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Основно съдържание

STANDARDS

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US-AL

Math

Alabama Math

Grade 7 Accelerated: Proportional Reasoning

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

7A.1

Fully covered
Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions. [Grade 7, 1]

7A.2

Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

7A.2.a

Fully covered
Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

7A.2.b

Fully covered
Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7A.2.c

Fully covered
Explain in context the meaning of a point (x,y) on the graph of a proportional relationship, with special attention to the points (0,0) and (1, r) where r is the unit rate. [Grade 7, 2]

7A.3

Fully covered
Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease. [Grade 7, 3]

Analyze the relationship between proportional and non-proportional situations.

7A.4

Fully covered
Determine whether a relationship between two variables is proportional or non-proportional. [Grade 8, 7]

7A.5

Graph proportional relationships.

7A.5.a

Fully covered
Interpret the unit rate of a proportional relationship, describing the constant of proportionality as the slope of the graph which goes through the origin and has the equation y = mx where m is the slope. [Grade 8, 8]

7A.6

Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

7A.6.a

Mostly covered
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

7A.6.b

Fully covered
Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

7A.6.c

Not covered
Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.
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7A.6.d

Not covered
Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts. [Grade 8, 9]
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7A.7

Fully covered
Compare proportional and non-proportional linear relationships represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions) to solve real-world problems. [Grade 8, 10]