CC.2.1.7.D.1 Math.7.RP.1 7.RP.A.1 M07.A-R.1.1.1 M07.A-R.1.1.2 Math.7.RP.2a 7.RP.A.2.A Math.7.RP.2b 7.RP.A.2.B M07.A-R.1.1.3 M07.A-R.1.1.4 Math.7.RP.2c 7.RP.A.2.C Math.7.RP.2d 7.RP.A.2.D M07.A-R.1.1.5 MA.7.AR.4.1 MA.7.AR.4.2 MA.7.AR.4.3 MA.7.AR.4.4 MA.7.AR.4.5

Common Core Standards Interpret Proportional Relationships
Grade:	7th Grade
Standard:	CC.2.1.7.D.1
Description:	Analyze proportional relationships and use them to model and solve real-world and mathematical problems.
Standard:	Math.7.RP.1 or 7.RP.A.1
Description:	Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ^1/2/_1/4 miles per hour, equivalently 2 miles per hour.
Standard:	M07.A-R.1.1.1
Description:	Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.
Standard:	M07.A-R.1.1.2
Description:	Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin).
Standard:	Math.7.RP.2a or 7.RP.A.2.A
Description:	Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Standard:	Math.7.RP.2b or 7.RP.A.2.B
Description:	Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Standard:	M07.A-R.1.1.3
Description:	Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Standard:	M07.A-R.1.1.4
Description:	Represent proportional relationships by equations.
Standard:	Math.7.RP.2c or 7.RP.A.2.C
Description:	Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
Standard:	Math.7.RP.2d or 7.RP.A.2.D
Description:	Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Standard:	M07.A-R.1.1.5
Description:	Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.
Standard:	MA.7.AR.4.1
Description:	Determine whether two quantities have a proportional relationship by examining a table, graph or written description.
Standard:	MA.7.AR.4.2
Description:	Determine the constant of proportionality within a mathematical or real-world context given a table, graph or written description of a proportional relationship.
Standard:	MA.7.AR.4.3
Description:	Given a mathematical or real-world context, graph proportional relationships from a table, equation or a written description.
Standard:	MA.7.AR.4.4
Description:	Given any representation of a proportional relationship, translate the representation to a written description, table or equation.
Standard:	MA.7.AR.4.5
Description:	Solve real-world problems involving proportional relationships.

A rate is a ratio involving quantities, typically with different units.

A rate where the second quantity is 1 is called a unit rate.

The ratio is

\frac{1}{2}

pound of butter per

1 \frac{1}{2}

cups of flour.

To find the amount of butter per 1 cup of flour, or the unit rate, divide

\frac{1}{2}

pound of butter by

1 \frac{1}{2}

cups of flour.

Use the improper fraction

\frac{3}{2}

in place of the mixed number

1 \frac{1}{2}

\begin{array}{rcl} \frac{\frac{1}{2}}{\frac{3}{2}} & = & \frac{1}{2} \div \frac{3}{2} \\ = & \frac{1 \times 2}{2 \times 3} \\ = & \frac{2}{6} \\ = & \frac{1}{3} \end{array}

So,

\frac{1}{3}

pound of butter is needed for 1 cup of flour.

Common Core Standards

Interpret Proportional Relationships

CC.2.1.7.D.1

Analyze proportional relationships and use them to model and solve real-world and mathematical problems.

Math.7.RP.1 or 7.RP.A.1

M07.A-R.1.1.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

M07.A-R.1.1.2

Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin).

Math.7.RP.2a or 7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Math.7.RP.2b or 7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

M07.A-R.1.1.3

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

M07.A-R.1.1.4

Represent proportional relationships by equations.

Math.7.RP.2c or 7.RP.A.2.C

Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Math.7.RP.2d or 7.RP.A.2.D

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

M07.A-R.1.1.5

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate.

MA.7.AR.4.1

Determine whether two quantities have a proportional relationship by examining a table, graph or written description.

MA.7.AR.4.2

Determine the constant of proportionality within a mathematical or real-world context given a table, graph or written description of a proportional relationship.

MA.7.AR.4.3

Given a mathematical or real-world context, graph proportional relationships from a table, equation or a written description.

MA.7.AR.4.4

Given any representation of a proportional relationship, translate the representation to a written description, table or equation.

MA.7.AR.4.5

Solve real-world problems involving proportional relationships.

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