Standards - Mathematics

Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

Use unit rates to represent and describe ratio relationships.

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.

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

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.

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

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.

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.

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

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

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.

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.

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]

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]

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

Graph proportional relationships.

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]

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.

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.

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.

Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

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]

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]