Growth: High School Integrated Math 2 (2020) Gizmos | Browse by Core Curriculum

1: Number Sense, Properties, and Number Theory

1.1: Number Sense: Real Numbers

1.1.1: Exponents

1.1.1.1: [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

1.1.2.3: [RIT 241 - 245] Interprets the absolute value of rational numbers in terms of their relative position to 0 in a given real-world situation

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 - 275] Compares and orders real numbers

1.1.5: Rational Numbers: Equivalence

1.1.5.2: [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 201 - 235] Compares integers that represent quantities in a real-world context

1.1.6.5: [RIT 207 - 214] Justifies a comparison of two rational numbers using a number line

1.1.6.6: [RIT 207 - 211] Compares two rational numbers shown on a number line

1.1.6.7: [RIT 209 - 239] Compares integers given the meaning of zero within a real-world situation

1.1.6.8: [RIT 211 - 211] Compares integers

1.1.6.9: [RIT 213 - 230] Compares two rational numbers using a number line

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

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

1.1.6.12: [RIT 230 - 230] Orders 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

1.1.7.5: [RIT 233 - 233] Locates the opposite of a negative rational number on a number line

1.1.7.6: [RIT 237 - 237] Identifies values that are a given distance from a point 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 221 - 253] Understands that the product of a negative number and a positive number is negative

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

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

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

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

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

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

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

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

2: Computation and Estimation with Real Numbers

2.1: Computation with Real Numbers

2.1.1: Numerical Expressions

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

2.1.2: Exponents

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

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

2.1.3: Properties and Relationships of Operations

2.1.3.2: [RIT 242 - 242] Determines the distance between two integers on a number line

2.1.4: Rational Numbers: Computation

2.1.4.1: [RIT 207 - 223] Identifies two rational numbers that combine to make 0

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

2.1.4.4: [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 203 - 203] Adds and subtracts integers using a number line

2.1.8.2: [RIT 205 - 220] Multiplies and divides integers

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

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

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

2.2: Ratio, Proportion, Percent, and Rate

2.2.1: Conversion of Units

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

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

2.2.2: Rates/Ratios/Proportions/Percents

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

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

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

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

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

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

2.2.2.8: [RIT 207 - 212] Identifies ratios between two quantities not from the same whole

2.2.2.9: [RIT 209 - 209] Recognizes a ratio within a context

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

2.2.2.12: [RIT 210 - 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 - 239] Identifies the part-to-part ratio between two quantities

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

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

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

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

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

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 - 252] Writes a proportion to solve a real-world problem

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

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

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

2.2.2.32: [RIT 242 - 256] Calculates simple interest

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

2.2.2.34: [RIT 247 - 255] Compares ratios within a real-world context

2.2.3: Rational Numbers: Equivalence

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

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

2.3: Estimation with Real Numbers

2.3.1: Real/Complex Numbers: Concepts/Properties

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

3: Measurement

3.1: Perimeter and Circumference

3.1.1: Perimeter/Circumference

3.1.1.1: [RIT 213 - 251] Determines the circumference of circles, formula not provided

3.1.1.2: [RIT 213 - 239] Determines the circumference of circles, given the formula

3.1.1.4: [RIT 231 - 231] Determines the ratio between perimeters of scaled figures

3.1.1.5: [RIT 232 - 240] Describes the effect on perimeter when dimensions of a non-rectangular polygon are changed

3.1.1.6: [RIT 233 - 244] Identifies the formula for the perimeter of a polygon

3.2: Area and Surface Area

3.2.1: Area

3.2.1.1: [RIT 213 - 250] Determines the area of parallelograms, formula not provided

3.2.1.3: [RIT 218 - 235] Determines the area of triangles, given the formula

3.2.1.4: [RIT 224 - 224] Determines the base or height given the area of a parallelogram

3.2.1.5: [RIT 224 - 252] Describes the effect on area when dimensions of a triangle are changed

3.2.1.7: [RIT 228 - 267] Solves problems involving areas of figures composed of polygons within a real-world or mathematical context

3.2.1.8: [RIT 232 - 232] Identifies the formula for the area of a circle

3.2.1.10: [RIT 234 - 239] Determines the area of circles, given the formula

3.2.1.11: [RIT 236 - 260] Determines the area of figures composed of polygons

3.2.1.12: [RIT 236 - 254] Determines the area of triangles, formula not provided

3.2.1.13: [RIT 240 - 269] Determines the ratio between areas of scaled figures

3.2.1.14: [RIT 242 - 259] Solves problems involving areas of polygons and circles, quarter circles, semicircles, or three-quarter circles within a real-world or mathematical context

3.2.1.15: [RIT 244 - 260] Determines the circumference given the area of a circle

3.2.1.18: [RIT 247 - 247] Determines the radius or diameter given the area of a circle

3.2.1.19: [RIT 249 - 257] Determines the area of circles, formula not provided

3.2.1.20: [RIT 251 - 251] Determines the area of figures composed of polygons and circles

3.2.1.23: [RIT 260 - 270] Describes the effect on area when the radius or diameter of a circle is changed

3.2.1.24: [RIT 261 - 261] Describes the effect on area when the circumference of a circle is changed

3.2.1.26: [RIT 265 - 265] Solves problems involving areas of circles within a real-world or mathematical context

3.2.3: Surface Area

3.2.3.1: [RIT 236 - 246] Uses the net of a prism to solve surface area problems within a real-world or mathematical context

3.2.3.3: [RIT 240 - 248] Determines the surface area of a prism given a net

3.2.3.4: [RIT 241 - 241] Determines the surface area of cylinders, given the formula

3.2.3.5: [RIT 246 - 246] Determines the surface area of cones, given the formula

3.2.3.6: [RIT 251 - 252] Determines the surface area of pyramids, given the formula

3.2.3.7: [RIT 252 - 256] Determines the surface area of pyramids, formula not provided

3.2.3.8: [RIT 252 - 252] Determines the surface area of triangular prisms, formula not provided

3.2.3.9: [RIT 255 - 263] Describes the effect on surface area when dimensions of a rectangular prism are changed

3.2.3.11: [RIT 260 - 263] Solves problems involving surface areas of prisms within a real-world or mathematical context

3.2.3.12: [RIT 266 - 269] Determines the surface area of cylinders, formula not provided

3.3: Volume

3.3.1: Conversion of Units

3.3.1.1: [RIT 282 - 282] Converts units of volume within the same measurement system

3.3.2: Volume

3.3.2.1: [RIT 227 - 268] Determines the volume of pyramids, given the formula

3.3.2.2: [RIT 237 - 240] Determines the volume of cylinders, given the formula

3.3.2.3: [RIT 239 - 273] Describes the effect on volume when dimensions of a rectangular prism are changed

3.3.2.5: [RIT 245 - 245] Determines the volume of spheres, given the formula

3.3.2.6: [RIT 250 - 275] Determines the volume of cylinders, formula not provided

3.3.2.8: [RIT 254 - 274] Determines the volume of pyramids, formula not provided

3.3.2.10: [RIT 258 - 258] Determines the radius or diameter of a cylinder given the volume and height

3.3.2.12: [RIT 259 - 278] Solves problems involving volumes of cylinders within a real-world or mathematical context

3.3.2.15: [RIT 266 - 266] Determines the volume of figures composed of rectangular and triangular prisms

3.3.2.16: [RIT 266 - 266] Solves problems involving volumes of 3-D figures composed of cones, cylinders, and spheres within a real-world or mathematical context

3.3.2.18: [RIT 269 - 281] Understands that the volume of a cone is one-third the volume of a cylinder with the same base area and height

3.3.2.19: [RIT 270 - 270] Determines the volume of spheres, formula not provided

3.3.2.20: [RIT 273 - 273] Determines the volume of cones, formula not provided

3.3.2.21: [RIT 276 - 276] Solves problems involving volumes of cones within a real-world or mathematical context

4: Geometry

4.1: Points, Lines, Planes, and Angles

4.1.1: Geometric Constructions

4.1.1.1: [RIT 257 - 257] Identifies the geometric construction of an angle bisector

4.1.1.2: [RIT 263 - 263] Identifies the geometric construction of a line segment bisector or the midpoint of a line segment

4.1.2: Points, Lines, Segments, Rays, and Angles

4.1.2.1: [RIT 248 - 248] Defines midpoints of line segments

4.1.2.2: [RIT 275 - 275] Defines bisectors of line segments

4.1.3: Relationships involving Lines, Angles, and Polygons

4.1.3.1: [RIT 226 - 257] Solves problems involving parallel lines cut by a transversal

4.1.3.2: [RIT 240 - 240] Defines complementary and supplementary angles

4.1.3.3: [RIT 245 - 249] Identifies corresponding, alternate interior, and alternate exterior angles

4.1.3.4: [RIT 248 - 258] Identifies complementary and supplementary angles

4.1.3.5: [RIT 253 - 267] Determines the conditions necessary to show that two lines are parallel

4.1.3.6: [RIT 269 - 269] Identifies vertical angles

4.1.4: Geometric Proof/Logic/Inductive and Deductive Reasoning

4.1.4.1: [RIT 253 - 267] Determines the conditions necessary to show that two lines are parallel

4.2: Polygons and Circles

4.2.1: Circles

4.2.1.1: [RIT 208 - 208] Knows the number of degrees in a circle

4.2.1.2: [RIT 218 - 231] Identifies radii and diameters of circles

4.2.1.4: [RIT 236 - 236] Recognizes the relationship between the diameter and the radius of a circle

4.2.1.6: [RIT 242 - 292] Uses properties of central and inscribed angles to solve problems involving circles

4.2.1.7: [RIT 243 - 271] Solves problems involving inscribed angles on a diameter

4.2.1.8: [RIT 250 - 263] Understands that the ratio between the circumference and the diameter of a circle is equal to pi

4.2.1.9: [RIT 256 - 271] Uses properties of chords to solve problems involving circles

4.2.1.12: [RIT 262 - 263] Recognizes a precise definition of circles

4.2.1.13: [RIT 263 - 274] Calculates arc lengths

4.2.1.15: [RIT 266 - 266] Solves problems involving arc measures of a circle

4.2.1.16: [RIT 285 - 285] Justifies relationships between the arc length, radius, and central angle measured in radians

4.2.1.17: [RIT 286 - 286] Describes properties of quadrilaterals inscribed in a circle

4.2.2: Identification and Classification of 2-D Shapes

4.2.2.1: [RIT 210 - 260] Knows properties of parallelograms, including special parallelograms such as squares, rhombuses, etc.

4.2.2.2: [RIT 213 - 245] Knows properties of special triangles, such as acute, right, scalene, etc.

4.2.3: Relationships involving Lines, Angles, and Polygons

4.2.3.1: [RIT 194 - 194] Identifies diagonals of polygons

4.2.3.2: [RIT 220 - 250] Applies the formula for the sum of the interior angles of a polygon

4.2.3.3: [RIT 221 - 233] Applies the Triangle Angle-Sum Theorem to determine the measure of an unknown angle

4.2.3.4: [RIT 223 - 241] Recognizes that the sum of the interior angles of a triangle is 180 degrees

4.2.3.5: [RIT 228 - 250] Applies properties of isosceles triangles to determine the measure of an unknown angle

4.2.3.7: [RIT 232 - 268] Solves problems by applying multiple properties of angles, including interior and exterior angles of triangles; complementary, supplementary, and vertical angles; and angles created by perpendicular lines or parallel lines cut by a transversal

4.2.3.9: [RIT 238 - 246] Solves multi-step problems by applying the Triangle Angle-Sum Theorem

4.2.3.10: [RIT 240 - 240] Determines the number of diagonals that can be drawn from one vertex in a polygon

4.2.3.11: [RIT 241 - 276] Applies the Triangle Inequality Theorem

4.2.3.12: [RIT 242 - 249] Applies the Triangle Exterior Angle Theorem to determine the measure of an unknown angle

4.2.3.13: [RIT 256 - 258] Applies the formula for the measure of each exterior angle of a regular polygon

4.2.3.15: [RIT 269 - 269] Applies the formula for the measure of each interior angle of a regular polygon

4.2.4: Geometric Proof/Logic/Inductive and Deductive Reasoning

4.2.4.1: [RIT 252 - 275] Proves theorems involving the properties of parallelograms

4.2.4.3: [RIT 285 - 285] Justifies relationships between the arc length, radius, and central angle measured in radians

4.3: Three-Dimensional Figures

4.3.1: Identification and Classification of 3-D Shapes

4.3.1.2: [RIT 241 - 241] Identifies and names polyhedrons

4.3.2: Spatial Concepts and Symmetry

4.3.2.1: [RIT 184 - 229] Identifies and creates nets for prisms

4.3.2.2: [RIT 186 - 202] Identifies and creates nets for pyramids

4.3.2.3: [RIT 211 - 269] Identifies the cross-sections of 3-D shapes

4.4: Congruence and Similarity

4.4.1: Congruence

4.4.1.1: [RIT 153 - 184] Identifies congruent shapes, given informal language

4.4.1.2: [RIT 186 - 230] Identifies congruent shapes, given formal language

4.4.1.4: [RIT 194 - 206] Identifies corresponding sides and angles in congruent figures

4.4.1.7: [RIT 229 - 229] Uses formal notation to denote corresponding sides and angles in congruent triangles

4.4.1.9: [RIT 251 - 255] Identifies congruent triangles using AAS, ASA, SAS, or SSS

4.4.1.10: [RIT 252 - 284] Identifies the congruence postulate that proves two triangles are congruent

4.4.1.12: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent

4.4.2: Similarity

4.4.2.1: [RIT 180 - 181] Identifies similar figures

4.4.2.2: [RIT 204 - 253] Applies scale factors to solve problems involving scale drawings, maps, and models

4.4.2.3: [RIT 212 - 260] Determines lengths of corresponding sides in similar figures

4.4.2.4: [RIT 212 - 212] Determines scale factors in problems involving scale drawings, maps, and models

4.4.2.5: [RIT 213 - 226] Identifies corresponding sides and angles in similar figures

4.4.2.6: [RIT 215 - 249] Applies properties of similar triangles to solve real-world problems involving indirect measurements

4.4.2.7: [RIT 220 - 220] Knows the definition of similarity

4.4.2.8: [RIT 223 - 239] Determines scale factors in problems involving scale drawings of geometric figures

4.4.2.10: [RIT 224 - 224] Determines the ratio between perimeters of similar figures

4.4.2.11: [RIT 225 - 252] Applies scale factors to solve problems involving scale drawings of geometric figures

4.4.2.12: [RIT 228 - 276] Determines the conditions necessary to prove two triangles are similar

4.4.2.13: [RIT 232 - 257] Applies properties of similar figures to determine a perimeter

4.4.2.15: [RIT 235 - 235] Applies properties of similar figures to determine an area

4.4.2.16: [RIT 239 - 239] Identifies the proportion of corresponding sides of similar figures

4.4.2.17: [RIT 244 - 263] Applies similarity postulates to solve for missing lengths and angles

4.4.2.18: [RIT 245 - 256] Identifies similar triangles using AA

4.4.2.19: [RIT 247 - 247] Applies similarity postulates to identify corresponding sides and angles

4.4.2.22: [RIT 260 - 279] Applies the geometric mean to solve for missing lengths and angles in triangles

4.4.2.23: [RIT 261 - 271] Identifies the similarity postulate that proves two triangles are similar

4.4.2.26: [RIT 285 - 286] Determines the ratio between areas of similar figures

4.4.2.27: [RIT 288 - 288] Solves problems involving multiple theorems of similar triangles, including the Triangle Proportionality Theorem, segment proportionality property for parallel lines, and similarity postulates

4.4.3: Geometric Proof/Logic/Inductive and Deductive Reasoning

4.4.3.1: [RIT 228 - 276] Determines the conditions necessary to prove two triangles are similar

4.4.3.2: [RIT 252 - 284] Identifies the congruence postulate that proves two triangles are congruent

4.4.3.3: [RIT 261 - 271] Identifies the similarity postulate that proves two triangles are similar

4.4.3.4: [RIT 262 - 262] Determines the conditions necessary to prove two triangles are congruent

4.5: Pythagorean Theorem, Right Triangle Trig

4.5.1: Pythagorean Theorem

4.5.1.1: [RIT 241 - 275] Uses the Pythagorean Theorem to solve real-world or mathematical problems

4.5.1.2: [RIT 242 - 266] Uses the Pythagorean Theorem to calculate the length of a missing side of a right triangle

4.5.1.3: [RIT 250 - 268] Applies the converse of the Pythagorean Theorem to identify right triangles

4.5.1.5: [RIT 280 - 280] Uses similarity to prove the Pythagorean Theorem

4.5.2: Trigonometry

4.5.2.1: [RIT 241 - 263] Represents the sine of an angle as a ratio of sides in a right triangle

4.5.2.2: [RIT 246 - 266] Represents the tangent of an angle as a ratio of sides in a right triangle

4.5.2.3: [RIT 247 - 263] Represents the cosine of an angle as a ratio of sides in a right triangle

4.5.2.4: [RIT 250 - 272] Uses sine, cosine, or tangent to determine the length of a side in a right triangle

4.5.2.6: [RIT 263 - 273] Uses sine, cosine, and tangent to determine lengths to solve real-world and mathematical problems

4.5.3: Relationships involving Lines, Angles, and Polygons

4.5.3.1: [RIT 255 - 279] Uses the 45-45-90 and 30-60-90 right triangle relationships to solve real-world and mathematical problems

4.5.3.2: [RIT 258 - 279] Uses the 45-45-90 and 30-60-90 right triangle relationships to calculate the length of a missing side of a right triangle

4.5.4: Geometric Proof/Logic/Inductive and Deductive Reasoning

4.5.4.1: [RIT 280 - 280] Uses similarity to prove the Pythagorean Theorem

4.6: Transformations and Symmetry

4.6.1: Spatial Concepts and Symmetry

4.6.1.1: [RIT 165 - 228] Determines the number of lines of symmetry in 2-D figures

4.6.1.2: [RIT 206 - 217] Identifies 2-D figures which have rotational symmetry

4.6.1.4: [RIT 275 - 284] Identifies the rotational or reflectional symmetry of a shape

4.6.2: Transformations

4.6.2.1: [RIT 196 - 251] Describes a single transformation that shows two shapes are congruent, without the coordinate plane

4.6.2.2: [RIT 198 - 227] Describes a single transformation that will map one figure onto another, without the coordinate plane

4.6.2.4: [RIT 207 - 232] Understands that rigid transformations preserve congruency

4.6.2.5: [RIT 214 - 214] Identifies the degree of rotation that shows that two given figures are congruent, without a coordinate plane

4.6.2.7: [RIT 221 - 254] Determines the image of a polygon on a coordinate plane after a reflection or a series of reflections

4.6.2.8: [RIT 223 - 254] Determines the coordinates of the vertices of a polygon after a dilation or a series of dilations, with center at the origin

4.6.2.9: [RIT 225 - 241] Determines the coordinates of the vertices of a polygon after a translation or a series of translations

4.6.2.10: [RIT 226 - 226] Determines the image of a polygon on a coordinate plane after a rotation or a series of rotations

4.6.2.13: [RIT 231 - 242] Describes the effects of dilation on lengths and angle measures

4.6.2.14: [RIT 231 - 259] Determines the coordinates of the vertices of a polygon after a reflection or a series of reflections

4.6.2.15: [RIT 232 - 268] Describes a single transformation that will map one figure onto itself, without the coordinate plane

4.6.2.16: [RIT 235 - 271] Determines the coordinates of the vertices of a polygon after a rotation or a series of rotations

4.6.2.17: [RIT 237 - 246] Describes a series of transformations that show two shapes are congruent on the coordinate plane

4.6.2.18: [RIT 239 - 239] Represents translations in the plane using matrices

4.6.2.19: [RIT 240 - 240] Determines the image of a translation represented in coordinate notation

4.6.2.22: [RIT 243 - 261] Describes a single transformation that shows two shapes are congruent on the coordinate plane

4.6.2.23: [RIT 249 - 263] Describes a translation using coordinate notation

4.6.2.24: [RIT 250 - 250] Determines the image of a polygon on a coordinate plane after a series of translations, reflections, or rotations

4.6.2.25: [RIT 251 - 251] Determines the image of a dilation represented in coordinate notation

4.6.2.26: [RIT 252 - 252] Identifies the center and scale factor used in a dilation represented in the coordinate plane

4.6.2.27: [RIT 253 - 253] Applies the scale factor in a dilation to solve for unknown lengths

4.6.2.30: [RIT 264 - 264] Determines the image of a reflection represented in coordinate notation

4.6.2.31: [RIT 275 - 278] Describes a series of transformations that will map one figure onto another, without the coordinate plane

4.6.3: Geometric Proof/Logic/Inductive and Deductive Reasoning

4.6.3.1: [RIT 263 - 268] Describes a series of transformations that show two given circles are similar on the coordinate plane

4.7: Coordinate Graphing and Distance

4.7.1: Coordinate Geometry

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

4.7.1.2: [RIT 183 - 236] Plots points in all four quadrants of a coordinate plane

4.7.1.3: [RIT 202 - 242] Determines the quadrant for a given ordered pair

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

4.7.1.8: [RIT 235 - 235] Determines a side length of a polygon given the coordinates of the vertices with the same first or second coordinate

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

4.7.1.12: [RIT 251 - 280] Identifies collinear points

5: Statistics and Probability

5.1: Collect, Organize, Analyze Data

5.1.2: Bivariate Data

5.1.2.1: [RIT 189 - 234] Constructs scatter plots of bivariate data

5.1.2.2: [RIT 198 - 198] Reads and interprets data from a scatter plot

5.1.2.3: [RIT 199 - 236] Describes and interprets data in a scatter plot

5.1.2.4: [RIT 206 - 249] Describes the correlation or association between two variables, including the direction and strength of linear and nonlinear relationships

5.1.2.7: [RIT 213 - 264] Analyzes linear trends in scatter plots to make predictions

5.1.2.8: [RIT 219 - 268] Describes and interprets outliers and clusters in a scatter plot

5.1.2.9: [RIT 220 - 220] Determines whether two quantitative variables have a positive linear, negative linear, or zero association

5.1.2.10: [RIT 221 - 221] Distinguishes between linear and nonlinear relationships in scatter plots

5.1.2.11: [RIT 222 - 270] Understands the relationship between the value of the correlation coefficient and the strength and direction of a linear relationship

5.1.2.12: [RIT 222 - 237] Uses a given equation of a line of best fit to make predictions

5.1.2.13: [RIT 230 - 267] Interprets the meaning of the slope or y-intercept of a line of best fit or regression line

5.1.2.14: [RIT 231 - 271] Determines a pair of quantitative variables that has either a positive, negative, or zero correlation

5.1.2.15: [RIT 233 - 233] Approximates the line of best fit on a scatter plot

5.1.2.16: [RIT 242 - 271] Compares two sets of bivariate data to draw conclusions

5.1.2.18: [RIT 246 - 260] Estimates the slope of a line of best fit

5.1.2.19: [RIT 261 - 261] Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a real-world context

5.1.2.20: [RIT 261 - 276] Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a scatter plot

5.1.2.21: [RIT 262 - 262] Approximates the equation of the line of best fit

5.1.3: Data Analysis

5.1.3.1: [RIT 163 - 210] Reads and interprets data from a circle graph

5.1.3.3: [RIT 193 - 235] Identifies the median, quartiles, extreme values, and outliers from a box plot

5.1.3.4: [RIT 198 - 198] Reads and interprets data from a scatter plot

5.1.3.13: [RIT 243 - 243] Compares the means and medians of related data sets from random samples represented in histograms

5.1.4: Data Representation

5.1.4.1: [RIT 189 - 234] Constructs scatter plots of bivariate data

5.1.4.2: [RIT 196 - 224] Represents data in circle graphs

5.1.4.6: [RIT 247 - 261] Represents data in box plots

5.1.5: Measures of Center and Spread (Variability)

5.1.5.1: [RIT 193 - 235] Identifies the median, quartiles, extreme values, and outliers from a box plot

5.1.5.5: [RIT 238 - 243] Explains why the mean and median differ in a single data set

5.1.5.7: [RIT 243 - 243] Compares the means and medians of related data sets from random samples represented in histograms

5.1.5.9: [RIT 255 - 272] Compares the measures of center of two data sets after the addition or deletion of data values, including outliers

5.1.6: Populations/Random Processes

5.1.6.1: [RIT 187 - 217] Identifies a data collection method that best answers a question

5.1.6.2: [RIT 202 - 202] Identifies random samples

5.1.6.4: [RIT 214 - 250] Writes and solves proportions to make inferences about populations

5.1.6.6: [RIT 226 - 241] Identifies valid inferences given a population sample

5.1.6.7: [RIT 230 - 247] Identifies a sampling method that produces the most representative sample

5.1.6.8: [RIT 230 - 231] Identifies an appropriate research design, including surveys, experiments and observational studies, to answer a question

5.1.6.9: [RIT 243 - 243] Writes proportions to make inferences about populations

5.1.6.10: [RIT 246 - 254] Explains the difference between values describing a population and values describing a sample within a real-world context

5.2: Probability

5.2.1: Probability

5.2.1.1: [RIT 168 - 218] Identifies a simple event given the likelihood of the event as more likely, less likely, neither likely nor unlikely, impossible, or certain

5.2.1.3: [RIT 185 - 213] Describes the likelihood of simple events occurring

5.2.1.4: [RIT 190 - 249] Determines theoretical probabilities of simple events

5.2.1.5: [RIT 193 - 241] Makes predictions based on theoretical probabilities of simple events

5.2.1.6: [RIT 207 - 244] Makes predictions based on experimental probabilities of simple events

5.2.1.7: [RIT 208 - 220] Identifies the likelihood of a simple event as more likely, less likely, neither likely nor unlikely, impossible, or certain, given the probability of the event

5.2.1.8: [RIT 213 - 242] Determines experimental probabilities of simple events

5.2.1.10: [RIT 215 - 230] Determines the probability of the complement of an event

5.2.1.11: [RIT 219 - 232] Describes the likelihood of compound events occurring

5.2.1.12: [RIT 221 - 268] Determines probabilities of compound independent events

5.2.1.13: [RIT 221 - 271] Distinguishes between independent and dependent events in situations

5.2.1.14: [RIT 222 - 239] Understands independence as it relates to previous outcomes

5.2.1.15: [RIT 224 - 224] Determines the odds of simple events

5.2.1.16: [RIT 224 - 224] Writes proportions to make predictions based on experimental probabilities

5.2.1.19: [RIT 238 - 286] Determines probabilities of two compound events given organized lists, tree diagrams, or charts

5.2.1.20: [RIT 239 - 242] Determines conditional probabilities of events without replacement

5.2.1.21: [RIT 240 - 240] Modifies sample space to change the probability of an event

5.2.1.22: [RIT 244 - 288] Interprets conditional probability with and without a context

5.2.1.23: [RIT 245 - 266] Determines probabilities using geometric models

5.2.1.24: [RIT 246 - 246] Makes predictions based on probability distributions

5.2.1.25: [RIT 257 - 257] Makes predictions based on theoretical probabilities of compound events

5.2.1.26: [RIT 257 - 276] Determines probabilities using the general Multiplication Rule of probability

5.2.1.27: [RIT 257 - 278] Determines conditional probabilities of compound events using relative frequencies

5.2.1.28: [RIT 258 - 266] Determines probabilities of compound dependent events

5.2.1.31: [RIT 276 - 284] Justifies the independence of two events using the product of their probabilities

5.2.2: Sample Spaces

5.2.2.1: [RIT 187 - 219] Determines the sample space for a simple event using lists, tree diagrams, or charts

5.2.2.2: [RIT 201 - 242] Determines the sample space for two compound events using organized lists, tree diagrams, or charts

5.2.2.3: [RIT 212 - 232] Determines the sample space for more than two compound events using organized lists, tree diagrams, or charts

5.2.2.5: [RIT 220 - 272] Uses permutations and combinations to determine the number of possible outcomes

6: Algebraic Concepts

6.1: Patterns, Sequences: Arithmetic and Geometric

6.1.1: Patterns/Sequences/Series

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

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

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

6.1.1.6: [RIT 232 - 238] Recognizes arithmetic sequences

6.1.1.7: [RIT 243 - 272] Writes an expression or formula for the nth term of an arithmetic sequence given a number sequence

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

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

6.1.1.10: [RIT 277 - 277] Determines the value of a term in an arithmetic sequence defined recursively

6.2: Functions

6.2.1: Algebraic Expressions

6.2.1.1: [RIT 279 - 279] Identifies equivalent exponential expressions

6.2.2: Properties and Operations of Functions

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

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

6.2.2.3: [RIT 238 - 276] Performs operations with functions

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

6.2.2.6: [RIT 244 - 270] Distinguishes between linear and nonlinear functions given an equation, a graph, or a table of values

6.2.2.7: [RIT 245 - 246] Writes a function in the form f(x) = g(x) - h(x) to represent real-world scenarios

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

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

6.2.2.23: [RIT 283 - 283] Writes the inverse of an exponential function

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

6.2.3: Number Sentences/Equations/Equivalence

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

6.2.4: Polynomial Functions

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

6.2.4.2: [RIT 256 - 275] Applies the polynomial Remainder Theorem

6.2.4.3: [RIT 262 - 275] Factors polynomial functions to determine zeros

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

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

6.2.4.7: [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

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

6.2.5: Rate of Change/Slope

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

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

6.2.5.3: [RIT 212 - 225] Identifies the unit rate from the graph of a proportional relationship

6.2.5.4: [RIT 213 - 260] Calculates the rate of change from a graph representing a real-world linear relationship

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

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

6.2.5.8: [RIT 233 - 233] Interprets the meaning of the slope and y-intercept of a graph within the context of a real-world linear relationship

6.2.5.9: [RIT 236 - 246] Interprets the meaning of the slope for the equation y = mx + b within the context of a real-world linear relationship

6.2.5.10: [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

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

6.2.5.12: [RIT 239 - 259] Determines the y-intercept and the slope of a line given an equation of the line in a form other than y = mx + b

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

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

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

6.2.6: Quadratic Functions

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

6.2.6.2: [RIT 220 - 249] Describes the effects that changes in the constant terms have on the graphs of quadratic functions

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

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

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

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

6.2.6.9: [RIT 247 - 280] Graphs quadratic functions

6.2.6.10: [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

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

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

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

6.2.6.14: [RIT 258 - 275] Determines the vertex, intercepts, or axis of symmetry of a quadratic function given an equation

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

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

6.2.6.19: [RIT 262 - 273] Determines the zeros of a quadratic function by factoring

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

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

6.2.6.22: [RIT 266 - 274] Describes the effects of transformations on the graphs of quadratic functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

6.2.6.23: [RIT 269 - 288] Recognizes the advantages of standard, factored, and vertex form of quadratic functions

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

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

6.2.7: Linear Functions

6.2.7.1: [RIT 192 - 223] Graphs a linear function of the form y = mx given a simple scenario

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

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

6.2.7.4: [RIT 200 - 232] Translates between the graph of a piecewise linear function and a verbal description of the real-world relationship

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

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

6.2.7.9: [RIT 213 - 260] Calculates the rate of change from a graph representing a real-world linear relationship

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

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

6.2.7.12: [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

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

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

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

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

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

6.2.7.24: [RIT 233 - 233] Interprets the meaning of the slope and y-intercept of a graph within the context of a real-world linear relationship

6.2.7.25: [RIT 234 - 234] Interprets the meaning of the y-intercept for the equation y = mx + b within the context of a real-world linear relationship

6.2.7.27: [RIT 235 - 273] Determines whether a real-world situation can be modeled by a linear or an exponential function

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

6.2.7.30: [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

6.2.7.31: [RIT 236 - 246] Interprets the meaning of the slope for the equation y = mx + b within the context of a real-world linear relationship

6.2.7.32: [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

6.2.7.33: [RIT 237 - 273] Writes an equation in the form y = mx to represent a real-world proportional relationship for a given ratio

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

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

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

6.2.7.38: [RIT 239 - 259] Determines the y-intercept and the slope of a line given an equation of the line in a form other than y = mx+b

6.2.7.40: [RIT 239 - 239] Describes the effects of changes in parameters on linear functions that represent real-world relationships

6.2.7.41: [RIT 240 - 261] Describes the effects that changes in the constant terms have on the graphs of linear functions

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

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

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

6.2.7.50: [RIT 245 - 250] Graphs the equation of a line in the form y = mx + b

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

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

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

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

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

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

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

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

6.2.7.61: [RIT 255 - 255] Justifies that linear models increase and decrease by equal differences over equal intervals

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

6.2.7.63: [RIT 259 - 270] Writes the equation of a line in standard form given a table of values or two ordered pairs

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

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

6.2.8: Exponential and Logarithmic Functions

6.2.8.1: [RIT 225 - 225] Interprets the meaning of the y-intercept of a graph within the context of a real-world exponential relationship

6.2.8.2: [RIT 234 - 255] Identifies the appropriate linear or exponential model that represents a real-world situation

6.2.8.3: [RIT 235 - 273] Determines whether a real-world situation can be modeled by a linear or an exponential function

6.2.8.4: [RIT 235 - 264] Evaluates an exponential function for a given value in its domain to solve a real-world problem

6.2.8.5: [RIT 237 - 271] Understands that exponential models grow and decay by equal factors over equal intervals

6.2.8.6: [RIT 238 - 238] Describes the effects that changes in parameters have on the tables of values of exponential functions

6.2.8.7: [RIT 241 - 277] Writes exponential functions to represent real-world or mathematical problems

6.2.8.8: [RIT 244 - 244] Identifies a table of values that represents an exponential relationship

6.2.8.9: [RIT 246 - 261] Classifies exponential functions as representations of growth or decay

6.2.8.10: [RIT 248 - 272] Describes the effects of changes in parameters on exponential functions that represent real-world relationships

6.2.8.12: [RIT 252 - 264] Graphs an exponential function given a table of values

6.2.8.13: [RIT 254 - 261] Describes the effects that changes in parameters have on the graphs of exponential functions

6.2.8.14: [RIT 259 - 270] Graphs exponential functions

6.2.8.15: [RIT 260 - 260] Determines real-world situations that can be modeled by an exponential function

6.2.8.16: [RIT 261 - 261] Justifies that exponential models grow and decay by equal factors over equal intervals

6.2.8.17: [RIT 267 - 267] Writes an exponential function given a graph

6.2.8.18: [RIT 267 - 274] Writes the equation representing transformations of exponential functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

6.2.8.19: [RIT 270 - 270] Identifies the table of values given an exponential equation

6.2.8.20: [RIT 275 - 275] Understands the exponential impact of the growth factor on values of an exponential function

6.2.8.21: [RIT 283 - 283] Writes the inverse of an exponential function

6.2.9: Piecewise/Absolute Value Functions

6.2.9.1: [RIT 200 - 232] Translates between the graph of a piecewise linear function and a verbal description of the real-world relationship

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

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

6.2.9.5: [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

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

6.2.9.7: [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

6.2.9.8: [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

6.2.9.9: [RIT 270 - 280] Graphs piecewise functions

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

6.2.10: Rational Functions

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

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

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

6.2.10.4: [RIT 260 - 281] Graphs rational functions

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

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

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

6.2.11: Radical Functions

6.2.11.1: [RIT 278 - 278] Describes the effects of transformations on the graphs of radical functions, including the transformations y = af(x), y = f(ax), y = f(x - a), and y = f(x) + a

6.3: Evaluate and Simplify Expressions

6.3.1: Algebraic Expressions

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

6.3.1.2: [RIT 217 - 259] Generates equivalent linear expressions by using the associative, commutative, and distributive properties, and by combining like terms

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

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

6.3.1.8: [RIT 233 - 282] Identifies the mathematical components of an algebraic expression, including sum, product, quotient, term, and coefficient

6.3.1.9: [RIT 236 - 267] Uses properties of exponents to simplify algebraic expressions involving whole-number exponents

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

6.3.1.11: [RIT 239 - 253] Generates equivalent nonlinear expressions by combining like terms

6.3.1.12: [RIT 240 - 240] Writes algebraic expressions from a mathematical description of its component parts, including sum, product, quotient, term, and coefficient

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

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

6.3.1.16: [RIT 244 - 273] Simplifies rational expressions

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

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

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

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

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

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

6.3.2: Numerical Expressions

6.3.2.1: [RIT 211 - 247] Applies the order of operations, with grouping symbols and excluding exponents, to simplify numerical expressions involving positive rational numbers

6.3.2.2: [RIT 215 - 234] Represents real-world problems involving the addition and subtraction of integers with numerical expressions

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

6.3.2.5: [RIT 218 - 255] Rewrites the sum of two whole numbers as a product of a common factor and the sum of two whole numbers

6.3.2.6: [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

6.3.2.7: [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

6.3.2.8: [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

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

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

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

6.3.2.16: [RIT 256 - 271] Simplifies numerical expressions involving sums and differences of radicals

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

6.3.3: Exponents

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

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

6.3.3.4: [RIT 236 - 267] Uses properties of exponents to simplify algebraic expressions involving whole-number exponents

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

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

6.3.5: Radicals

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

6.3.5.2: [RIT 256 - 271] Simplifies numerical expressions involving sums and differences of radicals

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

6.4: Operations with Algebraic Expressions

6.4.1: Algebraic Expressions

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

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

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

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

6.4.1.6: [RIT 247 - 261] Factors quadratic trinomials

6.4.1.7: [RIT 248 - 257] Multiplies monomials

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

6.4.1.13: [RIT 256 - 267] Multiplies polynomials

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

6.4.1.16: [RIT 263 - 267] Squares binomial expressions

6.4.2: Exponents

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

6.5: Linear Equations

6.5.1: Number Sentences/Equations/Equivalence

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

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

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

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

6.5.1.5: [RIT 218 - 240] Determines the number of solutions of a linear equation in one variable given the corresponding equation in the form x=a, x=x, or a=b

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

6.5.1.7: [RIT 222 - 242] Evaluates formulas or linear equations at given values for the variables

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

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

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

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

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

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

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

6.5.1.15: [RIT 242 - 258] Determines the number of solutions of a linear equation in one variable by transforming the equation into an equivalent one to reach a decision

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

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

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

6.5.1.19: [RIT 265 - 290] Justifies the steps in solving a linear equation

6.6: Linear Inequalities

6.6.1: Inequalities

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

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

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

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

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

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

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

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

6.6.1.10: [RIT 234 - 245] Writes an inequality in the form x > c or x

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

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

6.6.1.13: [RIT 238 - 244] Writes an inequality in the form x > c or x

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

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

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

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

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

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

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

6.6.1.22: [RIT 248 - 253] Determines whether an absolute value equation or inequality is true for a given value of the variable

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

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

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

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

6.6.1.27: [RIT 260 - 275] Solves absolute value inequalities

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

6.6.1.29: [RIT 270 - 275] Writes an absolute value inequality to represent a real-world or mathematical context

6.7: Systems of Linear Equations and Inequalities

6.7.1: System of Equations/Inequalities

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

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

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

6.7.1.4: [RIT 222 - 254] Writes a system of linear equations to represent a real-world or mathematical context

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

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

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

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

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

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

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

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

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

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

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

6.7.1.16: [RIT 263 - 277] Determines the number of solutions to a system of linear equations

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

6.7.1.20: [RIT 286 - 286] Solves a system of linear equations using matrices

6.8: Non-Linear Equations

6.8.1: Number Sentences/Equations/Equivalence

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

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

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

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

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

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

6.8.1.12: [RIT 257 - 257] Solves polynomial equations

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

6.8.1.17: [RIT 271 - 297] Solves literal equations for nonlinear variables

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