Fractions Task 2

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
Below are six examples of student work on this task.  Three are from students who used a basal textbook and three are from students who learned fractions in a measurement context (the “Measure Up” curriculum):

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.