Jason has 3% candy bars. He wants to share the candy bars with his friends. He gives as many of his friends as possible % of a candy bar. He keeps the rest for himself.

Part A: How many friends can he give % of a candy bar to?

Part B: How much of the candy bar will Jason keep for himself?

Part C: How does Jason’s portion compare with his friend’s portion?

Explain your thinking for each part.

The following lesson was delivered in a multi-grade lesson study team of fifth- through seventh-grade teachers. One of the ways, a seventh-grade teacher tried to motivate her students to consider the various interpretations for fractions: she posed the question of what candy they like and then talked about how each could be used to form a fraction (see Figure 8.5).

She then introduced the task called “Share My Candy.”

Jason has 3 ^{l}A candy bars. He wants to share the candy bars with his friends. He gives as

many of his friends as possible % of a candy bar and keeps the rest for himself.

1. How many friends can he give % of a candy bar to?

2. How much of the candy bar will Jason keep for himself?

3. How does Jason’s portion compare with his friends’ portion?

4. Use words, pictures and numbers to show your work.

Students were quick to draw or to turn the mixed number and fraction into decimals and use division. The teacher asked if they could use the tiles or construction paper to make manipulatives to solve the problem another way without using division with decimals. Using poster proofs, the teacher asked students to publish their thinking (see Figures 8.6 and 8.7).

Figure 8.5 Different ways to illustrate fractions.

Figure 8.6 Using color tiles as chocolate bars.

Figure 8.7 Student using decimals to make sense of dividing by a fraction. Source: Authors.

Again, in the student sample below, students in this group were quick to convert to decimals and use division. They answered 4 friends after arriving at the answer 4.66. From candy bar experience, this group chose to split the bars into twelve pieces making the work slightly more challenging, but they successfully split the candy and realized that Jason would have У2 of a candy bar left for himself. The class had a nice discussion about the answer for Jason’s portion of У2 of a candy bar. No group ever mentioned Уъ as a good analysis of Jason’s portion in comparison to his friends’ portions.

The teacher pointed to one group’s drawings of the portions and asked the class, “What fraction of each friend’s portion does Jason have for himself?” Asking in that way as students looked at the drawings helped them to see that Jason had Уъ as much as his friends. With that connection, the class revisited the division of decimals and could see the connection to this answer and the 4.66; it’s 4 and Уъ portions!! Using multiple representations (manipulatives, pictures, numbers) allowed for teachers to assess students’ level of understanding.

Table 8.1 below maps out the conversations teachers had about Share My Candy problem and the learning progressions in fraction related to this problem. Having a vertical team of teachers also offered opportunities to think about the Share My Candy problem and consider ways they could differentiate this problem to extend the conceptual understanding of operations with fractions.

Table 8.1 Learning progressions across vertical-grade bands for Share My Candy

Learning Progressions across Vertical Grade Bands

Grades 3-4

Grades 5-6

Grades 7-8

Students are not asked to make the connection between 2/3 of a share and ‘Л of a candy bar.

Students are prompted to make the connection between 2/3 of a share and Vi of a candy bar, but not expected to make it.

Students were asked to explain/debate:

When they drew a picture they got

“4 '/_{2}”

When they “Did the math”

Why is there a difference?

I/2 candy bar vs. serving size

Extensions:

Ask students to create a similar problem utilizing fractions and any food item. Have students see if they can even out the portions between Jason and his friends. Ask how much each student would get if all children shared the candy bar equally.