[C, CN, ME, PS]
Note: It is intended that positive fractions be interpreted to include both whole numbers and mixed numbers as well as common fractions. | |
(a) |
Identify and describe situations relevant to self, family, or community in which multiplication and division of fractions are involved. |
(b) |
Model the multiplication of two positive fractions and record the process symbolically. |
(c) |
Compare the multiplication of positive fractions to the multiplication of whole numbers, decimals, and integers. |
(d) |
Generalize and apply strategies for determining estimates of products of positive fractions |
(e) |
Generalize and apply strategies for multiplying positive fractions. |
(f) |
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 $1/2$). |
(g) |
Explain, using concrete or pictorial models as well as symbolic reasoning, how the distributive property can be used to multiply mixed numbers. For example, $2{1/2} x 3{1/4} = (2 + 1/2) x (3 + 1/4) = (2 x 3) + (2 x 1/4) + (1/2 x 3) + (1/2 x 1/4)$. |
(h) |
Model the division of two positive fractions and record the process symbolically. |
(i) |
Compare the division of positive fractions to the division of whole numbers, decimals, and integers. |
(j) |
Generalize and apply strategies for determining estimates of quotients of positive fractions. |
(k) |
Estimate the quotient of two given positive fractions and explain the strategy used. |
(l) |
Generalize and apply strategies for determining the quotients of positive fractions. |
(m) |
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 $1/2 \or 1/4$). |
(b) |
Identify, without calculating, the operation required to solve a problem involving fractions and justify the reasoning. |
(c) |
Create, represent (concretely, pictorially, or symbolically) and solve problems that involve one or more operations on positive fractions (including multiplication and division). |
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