Fractions Task 2
Task 2: Find two fractions between 1/2 and 1.
Discussion Questions:
- How did you solve the problem, and how might students solve the problem?
- What understandings and misunderstandings about fractions might this problem reveal?
- Look at the student solutions to Task 2. What do the student responses suggest that each student understands and does not understand about fractions?
- Do you notice any differences in the responses of students who used the basal textbook and the students who participated in the “Measure Up” curriculum?
Task 2 Student Solutions
Context 1: Basal Text
| Student Response | Rationale |
| Student 1 1/4 1/5 | because 4 is bigger than 1 because 5 is bigger than 1 |
| Student 2 3/4 7/8 | are between 1/2 and 1. Both are missing one part. |
| Student 3 2/3 4/5 | 2 is more than 1
3 is more than 2 4 is more than 1 5 is more than 2 |
Student work from Work Session presented by Barbara Dougherty and Barbara Fillingim, NCTM Annual Meeting Research Presession, April 21, 2009, Washington D.C., reproduced by permission of first author.
Context 2: “Measure Up” Curriculum (Measurement Context)
| Student Response | Rationale |
| Student 1 2/3 3/4 | If there is a lot of parts, there are smaller pieces. So you have to use a lot of them to get close to 1. So 2 out of 3 parts is close to 1 and so is 3 out of 4 parts |
| Student 2 5/8 7/8 | If you have 8 parts, then 4 parts are 1/2 so 5 parts and 7 parts are more then (sic) 1/2. But there (sic) not 1 because you need all the parts. |
| Student 3 5/9 6/10 | What I did was think of the number of parts and then what is haf (sic). Then I added one to it. |
The “Measure Up” curriculum emphasizes use of units of length, area, and volume to explore basic mathematical ideas such as equivalence. For example, students might compare two lengths by using a third length. Students using this curriculum become very attuned to asking, “What is the unit?” since different units (such as a hexagon and six triangles) might be used to create equivalence.
