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

PETE: The pizzas don’t get smaller, the pieces do.

TARA: Yeah, remember they get skinnier and skinnier and the more people,

the hungrier they get.

TEACHER: Wow! I really love this story about more people coming in and

the pieces getting skinnier and the people getting less to eat. I think it is im-

portant what Pete said; that the pieces get smaller. All the pizzas are the

same size though.

JHALI: But now we have to make a new story because we don’t have pizzas

with these fractions [pointing to the new fraction cards].

TARA: Look, look at. We cut 4 pieces and you get bigger pieces. And look

at the 5, you get 5 smaller pieces.

TEACHER: Does anyone think they can use the story they wrote in their

journal last time with these fractions?

KEISHA: The denominator is the people and now we have more pizzas.

TEACHER: What do you mean we have more pizzas?

KEISHA: Now there are 3 pizzas instead of 1. But the people still have to

share them, and it is the same pizzas getting shared.

TEACHER: Well, you are thinking really hard about this idea. And it is re-

ally an important idea for understanding fractions. Thinking about what the

denominator tells you about the size of the pieces when the numerators are

equal.

Using Assessment Information to Inform Next Steps

I was pleased that these students were able to apply the same strategies they had
developed in working with unit fractions to thinking about the order of nonunit
fractions. But I couldn’t tell from the ordering conversation whether they also un-
derstood the relationship between the amount of pizza 4 people sharing 3 pizzas
would get and of a single pizza. I decided to introduce other ways to visualize
fractions to support the connection between these two ways to think about. I
continued our study of nonunit fractions by using

• fraction cards that included both the drawing and the fraction (see Figure
  8–2)


• rectangles on grid paper


• geoboards

The geoboards are related to the rectangle work we had done earlier in the
whole-class work, and they gave the students equal-size wholes that they could
subdivide into many fractional parts at once, such as and. Geoboards eliminated
the drawing challenges that some of the students encountered with the rectangle

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