· Web viewThe mathematics curriculum provides sequential and comprehensive K-12 instruction in a...
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District Overview The mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21 st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real- life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere. Geometry Description Geometry covers basic geometric figures, along with some proofs of theorems relation to these geometric figures. Specific topics covered are as follows: parallel lines, congruent triangles, polygons, quadrilaterals, similar triangles, circles, area, coordinate geometry, and elementary right triangle trigonometry. Grade X Units: The units should equate to a full course (full-year/semester) of instruction. Unit 1: Tools of Geometry Unit 2: Geometric Reasoning Unit 3: Parallel and Perpendicular Lines Unit 4: Congruent Triangles Unit 5: Relationships in Triangles Unit 6: Polygons and Quadrilaterals Unit 7: Proportions and Similarity Unit 8: Triangles and Trigonometry Unit 9: Area and Volume of Polygons and Circles
Transcript of · Web viewThe mathematics curriculum provides sequential and comprehensive K-12 instruction in a...
District OverviewThe mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real-life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere.
Geometry DescriptionGeometry covers basic geometric figures, along with some proofs of theorems relation to these geometric figures. Specific topics covered are as follows: parallel lines, congruent triangles, polygons, quadrilaterals, similar triangles, circles, area, coordinate geometry, and elementary right triangle trigonometry.
Grade X Units:The units should equate to a full course (full-year/semester) of instruction.
Unit 1: Tools of Geometry Unit 2: Geometric Reasoning Unit 3: Parallel and Perpendicular Lines Unit 4: Congruent Triangles Unit 5: Relationships in Triangles Unit 6: Polygons and Quadrilaterals Unit 7: Proportions and Similarity Unit 8: Triangles and Trigonometry Unit 9: Area and Volume of Polygons and Circles
Subject: Geometry
Grade:9-12
Suggested Timeline: 5 weeks
Unit Title: Tools of Geometry
Unit Overview/Essential Understanding: Students will:
Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning and theorems. Use construction to explore attributes of geometric figures and to make conjectures about geometric relationships. Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. Find areas of regular polygons, circles, and composite figures.
Unit Objectives: At the end of this module, students will be able to independently use their learning to:
Identify and model points, lines, planes, intersecting lines and intersecting planes Measure line segments and calculate with measures Find the distance between two points and find the midpoint of a segment Measure and classify angles Identify and use congruent angles and the bisector of an angle Identify and use special pairs of angles and perpendicular lines Identify and name polygons Find the perimeter, circumference and area of two-dimensional figures Identify and name three-dimensional figures Find surface area and volume
Focus Standards Addressed in this Unit: CC.2.3.HS.A.3 – Verify and apply geometric theorems as they relate to geometric figures CC.2.3.HS.A.11 – Apply coordinate geometry to prove simple geometric theorems algebraically CC.2.3.HS.A.12 – Explain volume formulas and use them to solve problems CC.2.3.HS.A.13 – Analyze relationships between two-dimensional and three-dimensional objects
Important Standards Addressed in this Unit: CC.2.3.HS.A.14 – Apply geometric concepts to model and solve real-world problems
Misconceptions:
Measuring line segments, angle measures, and distances differently when involving variables.
Concepts/Content: Points, Lines, and Planes Linear Measure Distance and Midpoints Angle Measure and Relationships Two-Dimensional and Three-
Dimensional Figures
Competencies/Skills: Find distances between points
and midpoints of the segments. Identify angle relationships. Find perimeters, areas, surface
areas, and volumes.
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos
Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test
Interdisciplinary Connections:N/A
Additional Resources: Glencoe Geometry Textbook USA TestPrep
Subject: Geometry
Grade:9-12
Suggested Timeline: 3 weeks
Unit Title: Geometric ReasoningUnit Overview/Essential Understanding: Students will:
Use inductive reasoning to formulate a conjecture Use logical reasoning to prove statements are true and find counterexamples to disprove statements that are false Determine the validity of a conditional statement, its converse, inverse, and contrapositive Use deductive reasoning to prove a statement
Unit Objectives: At the end of this module, students will be able to independently use their learning to:
Make conjectures based on inductive reasoning and find counterexamples Determine truth values of negations, conjunctions and disjunctions Analyze statements in if-then form Write converses, inverses and contrapositives Identify and use basic postulates about points, lines, and planes Write proofs involving segment addition, congruence, right angles, supplementary angles, and complementary angles
Focus Standards Addressed in this Unit: CC.2.3.HS.A.3 – Verify and apply geometric theorems as they relate to geometric figures
Important Standards Addressed in this Unit: CC.2.3.HS.A.14 – Apply geometric concepts to model and solve real-world problems
Misconceptions: Analyzing if-then statements in reverse.
Concepts/Content: Inductive Reasoning and
Conjecture Logic Conditional Statements Segment and Angle Postulates
Competencies/Skills: Make conjectures and find
counterexamples for statements. Use deductive reasoning to reach
valid conclusions. Write proofs involving segment
and angle theorems.
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos
Assessments:
informal questioning in-class formative assessments review of homework periodic quizzes unit test
Interdisciplinary Connections:N/A
Additional Resources: Glencoe Geometry Textbook USA TestPrep
Subject: Geometry
Grade:9-12
Suggested Timeline: 4 weeks
Unit Title:
Parallel and Perpendicular LinesUnit Overview/Essential Understanding: Students will:
Make conjectures about lines and angles and determine the validity of the conjectures Use slopes of equations of lines to investigate geometric relationships, including parallel and perpendicular lines Use one- and two-dimensional coordinate systems to represent lines
Unit Objectives: At the end of this module, students will be able to independently use their learning to:
Identify the relationship between two lines or two planes Name angle pairs formed by parallel lines and transversals Use theorems to determine the relationships between specific pairs of angles Use algebra to find angle measurements Find slopes of lines and use slops to identify parallel and perpendicular lines Write an equation of a line given information about the graph Solve problems by writing equations Recognize angle pairs that occur with parallel lines Prove that two lines are parallel Find the distance between a point and a line Find the distance between two parallel lines
Focus Standards Addressed in this Unit: CC.2.2.HS.C.1 – Use the concept and notation of functions to interpret and apply them in terms of their context CC.2.3.HS.A.2 – Apply rigid transformations to determine and explain congruence CC.2.3.HS.A.11 – Apply coordinate geometry to prove simple geometric theorems algebraically
Important Standards Addressed in this Unit: CC.2.3.HS.A.14 – Apply geometric concepts to model and solve real-world problems
Misconceptions: Applying parallel transversal postulates and theorems to non-parallel transversals.
Concepts/Content: Parallel Lines and Transversals Angles and Parallel Lines Slopes and Equations of Lines
Competencies/Skills: Identify and prove angle
relationships that occur with parallel lines and a transversal
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work
Proving Lines Parallel Perpendiculars and Distance
Use slope to analyze a line and to write its equation
Find the distance between a point and a line and between two parallel lines
Small group collaboration Online remedial/enrichment videos
Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test
Interdisciplinary Connections:N/A
Additional Resources: Glencoe Geometry Textbook USA TestPrep
Subject: Geometry
Grade:9-12
Suggested Timeline: 4 weeks
Unit Title: Congruent Triangles
Unit Overview/Essential Understanding: Students will:
Make conjectures about polygons Use numeric and geometric patterns to make generalizations about geometric properties Use logical reasoning to prove statements are true
Unit Objectives: At the end of this module, students will be able to independently use their learning to:
Identify and classify triangle by angle measure and side measures Apply the Triangle Angle-Sum Theorem Apply the Exterior Angle Theorem Name and use corresponding parts of congruent polygons Use the SSS and SAS Postulates to test for triangle congruence Use the ASA and AAS Postulates to test for triangle congruence Explore congruence in right triangles Use properties of isosceles and equilateral triangle Identify reflections, transformations and rotations
Focus Standards Addressed in this Unit: CC.2.3.HS.A.2 – Apply rigid transformations to determine and explain congruence CC.2.3.HS.A.3 – Verify and apply geometric theorems as they relate to geometric figures
Important Standards Addressed in this Unit: CC.2.3.HS.A.14 – Apply geometric concepts to model and solve real-world problems
Misconceptions: Understanding which angle is the included angle in SAS
Concepts/Content: Classifying Triangles Angles of Triangles Congruent Triangles SSS, SAS, ASA, AAS, and HL
Competencies/Skills: Apply special relationships about
the interior and exterior angles of triangles
Identify corresponding parts of
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration
Triangle Congruence Isosceles and Equilateral Triangles
congruent triangles and prove triangles congruent
Learn about the special properties of isosceles and equilateral triangles
Online remedial/enrichment videos
Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test
Interdisciplinary Connections:N/A
Additional Resources: Glencoe Geometry Textbook USA TestPrep
Subject: Geometry
Grade:9-12
Suggested Timeline: 4 weeks
Unit Title: Relationships in Triangles
Unit Overview/Essential Understanding: Students will:
Use slope and equations of lines to investigate geometric relationships, including special segments of triangles Recognize and know historical development of geometric systems and know that mathematics was developed for a variety of purposes Analyze geometric relationships in order to verify conjectures
Unit Objectives: At the end of this module, students will be able to independently use their learning to:
Identify and use perpendicular bisectors and angle bisectors in triangles Identify and use medians and altitudes in triangles Recognize and apply properties of inequalities to the measure of the angles of a triangle Recognize and apply properties of inequalities to the relationships between the angles and the sides of a triangle Use the Triangle Inequality Theorem to identify possible triangles Prove triangle relationships using the Triangle Inequality Theorem Apply the Hinge Theorem or its converse to make comparisons in two triangles
Focus Standards Addressed in this Unit: CC.2.3.HS.A.3 – Verify and apply geometric theorems as they relate to geometric figures CC.2.3.HS.A.13 – Analyze relationships between two-dimensional and three-dimensional objects
Important Standards Addressed in this Unit: CC.2.3.HS.A.14 – Apply geometric concepts to model and solve real-world problems
Misconceptions: Identifying the true center of a triangle.
Concepts/Content: Bisectors of Triangles Medians and Altitudes of
Triangles Inequalities in One Triangle The Triangle Inequality Theorem Inequalities in Two Triangles
Competencies/Skills: Learn about special segments and
points related to triangles. Learn about relationships
between the sides and angles of triangles.
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos
Assessments: informal questioning
in-class formative assessments review of homework periodic quizzes unit test
Interdisciplinary Connections:N/A
Additional Resources: Glencoe Geometry Textbook USA TestPrep
Subject: Geometry
Grade:9-12
Suggested Timeline: 4 weeks
Unit Title: Quadrilaterals and PolygonsUnit Overview/Essential Understanding: Students will:
Use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons
Formulate and test conjectures about the properties and attributes of polygons Derive and use formulas involving length, slope, and midpoint Formulate and test conjectures about the properties and attributes of polygons
Unit Objectives: At the end of this module, students will be able to independently use their learning to:
Find and use the sum of the measures of the interior angles of a polygon Find and use the sum of the measures of the exterior angles of a polygon Recognize and apply properties of the sides and angles of parallelograms Recognize and apply properties of the diagonals of parallelograms Recognize the conditions that ensure a quadrilateral is a parallelogram Prove that a set of points forms a parallelogram in the coordinate plane Recognize and apply properties of rectangles Determine whether parallelograms are rectangles Recognize and apply the properties of rhombi and squares Determine whether quadrilaterals are rectangles, rhombi, or squares Apply properties of trapezoids and kites
Focus Standards Addressed in this Unit: CC.2.3.HS.A.3 – Verify and apply geometric theorems as they relate to geometric figures CC.2.3.HS.A.11 – Apply coordinate geometry to prove simple geometric theorems algebraically CC.2.3.HS.A.13 – Analyze relationships between two-dimensional and three-dimensional objects
Important Standards Addressed in this Unit: CC.2.3.HS.A.14 – Apply geometric concepts to model and solve real-world problems
Misconceptions: All quadrilateral properties apply to squares but not all square properties apply to other quadrilaterals
Concepts/Content: Angles of Polygons Parallelograms and Tests for
Parallelograms Rectangles, Rhombi, Squares,
Competencies/Skills: Find and use the sum of the
measures of the interior and exterior angles of a polygon
Recognize and apply properties of
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration
Trapezoids, and Kites quadrilaterals Compare quadrilaterals
Online remedial/enrichment videos
Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test
Interdisciplinary Connections:N/A
Additional Resources: Glencoe Geometry Textbook USA TestPrep
Subject: Geometry
Grade:9-12
Suggested Timeline: 4 weeks
Unit Title: Proportions and Similarity
Unit Overview/Essential Understanding: Students will:
Use ratios to solve problems involving similar figures
Formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models
Unit Objectives: At the end of this module, students will be able to independently use their learning to:
Write ratios, and write and solve proportions Use proportions to identify similar polygons Solve problems using the properties of similar polygons Identify similar triangles using the AA Similar Postulate and the SSS and SAS Similarity Theorems Use similar triangles to solve problems Use proportional parts within triangles and parallel lines Interpret scale models and use scale factors to solve problems
Focus Standards Addressed in this Unit: CC.2.3.HS.A.6 – Verify and apply theorems involving similarity as they relate to plane figures
Important Standards Addressed in this Unit: CC.2.3.HS.A.14 –Apply geometric concepts to model and solve real-world problems
Misconceptions: Similar and congruent are not the same.
Concepts/Content: Ratios and Proportions Similar Polygons and Triangles Parallel Lines and Proportional
Parts Parts of Similar Triangles Scale Drawings and Models
Competencies/Skills: Identify similar polygons and use
ratios and proportions to solve problems.
Identify and apply similarity transformations.
Use scale models and drawings to solve problems.
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos
Assessments: informal questioning in-class formative assessments review of homework periodic quizzes
unit test
Interdisciplinary Connections:N/A
Additional Resources: Glencoe Geometry Textbook USA TestPrep
Subject: Geometry
Grade:9-12
Suggested Timeline: 4 weeks
Unit Title: Triangles and TrigonometryUnit Overview/Essential Understanding: Students will:
Use and extend similarity properties to explore and justify conjectures about geometric figures Derive, extend, and use the Pythagorean Theorem Identify and apply patterns from right triangles to solve meaningful problems, including, special right triangles (45-45-90 and 30-60-90)
and triangles with sides that are Pythagorean triples Develop, apply, and justify triangle similarity relationships, such as trigonometric ratios using a variety of methods
Unit Objectives: At the end of this module, students will be able to independently use their learning to:
Use the Pythagorean Theorem Use the Converse of the Pythagorean Theorem Use the properties of 45-45-90 triangles Use the properties of 30-60-90 triangles Find trigonometric ratios using right triangles Use trigonometric ratios to find measures in right triangle
Focus Standards Addressed in this Unit: CC.2.2.HS.C.9 – Prove the Pythagorean Identity and use it to calculate trigonometric ratios CC.2.3.HS.A.7 – Apply trigonometric ratios to solve problems involving right triangles
Important Standards Addressed in this Unit: CC.2.3.HS.A.14 – Apply geometric concepts to model and solve real-world problems
Misconceptions: Trig ratios only apply to right triangles
Concepts/Content: The Pythagorean Theorem and Its
Converse Special Right Triangles Trigonometry
Competencies/Skills: Use the Pythagorean Theorem Use properties of special right
triangles Use trigonometry to find missing
measures of triangles
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos
Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test
Interdisciplinary Connections:N/A
Additional Resources: Glencoe Geometry Textbook USA TestPrep
Subject: Geometry
Grade:9-12
Suggested Timeline: 4 weeks
Unit Title: Areas of Polygons and CirclesUnit Overview/Essential Understanding: Students will:
Find areas of regular polygons, circles, and composite figures Find areas of sectors and arc lengths of circles using proportional reasoning
Unit Objectives: At the end of this module, students will be able to independently use their learning to:
Find perimeters and areas of parallelograms and triangles Find areas of trapezoids, rhombi, and kites
Focus Standards Addressed in this Unit: CC.2.3.HS.A.12 – Explain area and volume formulas and use them to solve problems CC.2.3.HS.A.8 – Apply geometric theorems to verify properties of circles CC.2.3.HS.A.9 – Extend the concept of similarity to determine arc lengths and areas of sectors of circles
Important Standards Addressed in this Unit: CC.2.3.HS.A.14 – Apply geometric concepts to model and solve real-world problems
Misconceptions: Finding the area of a regular polygon vs. an irregular polygon
Concepts/Content: Areas of Triangles and
Quadrilaterals Areas of Circles and Sectors Areas of Composite Figures
Competencies/Skills: Find areas of polygons Solve problems involving areas
and sectors of circles. Find scale factors using similar
figures.
Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos
Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test
Interdisciplinary Connections:N/A
Additional Resources: Glencoe Geometry Textbook USA TestPrep
