Linear Model for Fractions
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Fraction Segment Strips

Fraction Concepts, More Fraction Concepts, Fraction Operations, Decimals and Fractions

In previous fraction lessons, we used egg cartons and base ten mats as area concept models for fractions. In this lesson, we use a linear model, represented by segment strips. These are long, narrow strips of paper, which are subdivided into congruent segment lengths. In this lesson, they serve as a means for comparing fractions, given a relative unit, and as a model for combining various fractions. There are six segment strips:

segment strip models


The actual strips are about 11"

long - these are short versions

for demonstration.



If we consider the length of the white segment to be one linear unit, we can determine the relative lengths of the other segments:

comparing yellow and white

What fractions of a unit do the other segment lengths represent? How are you thinking about them?

Let's let one yellow segment be the linear unit. Now, what lengths are represented by the other segments? Let's find the blue segment's length, then you can try the others:

blue segment compared to yellow


Suppose 3 blue segments equal 1 linear unit. Then what is the length of 5 orange segments? Here's one way of figuring it out, maybe you can think of another:

comparing blue and orange

What about the other segments?

Another way to use the model is to choose a set of segment strips, say 2 blue and 2 orange segments:

What length would they represent if the linear unit were:

We also explore ideas like - If the segments above represent 3/4 linear unit, what combinations of other colors / fractions equal the same amount?

By exploring and discussing ideas like those above, students gain a deep understanding of fraction relationships and meanings. Activities in basic operations with fractions will further build off of this work. Try to your challenge child, or vice-versa with some situations to explore with the segment strips. (Your child has some!)