assess students' prior knowledge, give students a chance to explore the
relationship rods. Engage them in a conversation about the likenesses
and differences between the fraction strips and the rods.
To begin the lesson, give students one set of relationship rods (either homemade or commercial) and a copy of the Investigating Fraction Relationships activity sheet.
Give students a few minutes to explore the materials. Ask them to try to determine how the pieces are related to one another.
Most students will quickly figure out that the various colors
can be stacked one on top of the other to create a staircase. This
configuration makes comparing the various fractions much easier and is
illustrative of the linear model of fractions.
This staircase will appear as follows:
Have students consider the first question on the Investigating Fraction Relationships activity sheet: If white = 1, what value would you assign to all the other rods?
[Students should determine that red = 2, light
green = 3, purple = 4, yellow = 5, dark green = 6, black = 7,
brown = 8, blue = 9, and orange = 10. Discuss student responses as a
Demonstrate the correct answer by lining up the relationship rods being compared on an overhead projector or by using the Integer Bar Applet.
Have students complete the following table from the Investigating Fraction Relationships activity sheet.
|Integer Bars ||Size ||Color |
| ||3||Light Green|
| ||6||Dark Green|
Tell students that they will have an opportunity to use the Integer Bar Applet later in the lesson.
When comparing the two lengths for demonstration purposes, the
smaller length should be duplicated to simulate the length of the
longer rod. For example, when comparing white with yellow, where white
is one and yellow is five, five white relationship rods should be used
to directly compare to one yellow. Students can easily see that it
takes five whites to make one yellow; therefore, if white = 1, then
yellow = 5.
Have students consider the second question on the Investigating Fraction Relationships activity sheet: If red = 1, what value would you assign to all the other rods?
[Students should determine that white = ½,
light green = 1½, purple = 2, yellow = 2½, dark green = 3, black = 3½,
brown = 4, blue = 4½, and orange = 5.]
Continue exploring relationships with each color representing the whole by completing the Investigating Fraction Relationships activity sheet.
Students can repeat part or all of this activity using the Integer Bar Applet.