Hlavní obsah
Math
Virginia Math
Grade 8: Patterns, Functions, and Algebra
Represent algebraic expressions using concrete manipulatives or pictorial representations (e.g., colored chips, algebra tiles), including expressions that apply the distributive property.
(Content unavailable)
Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and properties of real numbers. Expressions may need to be expanded (using the distributive property) or require combining like terms to simplify. Expressions will include only linear and numeric terms. Coefficients and numeric terms may be rational.
Determine whether a relation, represented by a set of ordered pairs, a table, or a graph of discrete points is a function. Sets are limited to no more than 10 ordered pairs.
Identify the domain and range of a function represented as a set of ordered pairs, a table, or a graph of discrete points.
Determine how adding a constant (𝑏) to the equation of a proportional relationship 𝑦 = 𝑚𝑥 will translate the line on a graph.
(Content unavailable)
Describe key characteristics of linear functions including slope (𝑚), 𝑦-intercept (𝑏), and independent and dependent variables.
- Intercepts from a graph
- Intercepts from a table
- Intercepts from an equation
- Intercepts from an equation
- Intercepts of lines review (x-intercepts and y-intercepts)
- Interpreting a graph example
- Intro to intercepts
- Intro to slope
- Intro to slope
- Intro to slope-intercept form
- Linear equations word problems
- Linear equations word problems: graphs
- Linear functions word problem: fuel
- Linear functions word problem: pool
- Linear graphs word problem: cats
- Linear graphs word problems
- Positive & negative slope
- Rates & proportional relationships example
- Slope & direction of a line
- Slope formula
- Slope from equation
- Slope from equation
- Slope from graph
- Slope from two points
- Slope of a horizontal line
- Slope of a line: negative slope
- Slope review
- Slope-intercept equation from slope & point
- Slope-intercept equation from two points
- Slope-intercept form problems
- Slope-intercept form review
- Slope-intercept from two points
- Slope-intercept intro
- Worked example: intercepts from an equation
- Worked example: slope from two points
- Worked examples: slope-intercept intro
- Writing slope-intercept equations
- x-intercept of a line
Graph a linear function given a table, equation, or a situation in context.
- Graphing linear relationships word problems
- Graphing proportional relationships
- Graphing proportional relationships from a table
- Graphing proportional relationships from an equation
- Intro to the coordinate plane
- Linear function example: spending money
- Linear functions word problem: fuel
- Linear functions word problem: pool
- Recognizing linear functions
- Worked example: intercepts from an equation
Create a table of values for a linear function given a graph, equation in the form of 𝑦 = 𝑚𝑥 + 𝑏, or context.
Write an equation of a linear function in the form 𝑦 = 𝑚𝑥 + 𝑏, given a graph, table, or a situation in context.
- Linear functions word problem: iceberg
- Linear functions word problem: paint
- Modeling with linear equations: gym membership & lemonade
- Modeling with linear equations: snow
- Modeling with tables, equations, and graphs
- Slope-intercept equation from graph
- Slope-intercept equation from graph
- Slope-intercept equation from slope & point
- Slope-intercept equation from two points
- Slope-intercept form problems
- Slope-intercept form review
- Slope-intercept from two points
- Slope-intercept intro
- Writing linear functions word problems
- Writing slope-intercept equations
Create a context for a linear function given a graph, table, or equation in the form 𝑦 = 𝑚𝑥 + 𝑏.
(Content unavailable)
Represent and solve multistep linear equations in one variable with the variable on one or both sides of the equation (up to four steps) using a variety of concrete materials and pictorial representations.
Apply properties of real numbers and properties of equality to solve multistep linear equations in one variable (up to four steps). Coefficients and numeric terms will be rational. Equations may contain expressions that need to be expanded (using the distributive property) or require combining like terms to solve.
Write a multistep linear equation in one variable to represent a verbal situation, including those in context.
Create a verbal situation in context given a multistep linear equation in one variable.
(Content unavailable)
Solve problems in context that require the solution of a multistep linear equation.
(Content unavailable)
Interpret algebraic solutions in context to linear equations in one variable.
(Content unavailable)
Confirm algebraic solutions to linear equations in one variable.
Apply properties of real numbers and properties of inequality to solve multistep linear inequalities (up to four steps) in one variable with the variable on one or both sides of the inequality. Coefficients and numeric terms will be rational. Inequalities may contain expressions that need to be expanded (using the distributive property) or require combining like terms to solve.
(Content unavailable)
Represent solutions to inequalities algebraically and graphically using a number line.
(Content unavailable)
Write multistep linear inequalities in one variable to represent a verbal situation, including those in context.
(Content unavailable)
Create a verbal situation in context given a multistep linear inequality in one variable.
(Content unavailable)
Solve problems in context that require the solution of a multistep linear inequality in one variable.
(Content unavailable)
Identify a numerical value(s) that is part of the solution set of a given inequality.
(Content unavailable)
Interpret algebraic solutions in context to linear inequalities in one variable.
(Content unavailable)