1.1: In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line
1.1.a: Students can: Define irrational numbers.
1.1.b: Students can: Demonstrate informally that every number has a decimal expansion.
1.1.b.i: For rational numbers show that the decimal expansion repeats eventually.
1.1.b.ii: Convert a decimal expansion which repeats eventually into a rational number.
1.1.c: Students can: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.
1.1.d: Students can: Apply the properties of integer exponents to generate equivalent numerical expressions.
1.1.e: Students can: Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number.
1.1.f: Students can: Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
1.1.g: Students can: Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
1.1.h: Students can: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.
1.1.h.i: Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.
1.1.h.ii: Interpret scientific notation that has been generated by technology.
2.1: Linear functions model situations with a constant rate of change and can be represented numerically, algebraically, and graphically
2.1.b: Students can: Graph proportional relationships, interpreting the unit rate as the slope of the graph.
2.1.c: Students can: Compare two different proportional relationships represented in different ways.
2.1.d: Students can: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.
2.1.e: Students can: Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
2.2: Properties of algebra and equality are used to solve linear equations and systems of equations
2.2.a: Students can: Solve linear equations in one variable.
2.2.a.i: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
2.2.a.ii: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
2.2.b: Students can: Analyze and solve pairs of simultaneous linear equations.
2.2.b.i: Explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
2.2.b.ii: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
2.2.b.iii: Solve real-world and mathematical problems leading to two linear equations in two variables.
2.3: Graphs, tables and equations can be used to distinguish between linear and nonlinear functions
2.3.a: Students can: Define, evaluate, and compare functions.
2.3.a.i: Define a function as a rule that assigns to each input exactly one output.
2.3.a.ii: Show that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
2.3.a.iii: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
2.3.a.iv: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line.
2.3.a.v: Give examples of functions that are not linear.
2.3.b: Students can: Use functions to model relationships between quantities.
2.3.b.i: Construct a function to model a linear relationship between two quantities.
2.3.b.ii: Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
2.3.b.iii: Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
2.3.b.iv: Describe qualitatively the functional relationship between two quantities by analyzing a graph.
2.3.b.v: Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
3.1: Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge
3.1.a: Students can: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities.
3.1.b: Students can: Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
3.1.c: Students can: For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
3.1.d: Students can: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
3.1.e: Students can: Explain patterns of association seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.
3.1.e.i: Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.
3.1.e.ii: Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
4.1: Transformations of objects can be used to define the concepts of congruence and similarity
4.1.a: Students can: Verify experimentally the properties of rotations, reflections, and translations:
4.1.b: Students can: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
4.1.c: Students can: Demonstrate that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.
4.1.d: Students can: Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.
4.1.e: Students can: Demonstrate that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.
4.1.f: Students can: Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.
4.1.g: Students can: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
4.2: Direct and indirect measurement can be used to describe and make comparisons
4.2.a: Students can: Explain a proof of the Pythagorean Theorem and its converse.
4.2.b: Students can: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
4.2.c: Students can: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
4.2.d: Students can: State the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Correlation last revised: 9/22/2020