WEBVTT

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[Music] Welcome to the overview

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on Recognizing Fractions
as Numbers.

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Formal instruction about
rational numbers usually begins

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in the primary grades
with explorations

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of part-whole relationships.

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This approach connects strongly
with students' intuitive understanding

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of what fractions are
and how they work.

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But without further instruction
on other interpretations of

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fractions, students
may form misconceptions

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that will impede
future comprehension.

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It is critical that students
learn that fractions are numbers

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with magnitudes that
represent quantities--

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a concept that can be
difficult to grasp.

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A solid understanding
of fractions as

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numbers enables students
to both relate fractions

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to whole numbers and compare
fractions to other fractions.

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It provides the conceptual basis
for all operations with fractions.

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Measurement activities
are a good place to start

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because many students already
have informal experiences

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to build on, such as working
with recipes or measuring heights.

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Teachers can point out
that fractions allow

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for more precise
measurement of quantities

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than do whole numbers, and
then measure objects using

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fractional parts.

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Practice in measuring with
tools such as lengths of paper,

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or "fraction strips,"
reinforces the idea

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that fractions represent
quantities.

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Here, a student uses yellow
fraction strips as whole units;

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she has measured objects in the
room and recorded her findings.

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The chair is four
fraction strips high;

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her foot is one fraction
strip long.

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The stuffed bear, however,
is more than one strip long

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but not as much as two.

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She addresses the problem by
folding a yellow strip in half

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to measure the full
length of the bear.

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The teacher then gives her
blue strips that are half

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as long as the yellow strips.

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The student experiments

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and finds different ways
to measure the bear.

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Practice with fraction
strips is fun for children

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and develops a concept
of equivalence.

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Number lines are a key tool
in helping children learn

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that fractions are numbers.

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Researchers have demonstrated
that as early as preschool,

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children build number sense
when they use number lines.

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Students' early familiarity

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with the number line
makes it a useful tool

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for introducing fundamental
concepts about rational numbers,

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such as magnitude
and equivalence.

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Here, a second-grade
teacher is using number lines

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to help students make the
transition from working

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with whole numbers to
working with fractions.

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He asks the students to name the
whole numbers with him

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(zero, one, two, three, four).

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The students then watch as
he marks out fractional parts

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between zero and one
(one-fourth, two-fourths,

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three-fourths) and asks students
to count the segments with him.

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Then he has them
label the marks.

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The teacher asks students if
they can think of another way

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to label one; he starts
writing a fraction, putting four

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in the denominator, and
then shows four-fourths.

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With practice students
will be able to:

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Locate and compare fractions
on a presegmented number line,

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Compare fractions greater
than one to whole numbers,

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and Locate a fraction such as
one-fourth or three-fourths

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when eighths have been labeled.

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As students' understanding
develops,

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teachers can use number
lines to pose many challenges

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that build rational
number concepts.

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Is two-thirds closer
to one or zero?

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Where would we locate
five-sevenths on a number line?

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What about seven-fifths?

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Compare several fractions
with the same numerator,

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such as three- fourths, three-fifths, 
and three-sevenths.

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More advanced work with number
lines involves using parallel

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sets of labels, with each
set showing fractions

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with different denominators.

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For example, students could
be asked to compare two-thirds

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and three-fourths and
identify which is greater.

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This use of the number
line helps children develop

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understanding of the
relative size of fractions.

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As students progress, their experience
with number lines can be expanded

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to teach more sophisticated
concepts related

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to rational numbers,
for example,

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that equivalent fractions
describe the same magnitude.

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The number line helps
students understand

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that there are an infinite
number of fractions

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between any two numbers.

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And, for older students, number
line experiences will come

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in handy when they
are introduced

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to negative fractions.

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On a number line, students
can represent fractions

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as decimals and percentages.

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Different sets of labels
help students compare the

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representations and see
that three-fourths, 0.75,

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and 75 percent are equivalent.

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The number line is a robust and
flexible tool that can be used

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in many ways to build up
the conceptual understanding

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that students need in
order to make progress

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with rational numbers
and understand algebra.

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Children who have
extensive experience

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with number lines won't be
baffled by improper fractions

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and negative fractions.

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They will be less likely to
think of fractions as made

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up of whole numbers and
make operational mistakes

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such as trying to add
fractions by adding numerators

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and adding denominators.

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To learn more about Recognizing
Fractions as Numbers,

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explore the additional resources
on the Doing What Works website.