Identify and describe situations relevant to self, family, or community in which multiplication and division of fractions are involved.

Model the multiplication of two positive fractions and record the process symbolically.

Compare the multiplication of positive fractions to the multiplication of whole numbers, decimals, and integers.

Generalize and apply strategies for determining estimates of products of positive fractions

Generalize and apply strategies for multiplying positive fractions.

Critique the statement “Multiplication always results in a larger quantity” and reword the statement to capture the points of correction or clarification raised (e.g., $1/2 x 1/2 - 1/4$ which is smaller than $1/2$).

Explain, using concrete or pictorial models as well as symbolic reasoning, how the distributive property can be used to multiply mixed numbers. For example, $2{1/2} x 3{1/4} = (2 + 1/2) x (3 + 1/4) = (2 x 3) + (2 x 1/4) + (1/2 x 3) + (1/2 x 1/4)$.

Model the division of two positive fractions and record the process symbolically.

Compare the division of positive fractions to the division of whole numbers, decimals, and integers.

Generalize and apply strategies for determining estimates of quotients of positive fractions.

Estimate the quotient of two given positive fractions and explain the strategy used.

Generalize and apply strategies for determining the quotients of positive fractions.

Critique the statement “Division always results in a smaller quantity” and reword the statement to capture the points of correction or clarification raised (e.g., ${1/2} ÷ {1/4} = 2$ but 2 is bigger than $1/2 \or 1/4$).

Identify, without calculating, the operation required to solve a problem involving fractions and justify the reasoning.

Create, represent (concretely, pictorially, or symbolically) and solve problems that involve one or more operations on positive fractions (including multiplication and division).