The Understanding Fractions Unit involves representing fractional parts of whole objects, lines, and sets in order to answer questions such as:

• How does knowing what one whole is help to identify fractional parts?

• If you know one of the fractional parts, how can you figure out what the whole is? How many fractional parts does it take to equal one whole?

• What models can be used to represent the meaning of the numerator and the meaning of the denominator?

• How can you prove that the greater the denominator, the smaller the fractional part and the smaller the denominator, the greater the fractional part?

Math Concepts and Skills: 

The student represents and describes the meanings of fractions.

The student:

• represents fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using a variety of tools such as linear models (including number lines), area models, and sets.

• explains that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a whole number greater than zero.

• composes and decomposes a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b.

• solves problems involving sharing an object or a set of objects among two or more recipients using a variety of models.