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Critical Fraction Concepts for Understanding

28 Mar

Fractions are challenging for many people, children and adults alike.  Here are some of the critical understandings, or big ideas, for fractions.

1. A fraction has a numerator and a denominator.  The denominator tells how many equal parts the whole is divided into and the numerator tells how many parts there are.
2. Fractions can mean different things:  part of a set, part of a region, as a measure, division & as a ratio.

Here is a sample of Kaitlynn’s explanation of what she knows about fractions.  She has explained them very well and used several different models to demonstrate her understanding.

3.  A fraction is not meaningful without knowing what the whole is (if you only see the numerals when comparing fractions you assume the whole is the same).

For example, in class one day I asked the students if they would rather have half of a chocolate bar or one forth of a chocolate bar.  Most students said half but a few knew I was up to something.

The forth came from this chocolate bar:

and the half came from this one:

4.  If fractions have the same denominator, the one with the greater numerator is greater.  The denominator tells the total number of equal parts in the whole, and the numerator tells the number of parts accounted for:

4.  If fractions have the same numerator, the one with the greater denominator is less.  The denominator tells the total number of equal parts that the whole is divided into, and the numerator tells the number of parts accounted for.  The larger the denominator, the smaller the parts are:

Here is Kally’s explanation of this principle:

6.  There are proper fractions, improper fractions or mixed numbers.  The numerator is larger than the denominator in improper fractions.  The mixed number has a whole number and a fraction.  See below.

7.  Fraction can have different names, these are called equivalent fractions:

These are the big ideas we have investigated so far.  There is more to come, stay posted.

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