1: The student uses mathematical processes to acquire and demonstrate mathematical understanding.

1.A: apply mathematics to problems arising in everyday life, society, and the workplace;

Determining a Spring Constant
Estimating Population Size

1.B: use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

Estimating Population Size

1.D: communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

Biconditional Statements
Using Algebraic Expressions

1.E: create and use representations to organize, record, and communicate mathematical ideas;

Describing Data Using Statistics
Stem-and-Leaf Plots
Using Algebraic Expressions

1.G: display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Using Algebraic Expressions

2: The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures.

2.B: derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines; and

Circles
Distance Formula

3: The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity).

3.A: describe and perform transformations of figures in a plane using coordinate notation;

Dilations
Rotations, Reflections, and Translations
Translations

3.B: determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane;

Dilations
Rotations, Reflections, and Translations

3.D: identify and distinguish between reflectional and rotational symmetry in a plane figure.

Holiday Snowflake Designer

4: The student uses the process skills with deductive reasoning to understand geometric relationships.

4.A: distinguish between undefined terms, definitions, postulates, conjectures, and theorems;

Biconditional Statements
Investigating Angle Theorems
Isosceles and Equilateral Triangles

4.B: identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse;

Biconditional Statements
Conditional Statements

5: The student uses constructions to validate conjectures about geometric figures.

5.A: investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools;

Inscribed Angles
Polygon Angle Sum
Triangle Angle Sum

5.B: construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge;

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

5.C: use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships; and

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

5.D: verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.

Triangle Inequalities

6: The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.

6.A: verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems;

Investigating Angle Theorems
Segment and Angle Bisectors
Triangle Angle Sum

6.B: prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions;

Congruence in Right Triangles
Proving Triangles Congruent

6.C: apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles;

Dilations
Reflections
Rotations, Reflections, and Translations
Translations

6.D: verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems; and

Cosine Function
Isosceles and Equilateral Triangles
Polygon Angle Sum
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Triangle Angle Sum
Triangle Inequalities

6.E: prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems.

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

7: The student uses the process skills in applying similarity to solve problems.

7.A: apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles; and

Circles
Dilations
Similar Figures

7.B: apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems.

Perimeters and Areas of Similar Figures

8: The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart.

8.A: prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems; and

Similar Figures

8.B: identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.

Similarity in Right Triangles

9: The student uses the process skills to understand and apply relationships in right triangles.

9.A: determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems; and

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine
Tangent Function

9.B: apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems.

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

10: The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures.

10.B: determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change

Perimeter and Area of Rectangles
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

11: The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures.

11.A: apply the formula for the area of regular polygons to solve problems using appropriate units of measure;

Area of Triangles

11.B: determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure;

Area of Triangles

11.C: apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure; and

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

11.D: apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.

Prisms and Cylinders
Pyramids and Cones

12: The student uses the process skills to understand geometric relationships and apply theorems and equations about circles.

12.A: apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems;

Chords and Arcs
Inscribed Angles

12.E: show that the equation of a circle with center at the origin and radius r is x² + y² = r² and determine the equation for the graph of a circle with radius r and center (h, k), (x - h)² + (y - k)² =r².

Circles

13: The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events.

13.A: develop strategies to use permutations and combinations to solve contextual problems;

Binomial Probabilities
Permutations and Combinations

13.C: identify whether two events are independent and compute the probability of the two events occurring together with or without replacement;

Binomial Probabilities
Independent and Dependent Events

13.D: apply conditional probability in contextual problems; and

Independent and Dependent Events

13.E: apply independence in contextual problems.

Independent and Dependent Events