Growth: Algebra 1 International (2017) Gizmos | Browse by Core Curriculum

1: Number Sense, Properties, and Number Theory

1.1: Number Sense: Real Numbers

1.1.1: Exponents

1.1.1.2: [RIT 221 - 233] Represents a whole number as a power of a whole number

1.1.2: Absolute Value: Concepts/Properties

1.1.2.1: [RIT 227 - 228] Evaluates the absolute value of a number

1.1.3: Properties and Relationships of Operations

1.1.3.1: [RIT 209 - 217] Understands that a number and its opposite are the same distance from 0 on a number line

1.1.4: Real/Complex Numbers: Concepts/Properties

1.1.4.3: [RIT 231 - 261] Compares and orders real numbers

1.1.5: Rational Numbers: Equivalence

1.1.5.1: [RIT 209 - 232] Converts between decimals and fractions with denominators of 10 or 100

1.1.5.2: [RIT 211 - 237] Converts between decimals and fractions with denominators of 2, 4, or 5

1.1.5.5: [RIT 227 - 233] Converts between decimals and fractions with a denominator of 3

1.1.6: Rational Numbers: Compare/Order

1.1.6.3: [RIT 211 - 211] Compares integers

1.1.6.4: [RIT 218 - 255] Orders positive and negative rational numbers

1.1.6.5: [RIT 224 - 230] Compares positive rational numbers represented in multiple forms

1.1.7: Rational Numbers: Represent/Model

1.1.7.1: [RIT 191 - 219] Understands positive and negative numbers in terms of real-world situations

1.1.7.2: [RIT 200 - 218] Locates integers on a number line

1.1.7.3: [RIT 204 - 204] Locates positive and negative rational numbers on a number line

1.1.7.4: [RIT 214 - 232] Locates negative rational numbers on a number line

1.1.8: Scientific Notation

1.1.8.1: [RIT 224 - 230] Converts a number from scientific notation to standard form

1.1.8.2: [RIT 229 - 250] Converts a number from standard form to scientific notation

1.2: Properties of Real Numbers

1.2.1: Properties and Relationships of Operations

1.2.1.1: [RIT 184 - 214] Identifies the missing value in an equation to show that a number and its opposite have a sum of 0

1.2.1.3: [RIT 222 - 231] Locates the additive inverse of a number on a number line

1.2.1.4: [RIT 228 - 242] Understands the additive inverse property

1.2.1.5: [RIT 231 - 231] Names the property of operation shown by a given statement

1.2.1.6: [RIT 243 - 243] Understands the multiplicative inverse property

1.2.1.7: [RIT 243 - 243] Understands a negative number is less than its opposite

1.2.1.8: [RIT 245 - 245] Understands the multiplicative identity property

1.2.1.9: [RIT 245 - 245] Understands that the product of two negative numbers is positive

1.2.1.10: [RIT 262 - 262] Defines properties of equality

1.3: Number Theory

1.3.1: Whole Numbers: Concepts/Properties

1.3.1.1: [RIT 200 - 225] Identifies factors of numbers less than 100

1.3.1.2: [RIT 201 - 201] Determines prime factorization of a number using a factor tree

1.3.1.3: [RIT 208 - 242] Determines common multiples

1.3.1.4: [RIT 210 - 220] Determines greatest common factors

1.3.1.5: [RIT 211 - 253] Solves real-world problems involving the least common multiple

1.3.1.6: [RIT 213 - 256] Determines least common multiples

1.3.1.7: [RIT 214 - 214] Solves problems involving factors and multiples

1.3.1.8: [RIT 218 - 243] Determines the prime factorization of a number

1.3.1.10: [RIT 219 - 245] Determines common factors

1.3.1.11: [RIT 219 - 219] Identifies multiples of two-digit numbers

1.3.1.12: [RIT 222 - 223] Identifies prime and composite numbers

1.3.1.13: [RIT 235 - 240] Identifies true statements about number-theory concepts, including prime, composite, multiples, factors, least common multiples, and greatest common factors

1.3.1.14: [RIT 237 - 237] Identifies factors of numbers greater than 100

1.3.1.16: [RIT 259 - 259] Solves problems by applying multiple number-theory concepts, including prime numbers, multiples, factors, least common multiples, and greatest common factors

2: Computation and Estimation with Real Numbers

2.1: Computation with Real Numbers

2.1.1: Numerical Expressions

2.1.1.1: [RIT 227 - 227] Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving both positive and negative rational numbers

2.1.1.2: [RIT 234 - 234] Represents real-world problems involving the addition and subtraction of integers with numerical expressions

2.1.3: Exponents

2.1.3.1: [RIT 212 - 221] Evaluates numbers with whole-number bases and whole-number exponents

2.1.3.2: [RIT 235 - 235] Evaluates numbers with negative integer bases and whole-number exponents

2.1.4: Rational Numbers: Computation

2.1.4.1: [RIT 225 - 253] Multiplies rational numbers, including combinations of positive or negative fractions, decimals, and integers

2.1.4.2: [RIT 228 - 242] Adds and subtracts rational numbers, including combinations of positive or negative fractions, decimals, and integers

2.1.5: Rational Numbers: Solve Real-World and Mathematical Problems

2.1.5.1: [RIT 202 - 244] Solves real-world problems involving the addition and subtraction of integers

2.1.6: Scientific Notation

2.1.6.1: [RIT 233 - 244] Solves real-world problems with numbers expressed in scientific notation

2.1.6.2: [RIT 235 - 278] Multiplies and divides numbers expressed in scientific notation

2.1.7: Radicals

2.1.7.1: [RIT 228 - 260] Evaluates the square root of a perfect square

2.1.7.2: [RIT 263 - 273] Multiplies binomial radical expressions

2.1.8: Integers: Computation

2.1.8.1: [RIT 211 - 229] Adds and subtracts integers

2.1.8.2: [RIT 212 - 220] Multiplies and divides integers

2.1.8.3: [RIT 229 - 236] Represents addition and subtraction of integers on a number line

2.1.8.4: [RIT 231 - 231] Understands subtracting an integer is the same as adding its opposite

2.2: Ratio and Proportion

2.2.1: Conversion of Units

2.2.1.1: [RIT 224 - 257] Converts units of speed

2.2.2: Rates/Ratios/Proportions/Percents

2.2.2.1: [RIT 185 - 220] Represents percents less than 100% using models

2.2.2.2: [RIT 188 - 228] Solves for a missing value in a proportion by basic reasoning with equivalent fractions

2.2.2.3: [RIT 190 - 242] Uses a given unit rate to solve a one-step real-world problem

2.2.2.4: [RIT 191 - 251] Solves real-world and mathematical problems using ratios or proportional reasoning

2.2.2.5: [RIT 191 - 240] Uses ratios of whole numbers to calculate unit rates

2.2.2.7: [RIT 203 - 246] Solves one-step percent problems within a real-world or mathematical context

2.2.2.8: [RIT 203 - 239] Converts between decimals and percents less than 100%

2.2.2.9: [RIT 205 - 228] Uses ratios of whole numbers and fractions to calculate unit rates

2.2.2.10: [RIT 206 - 233] Uses ratios of whole numbers and decimals to calculate unit rates

2.2.2.11: [RIT 209 - 246] Calculates percents of numbers

2.2.2.12: [RIT 214 - 241] Identifies the part-to-whole ratio between two quantities

2.2.2.13: [RIT 214 - 249] Determines equivalent ratios

2.2.2.16: [RIT 216 - 253] Solves for a missing value in a proportion by taking a cross product

2.2.2.17: [RIT 216 - 263] Uses a given unit rate to solve a multi-step real-world problem

2.2.2.18: [RIT 217 - 247] Compares unit rates within a real-world context

2.2.2.19: [RIT 219 - 257] Converts unit rates to solve real-world problems

2.2.2.20: [RIT 219 - 239] Identifies the part-to-part ratio between two quantities

2.2.2.21: [RIT 219 - 236] Uses ratios of decimals to calculate unit rates

2.2.2.22: [RIT 219 - 244] Calculates the percent one number is of another number

2.2.2.23: [RIT 220 - 237] Calculates the whole when given a part and the percent

2.2.2.24: [RIT 220 - 231] Converts between percents and ratios expressed verbally or in the form a:b

2.2.2.26: [RIT 225 - 234] Determines the whole in a real-world percent problem given the part and the percent

2.2.2.27: [RIT 226 - 226] Applies scale factors to solve problems involving scale drawings, maps, and models

2.2.2.28: [RIT 227 - 258] Solves multi-step percent problems within a real-world or mathematical context

2.2.2.29: [RIT 230 - 252] Writes a proportion to solve a real-world problem

2.2.2.30: [RIT 235 - 256] Calculates the percent one number is of another number for percents greater than 100%

2.2.2.31: [RIT 235 - 258] Solves real-world problems involving percent or fractional increase

2.2.2.33: [RIT 242 - 244] Writes a corresponding linear equation for a given proportion

2.2.2.34: [RIT 242 - 256] Calculates simple interest

2.2.2.35: [RIT 251 - 255] Compares ratios within a real-world context

2.2.3: Rational Numbers: Equivalence

2.2.3.1: [RIT 196 - 228] Converts between percents and fractions with denominators of 10 or 100

2.2.3.2: [RIT 212 - 212] Determines equivalence between fractions, decimals, and percents

2.2.3.3: [RIT 214 - 214] Determines equivalence between fractions and percents using models

2.2.3.4: [RIT 215 - 229] Converts between percents and fractions with denominators other than 10 and 100

2.2.3.5: [RIT 218 - 218] Determines equivalence between decimals and percents using models

2.3: Estimation with Real Numbers

2.3.1: Whole Numbers and Decimals: Rounding/Estimation

2.3.1.1: [RIT 178 - 217] Estimates solutions to one-step word problems involving any of the four operations with whole numbers

2.3.1.2: [RIT 208 - 211] Estimates solutions to one-step word problems involving any of the four operations with decimals, including contexts involving money

2.3.2: Real/Complex Numbers: Concepts/Properties

2.3.2.1: [RIT 227 - 260] Approximates the value of an irrational number

3: Patterns, Functions, and Graphing

3.1: Patterns: Arithmetic and Geometric

3.1.1: Patterns/Sequences/Series

3.1.1.1: [RIT 190 - 226] Determines the rule, and extends or finds a missing term for growing/shrinking shape patterns

3.1.1.2: [RIT 195 - 233] Determines the two-step rule, and extends or finds a missing term for number patterns involving multiple operations

3.1.1.3: [RIT 197 - 227] Determines the rule for growing/shrinking shape patterns

3.1.1.8: [RIT 215 - 218] Determines the rule, and extends or finds a missing term given descriptions of number patterns within a real-world context

3.1.1.9: [RIT 218 - 258] Determines the value of a term in an arithmetic sequence given a contextual situation

3.1.1.11: [RIT 227 - 232] Determines the single-step rule, and extends or finds a missing term for number patterns involving fractions

3.1.1.13: [RIT 229 - 266] Determines the value of a term in a geometric sequence given a contextual situation

3.1.1.14: [RIT 229 - 285] Determines the value of a term in a geometric sequence defined by a list

3.1.1.15: [RIT 232 - 238] Recognizes arithmetic sequences

3.1.1.16: [RIT 243 - 275] Writes an expression or formula for the nth term of an arithmetic sequence given a number sequence

3.1.1.17: [RIT 252 - 252] Determines the rule, and extends or finds a missing term for number patterns which increase or decrease by a nonconstant amount, within a real-world context

3.1.1.19: [RIT 256 - 256] Determines the common ratio in a geometric sequence

3.1.1.20: [RIT 260 - 271] Writes an expression or formula for the nth term of a geometric sequence given a number sequence

3.2: Functions

3.2.1: Properties and Operations of Functions

3.2.1.1: [RIT 206 - 206] Expresses a relation defined by a mapping diagram as a set of ordered pairs

3.2.1.2: [RIT 235 - 239] Determines the input of a function given an output

3.2.1.3: [RIT 238 - 265] Performs operations with functions

3.2.1.4: [RIT 238 - 263] Identifies the type of function by its equation

3.2.1.6: [RIT 248 - 258] Distinguishes between linear and nonlinear functions given an equation, a graph, or a table of values

3.2.1.9: [RIT 261 - 270] Determines if a relation defined by a set of ordered pairs, a table of values, or a graph is a function

3.2.1.11: [RIT 264 - 280] Determines the domain of a rational function

3.2.1.17: [RIT 283 - 289] Graphs the inverse of a function

3.2.2: Number Sentences/Equations/Equivalence

3.2.2.1: [RIT 238 - 266] Identifies an ordered pair that is a solution to a two-variable equation

3.2.3: Patterns/Sequences/Series

3.2.3.1: [RIT 175 - 201] Determines missing values in a table representing a proportional relationship, given the function rule

3.2.3.2: [RIT 180 - 220] Determines missing values in a table representing a proportional relationship, function rule not given

3.2.3.3: [RIT 187 - 228] Determines missing values in a function table representing a nonproportional relationship, given the rule

3.2.3.5: [RIT 202 - 218] Determines the rule for a given function table representing a proportional relationship

3.2.3.6: [RIT 205 - 231] Determines the rule for a given function table representing a nonproportional relationship

3.2.3.7: [RIT 210 - 228] Identifies a function table that matches a given rule

3.2.4: Polynomial Functions

3.2.4.1: [RIT 227 - 254] Identifies the zeros of a polynomial function from a graph

3.2.4.2: [RIT 262 - 274] Factors polynomial functions to determine zeros

3.2.4.4: [RIT 267 - 267] Evaluates a polynomial function using synthetic division

3.2.4.5: [RIT 270 - 270] Identifies key features of a polynomial function given a graph

3.2.4.6: [RIT 270 - 270] Describes the effects of transformations on the graphs of polynomial functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

3.2.4.7: [RIT 284 - 286] Identifies the factors of a polynomial function from a graph

3.2.5: Rate of Change/Slope

3.2.5.1: [RIT 202 - 249] Compares the rate of change between two proportional relationships represented in different ways

3.2.5.2: [RIT 212 - 255] Interprets the meaning of the slope of a graph in a real-world linear relationship

3.2.5.3: [RIT 213 - 236] Calculates the rate of change from a graph representing a real-world linear relationship

3.2.5.4: [RIT 215 - 245] Calculates the rate of change from a table or description of a real-world linear relationship

3.2.5.5: [RIT 216 - 222] Determines the coordinates of the point representing the unit rate on a graph of a proportional relationship

3.2.5.6: [RIT 216 - 225] Identifies the unit rate from the graph of a proportional relationship

3.2.5.7: [RIT 227 - 257] Calculates the rate of change of a piecewise function over a given interval

3.2.5.9: [RIT 237 - 250] Identifies the y-intercept and the slope of a line given an equation of the line in the form y = mx+b

3.2.5.10: [RIT 238 - 258] Understands that the slope is the same between any two points on a line

3.2.5.11: [RIT 239 - 262] Determines the y-intercept and the slope of a line given an equation of the line in a form other than y = mx+b

3.2.5.12: [RIT 243 - 243] Compares the rate of change and intercepts between two nonproportional linear functions represented in the same way

3.2.5.13: [RIT 244 - 246] Interprets the meaning of the slope for the equation y = mx + b within the context of a real-world linear relationship

3.2.5.14: [RIT 247 - 250] Calculates the slope of a line on a graph

3.2.5.15: [RIT 248 - 259] Calculates the slope of a line given ordered pairs

3.2.6: Quadratic Functions

3.2.6.1: [RIT 214 - 214] Interprets zeros, extreme values, and symmetry of a graph within the context of a real-world quadratic relationship

3.2.6.3: [RIT 230 - 249] Describes the effects that changes in the constant terms have on the graphs of quadratic functions

3.2.6.4: [RIT 232 - 251] Evaluates a quadratic function for a given value in its domain

3.2.6.5: [RIT 237 - 259] Evaluates a quadratic function for a given value in its domain to solve a real-world problem

3.2.6.6: [RIT 239 - 255] Identifies the vertex, intercepts, or axis of symmetry of a quadratic function given a graph

3.2.6.7: [RIT 242 - 261] Determines the zeros of a quadratic function from a table of values

3.2.6.9: [RIT 247 - 280] Graphs quadratic functions

3.2.6.10: [RIT 249 - 276] Graphs transformations of quadratic functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

3.2.6.11: [RIT 250 - 280] Determines the maximum, minimum, y-intercept, or zeros of a quadratic function to solve real-world problems

3.2.6.12: [RIT 253 - 253] Recognizes the graph of a quadratic relationship

3.2.6.13: [RIT 254 - 268] Writes a quadratic function given the zeros

3.2.6.14: [RIT 259 - 259] Writes a quadratic function to represent real-world or mathematical contexts

3.2.6.16: [RIT 261 - 275] Determines an x-intercept of a quadratic function given the other x-intercept and the vertex or the axis of symmetry

3.2.6.17: [RIT 261 - 275] Determines the vertex, intercepts, or axis of symmetry of a quadratic function given an equation

3.2.6.18: [RIT 262 - 289] Describes the effects that changes in the coefficients have on the graphs of quadratic functions

3.2.6.19: [RIT 265 - 265] Understands the relationship between the zeros of a function and the x-intercepts of the graph of the function

3.2.6.20: [RIT 269 - 269] Determines the zeros of a quadratic function by factoring

3.2.6.21: [RIT 270 - 272] Writes a quadratic function given a graph

3.2.6.22: [RIT 272 - 277] Rewrites a quadratic equation into vertex form

3.2.7: Linear Functions

3.2.7.1: [RIT 192 - 233] Graphs a linear function of the form y = mx given a simple scenario

3.2.7.2: [RIT 195 - 256] Interprets the meaning of the y-intercept of a graph within the context of a real-world linear relationship

3.2.7.3: [RIT 198 - 206] Expresses the linear relationship between variables in words

3.2.7.4: [RIT 200 - 249] Translates between the graph of a piecewise linear function and a verbal description of the real-world relationship

3.2.7.7: [RIT 219 - 259] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given the slope and y-intercept

3.2.7.8: [RIT 219 - 232] Identifies the table of values given a graph of a linear relationship in the form y = mx + b

3.2.7.10: [RIT 224 - 252] Understands independent and dependent variables within a linear context

3.2.7.11: [RIT 226 - 240] Writes an equation in the form y = mx to represent the relationship between real-world quantities given a simple scenario

3.2.7.13: [RIT 228 - 259] Writes the equation of a line in the form y = mx + b given a table of values or two ordered pairs

3.2.7.14: [RIT 229 - 237] Translates between the graph of a linear function and a verbal description of the real-world relationship

3.2.7.16: [RIT 231 - 233] Describes a situation that can be represented by a given linear equation

3.2.7.17: [RIT 235 - 243] Interprets the meaning of the constant term in the equation y = mx + b within the context of a real-world linear relationship

3.2.7.20: [RIT 235 - 235] Identifies an intercept of a graph of a linear function

3.2.7.21: [RIT 237 - 274] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given a complex scenario

3.2.7.22: [RIT 238 - 253] Solves direct variation problems

3.2.7.26: [RIT 240 - 240] Writes an equation in the form y = mx + b to represent the relationship between real-world quantities given a simple scenario

3.2.7.28: [RIT 241 - 241] Writes an equation in standard form to represent the relationship between real-world quantities given a scenario

3.2.7.29: [RIT 243 - 243] Recognizes direct variation situations

3.2.7.30: [RIT 244 - 251] Graphs the equation of a line in the form y = mx + b

3.2.7.32: [RIT 245 - 261] Describes the effects that changes in the constant terms have on the graphs of linear functions

3.2.7.34: [RIT 250 - 262] Illustrates the result of changes in the slope and y-intercept within a real-world linear relationship

3.2.7.35: [RIT 250 - 250] Determines the y-intercept of a line given two points on the line

3.2.7.36: [RIT 253 - 253] Rewrites a linear equation in the form y = mx + b

3.2.7.37: [RIT 253 - 253] Graphs the equation of a line in standard form

3.2.7.38: [RIT 255 - 269] Rewrites a linear equation into the form Ax + By = C

3.2.7.39: [RIT 255 - 255] Represents a proportional relationship in more than one form, including tables, graphs, equations, and verbal descriptions

3.2.7.41: [RIT 257 - 257] Writes the equation of a line in the form y = mx + b given the slope and a point on the line

3.2.7.42: [RIT 259 - 259] Writes the equation of a line in standard form given a table of values or two ordered pairs

3.2.7.44: [RIT 268 - 268] Writes the equation of a line in standard form given the slope and y-intercept

3.2.7.45: [RIT 268 - 268] Writes the equation of a line in standard form given the slope and a point on the line

3.2.8: Piecewise/Absolute Value Functions

3.2.8.2: [RIT 249 - 276] Graphs absolute value functions

3.2.8.3: [RIT 250 - 250] Describes the effects of transformations on the graphs of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

3.2.8.4: [RIT 253 - 253] Determines the y-intercept of the transformation of an absolute value function, given the equation

3.2.8.5: [RIT 264 - 266] Writes the equation representing transformations of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

3.2.8.6: [RIT 269 - 269] Graphs transformations of absolute value functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

3.2.8.7: [RIT 270 - 280] Graphs piecewise functions

3.2.8.8: [RIT 276 - 276] Writes a piecewise function given a graph

3.2.9: Rational Functions

3.2.9.1: [RIT 251 - 291] Determines end behavior of rational functions

3.2.9.2: [RIT 253 - 253] Writes rational functions to represent real-world or mathematical problems

3.2.9.3: [RIT 260 - 265] Identifies the table of values that represents an inverse-variation relationship

3.2.9.4: [RIT 261 - 281] Graphs rational functions

3.2.9.5: [RIT 261 - 282] Determines x-intercepts for rational functions

3.2.9.6: [RIT 268 - 268] Determines points of discontinuity for rational functions

3.2.9.7: [RIT 269 - 269] Solves inverse variation problems

3.3: Coordinate Graphing

3.3.1: Coordinate Geometry

3.3.1.1: [RIT 181 - 229] Determines the coordinates of points in all four quadrants of a coordinate graph

3.3.1.2: [RIT 187 - 208] Interprets points with whole number coordinates in the first quadrant within the given context

3.3.1.3: [RIT 198 - 221] Determines the coordinates of points in the first quadrant of a coordinate plane

3.3.1.4: [RIT 201 - 218] Counts to find the distance between points on the coordinate plane

3.3.1.6: [RIT 203 - 215] Plots the coordinates of points in the first quadrant of a coordinate plane

3.3.1.7: [RIT 205 - 232] Determines the distance between two points with the same first or second coordinate

3.3.1.8: [RIT 214 - 235] Determines the coordinates of missing vertices of geometric figures in the first quadrant given the coordinates of the other vertices

3.3.1.9: [RIT 215 - 236] Plots points in all four quadrants of a coordinate plane

3.3.1.12: [RIT 242 - 268] Determines the distance between two points on the coordinate plane

3.3.1.15: [RIT 251 - 280] Identifies collinear points

4: Expressions

4.1: Evaluate and Simplify Expressions

4.1.1: Algebraic Expressions

4.1.1.1: [RIT 212 - 261] Writes linear expressions in one variable to represent real-world or mathematical contexts

4.1.1.2: [RIT 213 - 235] Evaluates linear expressions at given values with variables involving positive rational numbers

4.1.1.3: [RIT 216 - 247] Translates between verbal and algebraic expressions

4.1.1.5: [RIT 217 - 253] Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms

4.1.1.7: [RIT 221 - 248] Generates equivalent linear expressions by using the associative, commutative, or distributive property

4.1.1.9: [RIT 227 - 242] Generates equivalent linear expressions by combining like terms

4.1.1.10: [RIT 236 - 263] Uses properties of exponents to simplify algebraic expressions involving whole-number exponents

4.1.1.11: [RIT 237 - 267] Evaluates nonlinear expressions at given values with variables involving negative rational numbers

4.1.1.12: [RIT 239 - 239] Generates equivalent nonlinear expressions by combining like terms

4.1.1.13: [RIT 242 - 242] Interprets the variable in a linear expression within the context of a real-world relationship

4.1.1.15: [RIT 244 - 273] Simplifies rational expressions

4.1.1.16: [RIT 244 - 244] Determines the number of terms in a polynomial

4.1.1.17: [RIT 245 - 248] Uses algebra tiles to model polynomials

4.1.1.19: [RIT 254 - 269] Generates equivalent nonlinear expressions by using the associative, commutative, and distributive properties, and by combining like terms

4.1.1.20: [RIT 256 - 256] Interprets the constant in a quadratic expression within the context of a real-world relationship

4.1.1.21: [RIT 263 - 263] Writes linear expressions in two variables to represent real-world or mathematical contexts

4.1.1.22: [RIT 265 - 274] Writes quadratic expressions in one variable to represent real-world or mathematical contexts

4.1.1.23: [RIT 271 - 271] Writes rational expressions in one variable to represent real-world or mathematical contexts

4.1.2: Numerical Expressions

4.1.2.1: [RIT 181 - 204] Evaluates numerical expressions involving addition and subtraction with whole numbers and parentheses

4.1.2.2: [RIT 196 - 240] Evaluates numerical expressions involving multiple operations with whole numbers and parentheses

4.1.2.4: [RIT 211 - 218] Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers

4.1.2.5: [RIT 215 - 215] Represents real-world problems involving the addition and subtraction of integers with numerical expressions

4.1.2.7: [RIT 217 - 240] Evaluates numerical expressions involving multiple operations with whole numbers, no parenthesis

4.1.2.8: [RIT 218 - 264] Uses properties of exponents to simplify numerical expressions involving whole-number exponents only

4.1.2.9: [RIT 220 - 240] Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving both positive and negative rational numbers

4.1.2.10: [RIT 221 - 243] Applies the order of operations, with grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers

4.1.2.11: [RIT 223 - 232] Applies the order of operations, without grouping symbols and with whole-number exponents, to simplify numerical expressions consisting of positive rational numbers

4.1.2.14: [RIT 238 - 238] Applies the order of operations, without grouping symbols or whole-number exponents, to simplify numerical expressions involving positive rational numbers

4.1.2.15: [RIT 243 - 270] Uses properties of radicals to simplify radical expressions

4.1.2.17: [RIT 246 - 279] Uses properties of exponents to simplify numerical expressions involving negative integer exponents, including zero

4.1.2.18: [RIT 260 - 271] Simplifies numerical expressions involving sums and differences of radicals

4.1.2.20: [RIT 279 - 279] Simplifies numerical expressions containing radicals and rational exponents

4.1.4: Exponents

4.1.4.2: [RIT 225 - 232] Represents the value of digits in whole numbers using powers of 10 in exponential form

4.2: Operations with Algebraic Expressions

4.2.1: Algebraic Expressions

4.2.1.1: [RIT 233 - 257] Adds and subtracts polynomials

4.2.1.2: [RIT 237 - 260] Multiplies two binomial expressions

4.2.1.3: [RIT 238 - 260] Multiplies a polynomial by a monomial

4.2.1.5: [RIT 242 - 242] Generates equivalent nonlinear expressions by combining like terms

4.2.1.6: [RIT 246 - 257] Factors polynomials using a difference of squares

4.2.1.7: [RIT 247 - 261] Factors quadratic trinomials

4.2.1.8: [RIT 248 - 257] Multiplies monomials

4.2.1.12: [RIT 254 - 283] Uses properties of exponents to simplify algebraic expressions involving negative integer exponents, including zero

4.2.1.14: [RIT 256 - 267] Multiplies polynomials

4.2.1.15: [RIT 260 - 260] Writes a rational expression as a sum of a polynomial and a proper rational expression

4.2.1.17: [RIT 263 - 267] Squares binomial expressions

5: Equations and Inequalities

5.1: Linear Equations

5.1.1: Number Sentences/Equations/Equivalence

5.1.1.1: [RIT 173 - 245] Solves one-step linear equations with positive rational numbers

5.1.1.2: [RIT 194 - 231] Determines unknown parts in multi-step equations with whole numbers

5.1.1.3: [RIT 198 - 217] Determines unknown parts in multi-step equations with whole numbers and parentheses

5.1.1.4: [RIT 201 - 239] Solves one-step linear equations with negative rational numbers

5.1.1.5: [RIT 209 - 229] Writes a one-step linear equation in one variable to represent a real-world or mathematical context

5.1.1.6: [RIT 210 - 242] Writes and solves a two-step linear equation in one variable involving a real-world or mathematical context

5.1.1.7: [RIT 220 - 248] Solves two-step linear equations with positive rational numbers

5.1.1.8: [RIT 224 - 242] Evaluates formulas or linear equations at given values for the variables

5.1.1.9: [RIT 226 - 262] Solves multi-step linear equations with positive and negative rational numbers

5.1.1.10: [RIT 226 - 247] Solves two-step linear equations with negative rational numbers

5.1.1.11: [RIT 231 - 287] Writes a multi-step linear equation in one variable to represent a real-world or mathematical context

5.1.1.12: [RIT 237 - 237] Determines whether a linear equation or inequality is true for a given value of the variable

5.1.1.13: [RIT 239 - 239] Applies the multiplicative property of equality when solving an equation

5.1.1.14: [RIT 239 - 240] Writes a two-step linear equation in one variable to represent a real-world or mathematical context

5.1.1.15: [RIT 240 - 240] Writes the equation of a vertical line given a graph

5.1.1.16: [RIT 241 - 247] Applies the simple interest formula to solve for the interest rate, principal, or time invested

5.1.1.17: [RIT 243 - 274] Writes and solves a multi-step linear equation in one variable involving a real-world or mathematical context

5.1.1.18: [RIT 247 - 265] Solves literal equations for linear variables

5.1.1.19: [RIT 249 - 256] Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision

5.1.1.20: [RIT 250 - 250] Understands the slope of a vertical line is undefined

5.2: Linear Inequalities

5.2.1: Inequalities

5.2.1.1: [RIT 190 - 262] Determines whether a linear equation or inequality is true for a given value of the variable

5.2.1.2: [RIT 215 - 243] Identifies an ordered pair that is a solution to a two-variable linear inequality

5.2.1.3: [RIT 223 - 228] Writes a linear inequality in two variables to represent a real-world or mathematical context

5.2.1.4: [RIT 227 - 249] Writes a one-step linear inequality in one variable to represent a real-world or mathematical context

5.2.1.5: [RIT 228 - 243] Writes a multi-step linear inequality in one variable to represent a real-world or mathematical context

5.2.1.6: [RIT 229 - 229] Solves one-step linear inequalities with positive rational numbers

5.2.1.7: [RIT 229 - 261] Solves two-step linear inequalities

5.2.1.9: [RIT 231 - 260] Writes a compound inequality to represent a real-world or mathematical context

5.2.1.10: [RIT 236 - 246] Writes and solves a one-step linear inequality in one variable involving a real-world or mathematical context

5.2.1.11: [RIT 236 - 253] Solves one-step linear inequalities with negative rational numbers

5.2.1.12: [RIT 238 - 243] Writes an inequality in the form x > c or x

5.2.1.13: [RIT 241 - 246] Represents the solutions of a one-step linear inequality on a number line

5.2.1.14: [RIT 241 - 250] Represents the solutions of a compound linear inequality on a number line

5.2.1.15: [RIT 242 - 245] Writes an inequality in the form x>c or x

5.2.1.16: [RIT 243 - 243] Represents an inequality in the form x>c or x

5.2.1.17: [RIT 243 - 262] Solves multi-step linear inequalities

5.2.1.18: [RIT 243 - 243] Writes and solves a two-step linear inequality in one variable involving a real-world or mathematical context

5.2.1.19: [RIT 244 - 254] Represents the solutions of a two-step linear inequality on a number line

5.2.1.20: [RIT 244 - 271] Represents the solutions of an absolute value inequality on a number line

5.2.1.22: [RIT 252 - 252] Writes a linear inequality to represent a region on the coordinate plane

5.2.1.23: [RIT 255 - 255] Represents a compound inequality on a number line given a real-world or mathematical context

5.2.1.24: [RIT 257 - 266] Solves compound linear inequalities

5.2.1.25: [RIT 259 - 264] Represents the solutions of a two-variable linear inequality on the coordinate plane

5.2.1.26: [RIT 260 - 264] Represents the solutions of a multistep linear inequality on a number line

5.3: Systems of Linear Equations and Inequalities

5.3.1: System of Equations/Inequalities

5.3.1.1: [RIT 195 - 204] Solves a system of linear equations involving a real-world context, given a table

5.3.1.2: [RIT 215 - 259] Writes and solves a system of linear equations involving a real-world or mathematical context

5.3.1.3: [RIT 217 - 238] Solves a system of linear equations graphically

5.3.1.4: [RIT 230 - 254] Writes a system of linear equations to represent a real-world or mathematical context

5.3.1.5: [RIT 236 - 261] Solves a system of linear equations algebraically

5.3.1.6: [RIT 238 - 257] Identifies an ordered pair that is a solution to a system of linear inequalities

5.3.1.7: [RIT 240 - 253] Writes a system of linear inequalities to represent a real-world or mathematical context

5.3.1.8: [RIT 240 - 240] Solves a system of linear inequalities

5.3.1.9: [RIT 250 - 257] Shows the steps to solve a system of linear equations using linear combinations

5.3.1.10: [RIT 252 - 274] Solves a system of linear equations given a table

5.3.1.11: [RIT 253 - 261] Shows the steps to solve a system of linear equations using the substitution method

5.3.1.12: [RIT 259 - 259] Graphs a system of linear equations

5.3.1.13: [RIT 259 - 261] Writes a system of linear equations given a graph

5.3.1.14: [RIT 260 - 262] Graphs a system of linear inequalities

5.3.1.15: [RIT 262 - 262] Writes a system of linear inequalities given a graph

5.3.1.18: [RIT 283 - 283] Solves real-world problems involving rates and distances that lead to a system of linear equations

5.4: Non-Linear Equations

5.4.1: Number Sentences/Equations/Equivalence

5.4.1.2: [RIT 221 - 275] Solves quadratic equations in one variable using factoring, the quadratic formula, or other appropriate method

5.4.1.3: [RIT 226 - 265] Solves absolute value equations

5.4.1.5: [RIT 230 - 262] Writes and solves a multi-step quadratic equation in one variable involving a real-world or mathematical context

5.4.1.7: [RIT 240 - 267] Solves radical equations that lead to linear equations

5.4.1.9: [RIT 248 - 279] Writes a quadratic equation in one variable to represent a real-world or mathematical context

5.4.1.11: [RIT 254 - 264] Determines the nature of the solutions of a quadratic equation

5.4.1.12: [RIT 254 - 270] Solves quadratic equations with complex solutions

5.4.1.13: [RIT 257 - 257] Solves polynomial equations

5.4.1.15: [RIT 264 - 264] Writes an absolute value equation in one variable to represent a real-world or mathematical context

5.4.1.18: [RIT 278 - 278] Understands the relationship between the discriminant and the nature of solutions