1.1.1: knows, explains, and uses equivalent representations for real numbers and algebraic expressions including integers, fractions, decimals, percents, ratios; rational number bases with integer exponents; rational numbers written in scientific notation; absolute value; time; and money, e.g., -4/2 = (-2); a to the -2 power x b cubed = b cubed/a squared.
1.1.2: compares and orders real numbers and/or algebraic expressions and explains the relative magnitude between them, e.g., e.g., will (5n) squared always, sometimes, or never be larger than 5n? The student might respond with (5n)2 is greater than 5n if n > 1 and (5n) squared is smaller than 5 if o < n < 1.
1.2.3: names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects:
1.2.3.a: commutative (a + b = b + a and ab = ba), associative [a = (b + c) = (a + b) + c and a(bc) = (ab)c], distributive [a (b + c) = ab + ac], and substitution properties (if a = 2, then 3a = 3 x 2 = 6);
1.2.3.b: identity properties for addition and multiplication and inverse properties of addition and multiplication (additive identity: a + 0 = a, multiplicative identity: a x 1 = a, additive inverse: +5 + -5 = 0, multiplicative inverse: 8 x 1/8 = 1);
1.4.2: performs and explains these computational procedures:
1.4.2.a: addition, subtraction, multiplication, and division using the order of operations;
1.4.2.d: simplification of radical expressions (without rationalizing denominators) including square roots of perfect square monomials and cube roots of perfect cubic monomials;
1.4.2.e: simplification or evaluation of real numbers and algebraic monomial expressions raised to a whole number power and algebraic binomial expressions squared or cubed;
1.4.2.f: simplification of products and quotients of real number and algebraic monomial expressions using the properties of exponents;
2.1.1: identifies, states, and continues the following patterns using various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written:
2.1.1.b: patterns using geometric figures;
2.1.1.c: algebraic patterns including consecutive number patterns or equations of functions, e.g., n, n + 1, n + 2,... or f(n) = 2n – 1;
2.1.1.d: special patterns, e.g., Pascal’s triangle and the Fibonacci sequence.
2.1.2: generates and explains a pattern.
2.1.3: classify sequences as arithmetic, geometric, or neither.
2.1.4.a: a recursive or explicit formula for arithmetic sequences and finds any particular term,
2.1.4.b: a recursive or explicit formula for geometric sequences and finds any particular term.
2.2.1: knows and explains the use of variables as parameters for a specific variable situation, e.g., the m and b in y = mx + b or the h, k, and r in (x – h) squared + (y – k) squared = r squared.
2.2.3.a: linear equations and inequalities both analytically and graphically;
2.2.3.b: quadratic equations with integer solutions (may be solved by trial and error, graphing, quadratic formula, or factoring);
2.2.3.d: radical equations with no more than one inverse operation around the radical expression;
2.2.3.g: exponential equations with the same base without the aid of a calculator or computer, e.g., 3 to the power (x + 2) = 3 to the fifth power.
2.3.1: evaluates and analyzes functions using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or other appropriate technology.
2.3.2: matches equations and graphs of constant and linear functions and quadratic functions limited to y = ax squared + c.
2.3.3: determines whether a graph, list of ordered pairs, table of values, or rule represents a function.
2.3.4: determines x- and y-intercepts and maximum and minimum values of the portion of the graph that is shown on a coordinate plane.
2.3.5.: a. relationships given the graph or table,
2.3.6: recognizes how changes in the constant and/or slope within a linear function changes the appearance of a graph.
2.3.8: evaluates function(s) given a specific domain.
2.4.1: knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include:
2.4.1.a: process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations;
2.4.1.d: equations and inequalities to model numerical and geometric relationships;
2.4.1.f: coordinate planes to model relationships between ordered pairs and equations and inequalities and linear and quadratic functions
2.4.1.g: constructions to model geometric theorems and properties;
2.4.1.h: two- and three-dimensional geometric models (geoboards, dot paper, coordinate plane, nets, or solids) and real-world objects to model perimeter, area, volume, and surface area and isometric views of three-dimensional figures.
2.4.1.j: Pascal’s Triangle to model binomial expansion and probability;
2.4.1.l: frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-leaf plots, scatter plots, box-and-whisker plots, histograms, and matrices to organize and display data;
3.1.1: recognizes and compares properties of two-and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.
3.1.2: discusses properties of regular polygons related to:
3.1.4: recognizes that similar figures have congruent angles, and their corresponding sides are proportional.
3.1.5: uses the Pythagorean Theorem to:
3.1.5.b: find a missing side of a right triangle.
3.1.6: recognizes and describes:
3.1.6.b: the ratios of the sides in special right triangles: 30°-60°-90° and 45°-45°-90°.
3.1.7: recognizes, describes, and compares the relationships of the angles formed when parallel lines are cut by a transversal.
3.1.8: recognizes and identifies parts of a circle: arcs, chords, sectors of circles, secant and tangent lines, central and inscribed angles.
3.2.4: states, recognizes, and applies formulas for:
3.2.4.a: perimeter and area of squares, rectangle, and triangles;
3.2.4.b: circumference and area of circles;
3.2.4.c: volume of rectangular solids.
3.2.5: uses given measurement formulas to find perimeter, area, volume, and surface area of two- and three-dimensional figures (regular and irregular).
3.2.6: recognizes and applies properties of corresponding parts of similar and congruent figures to find measurements of missing sides.
3.2.7: knows, explains, and uses ratios and proportions to describe rates of change $, e.g., miles per gallon, meters per second, calories per ounce, or rise over run.
3.3.1: describes and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on two- and three-dimensional figures.
3.3.3: generates a two-dimensional representation of a three-dimensional figure.
3.4.2: determines if a given point lies on the graph of a given line or parabola without graphing and justifies the answer.
3.4.3: calculates the slope of a line from a list of ordered pairs on the line and explains how the graph of the line is related to its slope.
3.4.4: finds and explains the relationship between the slopes of parallel and perpendicular lines, e.g., the equation of a line 2x + 3y = 12. The slope of this line is 2/3. What is the slope of a line perpendicular to this line? Write an equation for a line perpendicular to 2x + 3y = 12 (or for multiple choice: Which is an equation of a line perpendicular to 2x + 3y = 12?
3.4.6: recognizes the equation of a line and transforms the equation into slope-intercept form in order to identify the slope and y-intercept and uses this information to graph the line.
3.4.7: recognizes the equation y = ax squared + c as a parabola; represents and identifies characteristics of the parabola including opens upward or opens downward, steepness (wide/narrow), the vertex, maximum and minimum values, and line of symmetry; and sketches the graph of the parabola.
3.4.8: explains the relationship between the solution(s) to systems of equations and systems of inequalities in two unknowns and their corresponding graphs, e.g., for equations, the lines intersect in either one point, no points, or infinite points; and for inequalities, all points in double-shaded areas are solutions for both inequalities.
4.1.1: finds the probability of two independent events in an experiment, simulation, or situation.
4.1.2: finds the conditional probability of two dependent events in an experiment, simulation, or situation.
4.2.1: organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays.
4.2.1.a: frequency tables;
4.2.1.b: bar, line, and circle graphs;
4.2.1.c: Venn diagrams or other pictorial displays;
4.2.1.d: charts and tables;
4.2.2: explains how the reader’s bias, measurement errors, and display distortions can affect the interpretation of data.
4.2.3: calculates and explains the meaning of range, quartiles and interquartile range for a real number data set.
4.2.5: approximates a line of best fit given a scatter plot and makes predictions using the equation of that line.
4.2.6: compares and contrasts the dispersion of two given sets of data in terms of range and the shape of the distribution including
4.2.6.b: skew (left or right),
Correlation last revised: 5/11/2018