Partition circles and rectangles into two, three, or four
equal shares, describe the shares using the words halves,
thirds, half of, a third of, etc., and describe the whole as
two halves, three thirds, four fourths. Recognize that equal
shares of identical wholes need not have the same shape.
Partition circles and rectangles into two and four equal shares,
describe the shares using the words halves, fourths, and quarters,
and use the phrases half of, fourth of, and quarter of. Describe
the whole as two of or four of the shares. Understand for these
examples that decomposing into more equal shares creates
smaller shares.
Two children are sharing a brownie how much will each child get?
Equal parts are parts of equal measurement.
Unit Fractions: fractions with a numerator of 1.
When you partition a whole into four equal parts each part
is ¼ of the whole, and 4 copies of that part make the
whole.
Build fractions from unit fractions:
The numerator 3 of ¾ is the quantity when you put 3 of
the 1/4ths together.
The fraction 5/3 is the quantity when you combine 5 parts
together when the whole is divided into 3 equal parts.
Fractions as numbers on a number line.
Students understand that the fractions on the number line the one on the left is smaller and the fraction on the right is larger. The fraction represents ¼ is smaller than ½ because it is closer to 0. the distance from 0, Students see that fractions that have the same denominator can
be compared- the fraction with the greater numerator is greater
because it is made of more unit fractions. (It is important to make
sure each fraction refers to the same size whole)
5 = 1 + 1 + 1 + 1 +1 Therefore: 5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3
Knowing that 1 = 3/3 then:
Knowing that 3 x 7 = 7 + 7 + 7 then:
In general:
It is not necessary to find a least common denominator to
calculate sums of fractions, and in fact the effort of finding a least
common denominator is a distraction from understanding
algorithms for adding fractions.
5/3 is 1/3 of 5
Which leads to 1/3 x 5 = 5/3
How much chocolate will each person get if 3 people share ½
pound of chocolate equally?