1: Number and Computation

1.1: The student demonstrates number sense for real numbers and algebraic expressions in a variety of situations.

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.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Part-to-part and Part-to-whole Ratios
Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

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.

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

1.2: The student demonstrates an understanding of the real number system; recognizes, applies, and explains their properties, and extends these properties to algebraic expressions.

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);

Equivalent Algebraic Expressions I

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);

Rational Numbers, Opposites, and Absolute Values
Simplifying Algebraic Expressions I

1.4: The student models, performs, and explains computation with real numbers and polynomials in a variety of situations.

1.4.2: performs and explains these computational procedures:

1.4.2.a: addition, subtraction, multiplication, and division using the order of operations;

Solving Algebraic Equations II

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;

Operations with Radical Expressions
Simplifying Radical Expressions

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;

Simplifying Algebraic Expressions II

1.4.2.f: simplification of products and quotients of real number and algebraic monomial expressions using the properties of exponents;

Dividing Exponential Expressions
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

2: Algebra

2.1: The student recognizes, describes, extends, develops, and explains the general rule of a pattern in a variety of situations.

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;

Arithmetic and Geometric Sequences
Finding Patterns

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;

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.1.1.d: special patterns, e.g., Pascal’s triangle and the Fibonacci sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.1.2: generates and explains a pattern.

Arithmetic Sequences
Geometric Sequences

2.1.3: classify sequences as arithmetic, geometric, or neither.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

2.1.4: defines:

2.1.4.a: a recursive or explicit formula for arithmetic sequences and finds any particular term,

Arithmetic Sequences
Arithmetic and Geometric Sequences

2.1.4.b: a recursive or explicit formula for geometric sequences and finds any particular term.

Arithmetic and Geometric Sequences
Geometric Sequences

2.2: The student uses variables, symbols, real numbers, and algebraic expressions to solve equations and inequalities in variety of situations.

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.

Solving Equations on the Number Line
Using Algebraic Equations

2.2.3: solves:

2.2.3.a: linear equations and inequalities both analytically and graphically;

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Systems of Linear Inequalities (Slope-intercept form)

2.2.3.b: quadratic equations with integer solutions (may be solved by trial and error, graphing, quadratic formula, or factoring);

Modeling the Factorization of x²+bx+c

2.2.3.d: radical equations with no more than one inverse operation around the radical expression;

Operations with Radical Expressions
Radical Functions

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.

Exponential Functions

2.3: The student analyzes functions in a variety of situations.

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.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

2.3.2: matches equations and graphs of constant and linear functions and quadratic functions limited to y = ax squared + c.

Addition and Subtraction of Functions
Exponential Functions
Point-Slope Form of a Line
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line
Translating and Scaling Functions
Zap It! Game

2.3.3: determines whether a graph, list of ordered pairs, table of values, or rule represents a function.

Exponential Functions
Introduction to Exponential Functions
Introduction to Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

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.

Quadratics in Vertex Form

2.3.5.: a. relationships given the graph or table,

Introduction to Functions

2.3.6: recognizes how changes in the constant and/or slope within a linear function changes the appearance of a graph.

Slope-Intercept Form of a Line

2.3.8: evaluates function(s) given a specific domain.

Logarithmic Functions

2.4: The student develops and uses mathematical models to represent and justify mathematical relationships found in a variety of situations involving tenth grade knowledge and skills.

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;

Modeling One-Step Equations

2.4.1.d: equations and inequalities to model numerical and geometric relationships;

Comparing and Ordering Decimals

2.4.1.f: coordinate planes to model relationships between ordered pairs and equations and inequalities and linear and quadratic functions

Points, Lines, and Equations

2.4.1.g: constructions to model geometric theorems and properties;

Segment and Angle Bisectors

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.

Classifying Quadrilaterals
Pyramids and Cones

2.4.1.j: Pascal’s Triangle to model binomial expansion and probability;

Binomial Probabilities

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;

Box-and-Whisker Plots
Compound Inequalities
Correlation
Describing Data Using Statistics
Distance-Time Graphs
Histograms
Least-Squares Best Fit Lines
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

3: Geometry

3.1: The student recognizes geometric figures and compares and justifies their properties of geometric figures in a variety of situations.

3.1.1: recognizes and compares properties of two-and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Similar Figures
Special Parallelograms

3.1.2: discusses properties of regular polygons related to:

3.1.2.b: diagonals.

Polygon Angle Sum

3.1.4: recognizes that similar figures have congruent angles, and their corresponding sides are proportional.

Similar Figures

3.1.5: uses the Pythagorean Theorem to:

3.1.5.b: find a missing side of a right triangle.

Cosine Function
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Tangent Function

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°.

Cosine Function
Sine Function
Tangent Function

3.1.7: recognizes, describes, and compares the relationships of the angles formed when parallel lines are cut by a transversal.

Constructing Congruent Segments and Angles
Triangle Angle Sum

3.1.8: recognizes and identifies parts of a circle: arcs, chords, sectors of circles, secant and tangent lines, central and inscribed angles.

Chords and Arcs
Circumference and Area of Circles
Inscribed Angles

3.2: The student estimates, measures and uses geometric formulas in a variety of situations.

3.2.4: states, recognizes, and applies formulas for:

3.2.4.a: perimeter and area of squares, rectangle, and triangles;

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

3.2.4.b: circumference and area of circles;

Circumference and Area of Circles

3.2.4.c: volume of rectangular solids.

Prisms and Cylinders
Pyramids and Cones

3.2.5: uses given measurement formulas to find perimeter, area, volume, and surface area of two- and three-dimensional figures (regular and irregular).

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

3.2.6: recognizes and applies properties of corresponding parts of similar and congruent figures to find measurements of missing sides.

Beam to Moon (Ratios and Proportions)
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles

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.

Direct and Inverse Variation

3.3: The student recognizes and applies transformations on two- and three- dimensional figures in a variety of situations.

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.

Circles
Dilations
Holiday Snowflake Designer
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

3.3.3: generates a two-dimensional representation of a three-dimensional figure.

Surface and Lateral Areas of Prisms and Cylinders

3.4: The student uses an algebraic perspective to analyze the geometry of two- and three-dimensional figures in a variety of situations.

3.4.2: determines if a given point lies on the graph of a given line or parabola without graphing and justifies the answer.

Points, Lines, and Equations

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.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line

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?

Cat and Mouse (Modeling with Linear Systems)

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.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a 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.

Addition and Subtraction of Functions
Parabolas
Translating and Scaling Functions
Zap It! Game

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.

Cat and Mouse (Modeling with Linear Systems)
Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

4: Data

4.1: The student applies probability theory to draw conclusions, generate convincing arguments, make predictions and decisions, and analyze decisions including the use of concrete objects in a variety of situations.

4.1.1: finds the probability of two independent events in an experiment, simulation, or situation.

Binomial Probabilities
Independent and Dependent Events
Theoretical and Experimental Probability

4.1.2: finds the conditional probability of two dependent events in an experiment, simulation, or situation.

Independent and Dependent Events

4.2: The student collects, organizes, displays, explains, and interprets numerical (rational) and non-numerical data sets in a variety of situations.

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;

Histograms

4.2.1.b: bar, line, and circle graphs;

Reaction Time 1 (Graphs and Statistics)

4.2.1.c: Venn diagrams or other pictorial displays;

Forest Ecosystem

4.2.1.d: charts and tables;

Describing Data Using Statistics
Stem-and-Leaf Plots

4.2.1.h: histograms.

Histograms

4.2.2: explains how the reader’s bias, measurement errors, and display distortions can affect the interpretation of data.

Polling: City
Polling: Neighborhood
Populations and Samples

4.2.3: calculates and explains the meaning of range, quartiles and interquartile range for a real number data set.

Reaction Time 1 (Graphs and Statistics)

4.2.5: approximates a line of best fit given a scatter plot and makes predictions using the equation of that line.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

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),

Mean, Median, and Mode

4.2.6.c: bimodal,

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram