Geometry

Geometry

 

Geometry

Beaumont ISD

Grade Level:

10th

Revision Date: 6/30/16

 

 

1st Nine Weeks

August 24 - October 14

Number of school days - 37

Number of instructional days - 25

Pre-test - Aug 26

Mid 9-Weeks Testing -  Sep 12 - 16

9-Weeks Testing - Oct 10 - 13

 

 

2nd Nine Weeks

October 17 - December 16

Number of school days - 38.5

Number of instructional days - 28

Pre-test - Oct 14

Mid 9-Weeks Testing - Nov 9 - 11

Midterm Testing - Dec 14 - 16

 

 

Refer to instructional timelines when planning units of instruction.

See list of Ongoing Process Standards that should be embedded in all Units of Instruction.

ALL Process Standards are eligible for incorporating into the assessment of at least 40% of Content Standards.

 

STAAR Standard Key:    Blue= STAAR Readiness Standard

                                              Yellow= STAAR Supporting Standard

                                                         Bold= Highest Stakes Standards (greatest need)

                        Italics= High Stakes Standards

 

Units

Unit 1: Transformation and Congruence (24 days)

Tools of Geometry, Transformations and Symmetry, Congruent Figures

 

Unit 2: Lines, Angles, and Triangles (Part 1) (10 days)

Lines and Angles, Triangle Congruence, Properties of Triangles, Special Segments of Triangles

 

Standards/SEs

 

Unit 1: Transformation and Congruence (24 days)

 

2.A  determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint.

 

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.

 

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

 

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.

 

3.C  identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane.

 

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

 

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

 

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.

 

4.C  verify that a conjecture is false using a counterexample.

 

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.

 

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

 

 

Unit 2: Lines Angles, And Triangles (Part 1) (10 days)

 

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.

 

2.C  determine an equation of a line parallel or perpendicular to a given line that passes through a given point.

 

4.D  compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.

 

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.

 

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.

 

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.

 

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

 

 

 

 

Units

Unit 2: Lines, Angles, and Triangles (Part 2) (18 days)

Lines and Angles, Triangle Congruence, Properties of Triangles, Special Segments of Triangles

 

Unit 3: Quadrilaterals and Coordinate Proof (16 days)

Properties of Quadrilaterals, Coordinate Proof Using Slope and Distance

 

Standards/SEs

 

Unit 2: Lines Angles, And Triangles (Part 2) (18 days)

 

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.

 

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.

 

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.

 

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

 

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

 

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.

 

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.

 

Unit 3: Quadrilaterals and Coordinate Proof (16 days)

 

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.

 

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.

 

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.

 

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.

 

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.

 

 

 

 

 

(Mathematical Process Standards embedded in instruction throughout all Units)

1.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

 

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

 

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;

 

1.C  select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

 

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

 

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

 

1.F  analyze mathematical relationships to connect and communicate mathematical ideas; and

 

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

 

 

Beaumont  22nd Century Skills

 


Critical Thinking and Reasoning:  Thinking Deeply, Thinking Differently

Information Literacy: Untangling the Web

Collaboration: Working Together, Learning Together

Self-Direction: Own Your Learning

Invention: Creating Solutions

 

Geometry

Beaumont ISD

Grade Level: 10th

Revision Date: 6/30/16

 

3rd Nine Weeks

January 3 - March 10

Number of school days - 47

Number of instructional days - 33

Pre-test - Jan 3

Mid 9-Weeks Testing - Jan 30 - Feb 3

9-Weeks Testing - Mar 6 - 9

 

 

4th Nine Weeks

March 20 - June 1

Number of school days - 51.5

Number of instructional days - 31

Pre-test - Mar 10

Mid 9-Weeks Testing - Apr 3 - 7

Final Testing - May 30 - Jun 1

 

Refer to instructional timelines when planning units of instruction.

See list of Ongoing Process Standards that should be embedded in all Units of Instruction.

ALL Process Standards are eligible for incorporating into the assessment of at least 40% of Content Standards.

 

STAAR Standard Key:    Blue= STAAR Readiness Standard

                                              Yellow= STAAR Supporting Standard

                                                         Bold= Highest Stakes Standards (greatest need)

                        Italics= High Stakes Standards

Units

Unit 4: Similarity (16 days)

Similarity and Transformations, Similar Triangles

 

Unit 5: Trigonometry (12 days)

 

Unit 6: Property of Circles (19 days)

Angles and Segments, Arc Length and Sector Area

Standards/SEs

 

Unit 4: Similarity (16 days)

 

2.A  determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint.

 

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.

 

3.C  identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane.

 

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

 

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.

 

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

 

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

 

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.

 

Unit 5: Trigonometry (12 days)

 

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.

 

9.B  apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem,

 

Unit 6: Properties of Circles (19 days)

 

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.

 

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.

 

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

 

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

 

12.B  apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems.

 

12.C  apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems.

 

12.D  describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle.

 

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.

 

 

 

Units

Unit 7: Measurement and Modeling in Two and Three Dimensions (26 days)

Volume, Visualizing Solids, Surface Area, Problem Solving

 

Unit 8: Probability (20 days)

Probability, Conditional Probability and Independence of Events

Standards/SEs

 

Unit 7: Measurement and Modeling in Two and Three Dimensions (26 days)

 

4.D  compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.

 

10.A  identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes.

 

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.

 

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

 

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.

 

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.

 

13.B  determine probabilities based on area to solve contextual problems.

 

Unit 8: Probability (20 days)

 

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

 

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

 

13.D  apply conditional probability in contextual problems.

 

13.E  apply independence in contextual problems.

 

 

 

(Mathematical Process Standards embedded in instruction throughout all Units)

1.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

 

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

 

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;

 

1.C  select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

 

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

 

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

 

1.F  analyze mathematical relationships to connect and communicate mathematical ideas; and

 

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

Beaumont  22nd Century Skills

 

Critical Thinking and Reasoning:  Thinking Deeply, Thinking Differently

Information Literacy: Untangling the Web

Collaboration: Working Together, Learning Together

Self-Direction: Own Your Learning

Invention: Creating Solutions