MA19.3.15

Mathematics (2019) Grade(s): 3

Students know:

Fractions with different names can be equal.
Two fractions are equivalent if they are the same size, cover the same area, or are at the same point on a number line.
Unit fraction counting continues beyond 1 and whole numbers can be written as fractions.
Use a variety of area models and length models to show that a whole number can be expressed as a fraction and to show that fractions can be equivalent to whole numbers.
Comparing two fractions is only reasonable if they refer to the same whole.
The meaning of comparison symbols , = .
Reason about the size of a fraction to help compare fractions.
Use a variety of area and length models to represent two fractions that are the same size but have different names.
Use a fraction model to explain how equivalent fractions can be found.
Use a variety of area models and length models to demonstrate that any fraction that has the same nonzero numerator and denominator is equivalent to 1.
Use models to show that the numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater numerator is the greater fraction.
Use models to show that the denominator of a fraction indicates the size of equal parts a whole is partitioned into, and that the greater the denominator, the smaller the parts.-Determine when two fractions can not be compared because they do not refer to the same size whole.

Students are able to:

Explain equivalence of two fractions using visual models and reasoning about their size.
Compare two fractions with same numerators or with same denominators using visual models and reasoning about their size.
Express whole numbers as fractions.
Identify fractions equivalent to whole numbers.
Record comparisons of two fractions using , or = and justify conclusion.
Explain that the whole must be the same for the comparing of fractions to be valid.

Students understand that:

A fraction is a quantity which can be illustrated with a length model or an area model.
Two fractions can be the same size but have different fraction names.
A fraction can be equivalent to a whole number.
Any fraction that has the same nonzero numerator and denominator is equivalent to 1.
The numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater number of parts is the greater fraction.
The denominator of a fraction indicates the size of equal parts in a whole, so the greater the denominator, the smaller the size of the parts in a whole.