Linear Measurement in the Early Grades: A Foundation for Fractions
As you consider fractions in a linear measurement context, you may also find it interesting to think about length and measurement activities that lay the groundwork in earlier grades. In the Japanese grade 1 curriculum, students measure common objects using different units; for example, they might measure their desks using pencil lengths and eraser lengths. They also compare the length of different objects placed on a grid, as shown in below.
If time permits, your group might want to discuss the following two issues:
- What understandings do students develop from using two different objects (such as a pencil and an eraser) to measure the length of their desk? How might such understandings support later understanding of fractions?
- Why are the objects on the grid arranged as they are? Why might the grid itself be useful? What knowledge from this task might support students’ later understanding of fractions and number lines?
Note that the Common Core State Standards also suggest measuring an object with two different units (2.MD.A.2), along with partitioning shapes into 2, 3, or 4 equal shares (2.G.A.3). These experiences may lay important groundwork for formal study of fractions in grade 3.