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Math
Virginia Math
Grade 7: Patterns, Functions, and Algebra
Determine the slope, 𝑚, as the rate of change in a proportional relationship between two quantities given a table of values, graph, or contextual situation and write an equation in the form 𝑦 = 𝑚𝑥 to represent the direct variation relationship. Slope may include positive or negative values (slope will be limited to positive values in a contextual situation).
Identify and describe a line with a slope that is positive, negative, or zero (0), given a graph.
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Graph a line representing a proportional relationship, between two quantities given an ordered pair on the line and the slope, 𝑚, as rate of change. Slope may include positive or negative values.
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Graph a line representing a proportional relationship between two quantities given the equation of the line in the form 𝑦 = 𝑚𝑥, where 𝑚 represents the slope as rate of change. Slope may include positive or negative values.
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Make connections between and among representations of a proportional relationship between two quantities using problems in context, tables, equations, and graphs. Slope may include positive or negative values (slope will be limited to positive values in a contextual situation).
- Constant of proportionality from graph
- Constant of proportionality from graphs
- Identify proportional relationships from graphs
- Identifying constant of proportionality graphically
- Identifying proportional relationships from graphs
- Identifying the constant of proportionality from equation
- Interpret constant of proportionality in graphs
- Proportional relationships: graphs
Use the order of operations and apply the properties of real numbers to simplify numerical expressions. Exponents are limited to 1, 2, 3, or 4 and bases are limited to positive integers. Expressions should not include braces { } but may include brackets [ ] and absolute value bars | |. Square roots are limited to perfect squares.
Represent equivalent algebraic expressions in one variable using concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles).
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Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and properties of real numbers. Expressions may require combining like terms to simplify. Expressions will include only linear and numeric terms. Coefficients and numeric terms may be positive or negative rational numbers.
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients & distribution
- Combining like terms with negative coefficients & distribution
- Combining like terms with rational coefficients
- Distributive property with variables (negative numbers)
- Equivalent expressions: negative numbers & distribution
- Equivalent expressions: negative numbers & distribution
- Factoring with the distributive property
- Simplifying expressions with rational numbers
- The distributive property with variables
- Understand subtraction as adding the opposite
Use the order of operations and apply the properties of real numbers to evaluate algebraic expressions for given replacement values of the variables. Exponents are limited to 1, 2, 3, or 4 and bases are limited to positive integers. Expressions should not include braces { } but may include brackets [ ] and absolute value bars | |. Square roots are limited to perfect squares. Limit the number of replacements to no more than three per expression. Replacement values may be positive or negative rational numbers.
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Represent and solve two-step linear equations in one variable using a variety of concrete materials and pictorial representations.
Apply properties of real numbers and properties of equality to solve two-step linear equations in one variable. Coefficients and numeric terms will be rational.
- Find the mistake: two-step equations
- Find the mistake: two-step equations
- Intro to two-step equations
- Two-step equations
- Two-step equations intuition
- Two-step equations review
- Two-step equations with decimals and fractions
- Two-step equations with decimals and fractions
- Two-step equations with decimals and fractions
- Two-step equations word problems
- Worked example: two-step equations
Confirm algebraic solutions to linear equations in one variable.
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Write a two-step linear equation in one variable to represent a verbal situation, including those in context.
Create a verbal situation in context given a two-step linear equation in one variable.
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Solve problems in context that require the solution of a two-step linear equation.
Apply properties of real numbers and the addition, subtraction, multiplication, and division properties of inequality to solve one- and two-step inequalities in one variable. Coefficients and numeric terms will be rational.
- One-step inequalities
- One-step inequalities examples
- One-step inequalities review
- One-step inequalities: -5c ≤ 15
- One-step inequality word problem
- Order of operations with negative numbers
- Testing solutions to inequalities
- Two-step inequalities
- Two-step inequalities
- Two-step inequality word problem: apples
- Two-step inequality word problem: R&B
- Two-step inequality word problems
Investigate and explain how the solution set of a linear inequality is affected by multiplying or dividing both sides of the inequality statement by a rational number less than zero.
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Represent solutions to one- or two-step linear inequalities in one variable algebraically and graphically using a number line.
Write one- or two-step linear inequalities in one variable to represent a verbal situation, including those in context.
Create a verbal situation in context given a one or two-step linear inequality in one variable.
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Solve problems in context that require the solution of a one- or two-step inequality.
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Identify a numerical value(s) that is part of the solution set of as given one- or two-step linear inequality in one variable.
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Describe the differences and similarities between solving linear inequalities in one variable and linear equations in one variable.
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