dose”
of the same sequence of tasks. Our class continued comparing fractions with like
denominators, such as , , , but we had also moved on to comparing fractions
with unlike denominators. Diane continued to review the fractions with like

3

4

2

4

1

4

3

4

2

4

1

4

2

5

2

4

2

5

2

4

1

4

1

5

1

4

1

5

1

4

2

5

2

4