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

strategy or story with more consistency. I asked them to jot down their own story
for comparing fractions and let them know that in a few days they would be shar-
ing their stories with the whole class. I wanted to use their sharing as an assess-
ment opportunity. Would they be able to tell these stories appropriately in the
whole group without any prompting from me?
During our next whole-class discussion, I invited the students from my small
group to remind the whole class how we could use what we knew about compar-
ing unit fractions to assist us in looking at the relationship between the fractions
we now were considering. Three of the students confidently read their stories from
their journals, and Pete added that he knew that one of the fractions we were con-
sidering had larger pieces because the denominator was smaller than the second
fraction. Verbalizing their stories helped the students connect the ideas they were
expressing to the area models they had drawn previously. I felt more confident that
they were beginning to make sense of the ideas we were discussing in class.

Assessing New Learning

When my ongoing assessments in the small-group observations led me to note
that students could consistently use a story and representation to explain frac-
tional relationships with unit fractions, I planned to move on to nonunit frac-
tions. Based on what I had learned when the students shared their stories, I
wanted to see if the students from the small group could generalize what they
learned about unit fractions to nonunit fractions with the same denominator.
Would they be able to use the stories they created to explain the order of , , and
to think about the order of , , and? In addition to figuring out that is smaller
than , would they understand that the fraction of a pizza that 6 people sharing 3
pizzas will get is equivalent to 3 pieces of a 6-piece pizza? I invited them to work
with me on a new “game” involving cards that listed fractions with unlike de-
nominators but like numerators that were not equal to 1. My plan was to have the
students compare three of these fractions. The first three cards were: , , and. I
began the discussion by reminding students of the work they had done comparing
unit fractions. We had been using the fraction cards that we made for some of the
fraction games.

TEACHER: So, the other day you all had some very interesting and useful

ways to think about comparing fractions like , , and. What do you think

about these fractions?

KEISHA: Well, I remember the pizza story! One pizza and then the people

come to eat the pizza and now with these fraction cards, there are sometimes

lots of people and the pizzas get smaller.

1

6

1

3

1

2

3

5

3

4

3

6

3

5

3

6

3

6

3

5

3

4

1
6

1

3

1

2

The Pieces Get Skinnier and Skinnier