Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 2, Part A:
Measuring Accurately

In This Part: Conservation, Transitivity, and Unit Iteration | Partitioning
Partitioning on a Number Line

 How many partitions of a number line are possible? To use a rational number to describe how far a point on the number line is from 0, you can begin by partitioning the unit interval into an arbitrary number of equal parts. Each of those parts can then be partitioned into an arbitrary number of equal parts, and those, in turn, can be partitioned again. This process is actually a composition of operations. You can use arrow notation to keep a record of your partitioning actions, as well as the size of the subintervals being produced. For example, what if you wanted to locate 17/48 on a number line from 0 to 1? You would start by drawing the number line on a piece of paper and repeatedly folding it, making sure to mark the locations of 0 and 1 before you start folding: Here's one set of partitioning actions to find 17/48:

 Video Segment In this video segment, the participants place a fractional value on a number line using the method of partitioning. They explore the reciprocal relationship that exists between partitioning and the number of units in a measure. Is there more than one way to do the partitioning to arrive at a particular fraction? If you are using a VCR, you can find this segment on the session video approximately 2 minutes and 40 seconds after the Annenberg Media logo.

Problem A6

Try these partitioning tasks: Note 6

 a. Locate 7/24: b. Locate 3/8:

 Problem A7 Find another way (or ways) to locate the fractions in Problem A6 (a) and (b).