**Linear Model for
Fractions ****
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**Fraction Segment
Strips**

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**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:

**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:**

**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:**

**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:**

**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:**

**1 white
segment?**
**1/4 white
segment?**
**2 green
segments?**
**1 orange and 1
pink?**
**your choice - make one
up...**

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

**What if they were 2/15?
1/3? 5/8?**

**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!)**