1: Calculations and Estimations

1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.1: Compare real numbers

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers

1.1.4: Locate real numbers on a number line (including approximations of irrational numbers)

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers

1.2: Compute fluently and make reasonable estimates

1.2.3: Mentally multiply and divide by powers of 10 to estimate results of computations involving numbers expressed in scientific notation

Estimating Population Size

1.2.4: Develop and use strategies to estimate the results of real number computations, determine the amount of error, and judge the reasonableness of results

Estimating Population Size

2: Statistics and Probability

2.1: Select and use appropriate statistical methods to analyze data

2.1.2: Analyze bivariate data and identify the type of function (linear, quadratic, exponential) that could be used to model the data

Exponential Functions - Activity A
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

2.2: Understand and apply basic concepts of probability

2.2.1: Compute the probability of a compound event (e.g., toss a coin three times to find the probability of two heads)

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

2.2.2: Determine probabilities of dependent and independent events (e.g., use colored marbles with and without replacement)

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

2.2.4: Determine all possible outcomes of a particular event or all possible arrangements of objects in a given set by applying counting strategies, combinations, and permutations

Binomial Probabilities
Permutations
Permutations and Combinations

2.3: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

2.3.1: Determine appropriate designs for simulations (surveys, observational studies, and experiments) and modeling to study a problem and construct empirical probability distributions to represent results

Geometric Probability - Activity A
Probability Simulations

2.3.2: Use matrices, histograms, scatter plots, stem-and-leaf plots, and box-and whisker-plots to interpret data

Box-and-Whisker Plots
Correlation
Histograms
Populations and Samples
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

2.4: Develop and evaluate inferences and predictions that are based on data

2.4.1: Make inferences and predictions from data in histograms, scatter plots, and parallel box plots

Correlation
Histograms
Populations and Samples
Scatter Plots - Activity A
Solving Using Trend Lines

3: Algebraic Relationships

3.1: Understand patterns, relations, and functions

3.1.1: Represent and generalize sequences resulting from linear, quadratic, and exponential relationships using recursive or explicit formulas tables of values and graphs

Arithmetic Sequences
Arithmetic and Geometric Sequences
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Geometric Sequences
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Using Tables, Rules and Graphs

3.1.3: Evaluate and make a table for two-variable formulas and match a graph or table of values to its formula

Exponential Functions - Activity A
Linear Functions
Logarithmic Functions: Translating and Scaling
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

3.1.4: Identify independent and dependent variables and determine the domain and range of a function in a problem situation

Functions Involving Square Roots
Introduction to Functions

3.2: Represent and analyze mathematical situations and structures using algebraic symbols

3.2.1: Algebraically represent situations and solve problems involving quadratic and exponential equations, including exponential growth and decay

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Roots of a Quadratic

3.2.2: Use graphs to solve non-linear equations, including quadratics

Roots of a Quadratic

3.2.3: Represent and solve system of linear equations with 2 variables using simultaneous equations and by graphing

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

3.2.6: Translate between and interpret quadratic and exponential relationships represented by words, symbols, tables, and graphs

Exponential Functions - Activity A
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Using Tables, Rules and Graphs

3.2.7: Determine and interpret maxima or minima and zeros of quadratic functions, and linear functions where y = constant

Linear Functions
Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

3.2.8: Graph linear inequalities in two variables

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

3.2.9: Graph quadratic and exponential equations

Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

3.2.10: Analyze how changing a parameter (i.e., k, b) in a quadratic or exponential function of the form y=k^x+b, y=kx^2+b, or y=k(x+b)^2 affects its graph

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Translating and Scaling Functions

3.3: Use mathematical models to represent and understand quantitative relationships

3.3.1: Model situations, make predictions and inferences, and solve problems using linear, quadratic, and exponential functions

Exponential Functions - Activity A
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

3.3.2: Determine when data represented in a table or graph represents a linear, quadratic, or exponential relationship

Exponential Functions - Activity A
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Using Tables, Rules and Graphs

3.4: Analyze change in various contexts

3.4.1: Approximate and interpret rates of change in graphical and numeric data

Direct Variation
Direct and Inverse Variation

3.4.2: Analyze the nature of change of each variable in a non-linear relationship as suggested by a table of values, a graph or a formula

Cosine Function
Cubic Function Activity
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Tangent Function
Unit Circle
Using Tables, Rules and Graphs

4: Measurement

4.1: Understand measurable attributes of objects and the units, systems and processes of measurement

4.1.1: Determine the appropriate units, scales, and tools for problem situations involving measurement

Dilations
Similar Figures - Activity A
Similar Polygons
Triple Beam Balance

4.1.3: Determine the precision of a given measuring tool (e.g., 1 degree for a standard protractor)

Triple Beam Balance

4.2: Apply appropriate techniques, tools, and formulas to determine measurements

4.2.1: Develop and use strategies and formulas for calculating surface area and volume of cones and spheres

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

4.2.2: Use formulas to solve problems involving finding missing dimensions given perimeter, area, surface area and volume of polygons, circles, prisms, pyramids, cones, cylinders, and spheres

Area of Parallelograms - Activity A
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

4.2.4: Determine perimeter and area of shapes of circles and polygons (annulus, etc.) in context

Area of Parallelograms - Activity A
Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

4.2.5: Determine the surface area and volume of a complex figure composed of a combination of two or more geometric figures or a figure derived from a regular solid (e.g., hemisphere, frustum of a cone)

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

4.2.6: Compare and contrast the formulas for surface area and volume of cylinders and cones

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

4.2.7: Determine a shape that has minimum or maximum perimeter, area, surface area, or volume under specified conditions

Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Rectangle: Perimeter and Area

5: Geometry

5.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

5.1.1: Determine defining properties that characterize classes of three-dimensional figures and their component parts

Classifying Triangles
Congruence in Right Triangles
Prisms and Cylinders - Activity A
Proving Triangles Congruent
Pyramids and Cones - Activity A

5.1.2: Recognize and represent three-dimensional figures and their component parts

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

5.1.3: Justify and use theorems involving the angles formed by parallel lines cut by a transversal

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

5.1.4: Develop, understand, and apply properties of circles and of inscribed and circumscribed polygons

Circles

5.1.5: Use measures of sides and of interior and exterior angles of polygons to classify figures and solve problems

Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals
Triangle Angle Sum - Activity A

5.1.6: Prove congruence of two triangles or their corresponding component parts

Biconditional Statement
Conditional Statement
Congruence in Right Triangles
Proving Triangles Congruent

5.1.7: Determine the measures of corresponding angles, sides, and corresponding parts of congruent and similar figures

Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

5.1.8: Use angle, side length and triangle inequality relationships to solve problems

Classifying Triangles
Triangle Inequalities

5.1.9: Use trigonometric functions, and angle and side relationships of special right triangles (30- 60-right triangles and isosceles right triangles) to solve for an unknown length and determine distances and solve problems

Cosine Function
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio

5.1.10: Investigate relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles

Chords and Arcs
Inscribing Angles

5.1.12: Justify and use theorems involving the properties of triangles, quadrilaterals, circles, and their component parts to verify congruence and similarity

Congruence in Right Triangles
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

5.2: Use visualization, spatial reasoning, and geometric modeling to solve problems

5.2.1: Model, sketch, label and where appropriate construct cones and spheres, and basic elements of geometric figures (e.g., altitudes, midpoints, medians, angle bisectors, and perpendicular bisectors) using compass and straightedge or technology

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones

5.2.2: Describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect)

Congruence in Right Triangles
Investigating Parallel Lines and Planes
Proving Triangles Congruent

5.2.3: Make a model of a three-dimensional figure from a two-dimensional drawing and make a two-dimensional representation of a three-dimensional object through scale drawings, perspective drawings, blueprints or computer simulations

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

5.3: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

5.3.2: Calculate slope, distance and midpoint between points with an emphasis on practical applications (use coordinate formulas)

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Slope - Activity B

5.4: Apply transformations and use symmetry to analyze mathematical situations

5.4.1: Use coordinate geometry to determine whether a figure is symmetrical with respect to a line or a point

Holiday Snowflake Designer

5.4.2: Determine whether a given pair of figures on a coordinate plane represent a translation, reflection, rotation and/or dilation

Dilations
Reflections
Rotations, Reflections and Translations
Translations

5.4.3: Determine the image of a figure on a coordinate graph under translations, reflections, and rotations

Reflections
Rotations, Reflections and Translations
Translations

5.4.4: Given a figure and its image on a coordinate graph, determine the translation vector or locate the axis of reflection

Holiday Snowflake Designer
Reflections
Rotations, Reflections and Translations
Translations
Vectors

5.4.5: Determine the coordinates of and draw the dilation of a figure on a coordinate graph

Dilations

5.4.6: Analyze the congruence, similarity, and line or rotational symmetry of figures using transformations

Constructing Congruent Segments and Angles
Holiday Snowflake Designer
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons