## Fractions!!!!! The Big Ideas!

30 Apr

Both classes have been working on fractions for the past few weeks (with some time off when some were swimming!).   The grade 5s have a test coming up on Monday, May 5th and the 4s will have on Wednesday, May 7th.   The grade 4s need to understand up to # 5 and the 5s need to understand all of the Big Ideas discussed below.

Fractions – Big Ideas

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 and be modeled in different ways:  part of a set, part of a region, as a measure, division & as a ratio.

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 fourth of a chocolate bar.  Most students said half but a few knew I was up to something.

The fourth came from this type of chocolate bar:

and the half from this:

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.  Since both pies are cut into 8ths all the pieces are the same size.  Therefore 5 pieces or 5/8 is more than 3/8:

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:

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.

..and the grade 5s discovered an algorithm to convert a mixed number to an improper fraction!  The whole number x the denominator + the numerator.   2 x 4 + 1 = 9

They also figured out how to go from improper fraction to mixed number.  Divide the numerator by the denominator (fractions are another way of expressing division after all!).  9 / 4 = 2 1/4

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