geometry curriculum pacing guide draft · investigations – please make sure these are a definite...

Milwaukee Public Schools Suggested Curriculum Pacing Guide for Discovering Geometry Draft 10/05/08 Fall 2008 – Spring 2009

Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898. Draft 10/05/08

Milwaukee Public Schools PACING GUIDE for

High School GEOMETRY Foundation Level



Dear Milwaukee Public School Geometry Teachers: With the adoption of a new textbook series for the Milwaukee Public Schools in the Spring of 2008, it became necessary to design pacing guides for these textbooks. The following is Draft One of the Pacing Guide for Discovering Geometry. Just like the headers to this document state, this is a draft. Our district is relying on your good judgment and teaching skills to provide us with insights, suggestions, modifications, corrections, and plans with the intent of incorporating these into Draft 2. Members of the Key Curriculum Press have told us that a first year pacing guide must be very tentative – we will not have a clear picture of just what our students can accomplish and what our teachers can complete until the full one year teaching and learning cycle is complete. Therefore, we not only suggest, but highly recommend, that you use this as a guide – modify to fit the needs of your style of teaching and the needs of your students. This means that you might have to add more time to one section of the text and then reduce time spent on another section. This also gives you the ability to eliminate a section or sections because time is not available. However, the Discovering Series is a series that builds on investigations – please make sure these are a definite part of your lesson plans, and teaching and learning in your classrooms. Usually there is more than one investigation in a section – at least one should be tried. We also hope that you are using the cooperative learning skills and strategies so important in this math curriculum. Many of our schools are on different school calendars – some are blocked; some start earlier in August; some are year-round schools. This pacing guide is set for 36 weeks. Time is allotted for semester exams – review and assessment. All explorations and algebra skills activities are also included. These are places where adjustments can be made. Six chapters are covered in Semester One and seven chapters are covered in Semester Two. We have heard that some teachers may be struggling to cover the first six chapters in one semester – especially in the blocked schools. This is OK! The first semester is loaded with vocabulary, concepts and skills that will be needed for semester two – taking more time on the first five chapters may prove beneficial when you approach the last chapters of the book. From Week 28 on, fewer sections are covered each week and more time is allowed for chapter assessments. These may be the weeks during which you can catch-up. If time does run out, we suggest that perhaps Chapter 13, Geometry as a Mathematical System, be one that you eliminate, at least for this first year. Please remember that all of the above are suggestions – the ultimate decision of how to cover the material in the text and to follow the pacing guide resides with the classroom teacher. We ask that all chapters are covered (with the possibility that you will not cover Chapter 13 and some sections may be eliminated). Your reflections and feedback will periodically be requested by your MTL and/or department chair to share with our Math Specialists, FTF Math Instructional Coach, Key Curriculum Press, and others who are part of the mathematics leadership in our district. Thank you in advance for your participation.



Drafted by: Sherrie K. Akinsanya, FTF Mathematics Instructional Coahc Time

(week) Lesson/ Activity

MPS Learning Targets LT1: The student will communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways, e.g. using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.

Benchmarks Embedded in Chapter Lessons

District Model CABS

Suggested vocabulary

Chapter 0 Geometric Art 0.1 Geometry in Art and Nature 0.2 Line Designs 0.3 Circle Designs 0.4 Op Art 0.6 Islamic Tiles

CHAPTER 0 LT2*: Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately. LT16: Apply transformations and their compositions to analyze geometric figures and create designs.

CHAPTER 0 2.2* Measure lengths using a metric/English ruler (to the appropriate degree of tenths of cm and sixteenths of an inch). 16.4 Determine whether a figure has point symmetry, line symmetry or neither. 16.5 Identify tessellations in art, construction and nature. 16.6 Design a real-world application of transformations and communicate the process used in the design.

Symmetry, axis of symmetry, compass, straightedge



Feedback Reflection



Time Lesson/

Activity MPS Learning Targets

LT1: The student will communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways, e.g. using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.


District Model CABS


Chapter 1 Introducing Geometry 1.1 Building Blocks of Geometry Algebra Review Midpoint 1.2 Poolroom Math 1.3 Widgets

CHAPTER 1 LT2*: Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately. LT8*: Use the two-dimensional coordinate plane to analyze, generalize and represent algebraic properties in mathematical and real-world applications. LT12*: Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions.

CHAPTER 1 2.3* Measure angles using a protractor (to appropriate degrees). 8.3* Use a coordinate plane and the distance and midpoint formulas to determine lengths and midpoints of segments. 12.1* Identify and name points, lines, rays, segments and planes. 12.2* Name and classify angles and line segments. 12.3* Identify and use angle-pair relationships in mathematical and real-world applications. 12.4* Classify and communicate the differences between pairs of lines. 12.6 * Prove statements about segments, lines, angles and angle relationships by using properties, postulates, and theorems.

Point, line, plane, collinear, coplanar, line segment, endpoint, congruent, midpoint, protractor, angle, vertex, counterexample, right angle, acute angle, obtuse angle, complementary angles, supplementary angles, vertical angles, linear pair, dimension



Feedback and Reflection Week 2



Time Lesson/ Activity



District Model CABS


Chapter 1: continued Assessment 1.4 Polygons 1.5 Triangles 1.6 Special Quadrilaterals Assessment 1.7 Circles 1.8 3-D Geometry

LT13*: Classify and describe polygons and 3- dimensional figures. LT14: Use and analyze geometric relationships and properties of polygons and 3-dimensional figures to solve mathematical and real-world applications. LT15: Apply the basic theorems of congruence and similarity to solve mathematical and real- world problems. LT18: Use perimeter, area, volume, and surface area to solve real-world applications.

13.1* Classify polygons by sides and angles. 13.2* Classify triangles by sides and angles. 13.3* Classify quadrilaterals by their parts. 13.5* Describe properties of quadrilaterals. 14.7 Make a two-dimensional representation of a 3-dimensional object.

15.1 Identify congruent and similar polygons. 18.8 Make a model of a 3-dimensional figure from a 2-dimensional drawing.

Polygon, right triangle, acute triangle, isosceles triangle, scalene triangle, equilateral triangle, obtuse triangle, quadrilateral, circle, chord, diameter, radius, tangent, arcs in circles



Feedback Reflection Week 3



Time Lesson/ Activity



District Model CABS


Chapter1: continued 1.9 Pictures Exploration: Geometric Probability Review Assessment Chapter 2 Reasoning in Geometry 2.1 Inductive Reasoning 2.2 Nth Term

Chapter 1: Learning Targets Covered: LT12 – Lines and Angles LT 13 – Classify Polygons LT 14 – Analyze Polygons LT 15 – Congruence and Similarity LT 18 – Geometric Formulas

CHAPTER 2 LT10*. Evaluate information, analyze patterns ,identify relationships, and represent them using algebraic expressions, functions, and equations, e.g., linear, exponential and quadratic, recognizing that a family of functions can model a variety of real-world applications. LT19: Use increased rigor in justifying conclusions to mathematical and real-world applications and in verifying the truth of geometric theorems.

CHAPTER 2

10.7* Identify a pattern in a numerical sequence and complete the pattern to a given term.

19.3 Write conjectures using characteristics, postulates and theorems of geometric figures. 19.4 Use and interpret Venn diagrams. 19.6 Use valid forms of deductive reasoning, including the laws of detachment and syllogism, to prove conjectures.

Venn diagram, probability, justification, inductive logic, deductive logic, line of best fit, conjecture, pattern, strategy, randomness, reasonableness, representations



Reflection and Feedback: Week 4



Time Lesson/




District Model CABS


Chapter 2: continued 2.3 Modeling Assessment 2.4 Deductive Logic 2.5 Angle Relationships 2.6 Angles and Parallel Lines

LT10*. Evaluate information, analyze patterns, identify relationships, and represent them using algebraic expressions, functions, and equations, e.g., linear, exponential and quadratic, recognizing that a family of functions can model a variety of

real- world applications. LT12*: Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric

constructions.

LT14: Use and analyze geometric relationships and properties of polygons and 3-dimensional figures to solve mathematical and real-world applications.

10.7* Identify a pattern in a numerical sequence and complete the pattern to a given term.

12.3* Identify and use angle-pair relationships in mathematical and real-world applications. 12.5* Classify the types of angles formed by two lines and a transversal. 14.6 Solve problems involving real-world applications using the relationships between pairs of angles.

Transversal



Feedback and Reflection: Week 5



Time Lesson/




District Model CABS


Chapter 2: continued Algebra Review: Slope Review Assessment Chapter 3: Using Tools of Geometry 3.1 Duplicating Segments and Angles 3.2 Construct Perpendicular. Bisectors

Learning Targets Covered: Chapter 2 LT 12 – Lines and Angles LT 14 – Analyze Polygons LT 19 – Proofs

CHAPTER 3 LT2*: Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately. LT12*: Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions.

CHAPTER 3 2.2* Measure lengths using a metric/English ruler (to the appropriate degree of tenths of cm and sixteenths of an inch). 2.3* Measure angles using a protractor (to appropriate degrees). 12.7* Perform basic geometric constructions.

Slope, coordinate system, rate of change, bisector, perpendicular



Time Lesson/




District Model CABS


Chapter 3: continued 3.3 Construct Perpendicular. Lines Assessment 3.4 Angle Bisectors 3.5 Parallel Lines Algebra Review Slopes of perpendicular and parallel lines

LT2*: Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately. LT12*: Identify and apply the definitions related to lines and angles in order to use them to solve problem and perform basic geometric constructions. LT16: Apply transformations and their compositions to analyze geometric figures and create designs.

2.3* Measure angles using a protractor (to appropriate degrees). 12.7* Perform basic geometric constructions. 16.1 Plot and label geometric figures using a coordinate plane.

Altitude, angle bisector, parallel



Time Lesson/




District Model CABS


Chapter 3: continued 3.6 Constructions Assessment Exploration: Perspective Drawing 3.7 Concurrency 3.8 Centroid Review Assessment

LT12*: Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions. LT18: Use perimeter, area, volume, and surface area to solve real-world applications. Learning Targets Covered: Chapter 3 LT 12 – Lines and Angles LT 16 – Transformations LT 18 – Geometric Formulas

12.7* Perform basic geometric constructions. 18. 7 Solve real-world application problems using scale drawings, perspective drawings, blueprints, or computer drawings as models of 3- dimensional objects.

Perspective, concurrency, circumcener, incenter, centroid, orthocenter




Time Lesson/




District Model CABS


Chapter 4: Discovering and Proving Triangle Properties 4.1 Triangle Sum 4.2 Isosceles Triangle Algebra Review Solving Equations 4.3 Triangle Inequalities Assessment

CHAPTER 4 LT12*: Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions.

LT14: Use and analyze geometric relationships and properties of polygons and 3-dimensional figures to solve mathematical and real-world applications.

LT18: Use perimeter, area, volume and surface area to solve real-world applications.

CHAPTER 4 12.7* Perform basic geometric constructions. 14.1 Determine if lengths of 14.2 three segments can form a triangle. 14.3 Determine the range in which the length of the third side of a triangle must be given the lengths of two sides. 18.5 Compare perimeters and areas of similar 2-dimensional figures using proportions.

Equation



Time Lesson/




District Model CABS


Chapter 4, continued 4.4 Congruence Shortcuts 4.5 Congruence Shortcuts 4.6 Congruence Shortcuts 4.7 Flow Charts 4.8 Extra Triangle Proofs

LT15: Apply the basic theorems of congruence and similarity to solve mathematical and real-world problems. LT19: Use increased rigor in justifying conclusions to mathematical and real-world applications and in verifying the truth of geometric theorems.

15.2 Justify congruency or similarity of polygons by using formal and informal proofs. 15.3 Prove two triangles are congruent using coordinate methods (e.g. distance and slope formulas). 15.4 Solve real-world applications using the properties of congruency and similarity. 19.7 Select and use various types of reasoning and methods to prove characteristics and properties of algebraic models and geometric figures.

Inequality




Time Lesson/




District Model CABS


Review Assessment Algebra Review: Systems of Equations WKCE Prep

Learning Targets Covered in Chapter 4: LT12 – Lines and Angles LT 14 – Analyze Polygons LT 15 – Congruency and Similarity LT 18 – Geometric Formulas LT 19 - Proofs




Time Lesson/




District Model CABS


WKCE prep WKCE test

NOTE: MPS High Schools choose their own dates within a specific window for the WKCE test. Two weeks are given in this pacing guide for WKCE review. Each school will decide who many days for review they want to take. The remainder of the days can be used to catch-up on the pacing guide if four chapters have NOT been covered and/or to start on Chapter 5.




Time Lesson/




District Model CABS


Chapter 5: Discovering and Proving Polygon Properties 5.1 Polygon Sum Conjecture 5.2 Exterior Angles of Polygons Assessment

CHAPTER 5

LT12. Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions. LT13*: Classify and describe polygons and 3- dimensional figures.

LT14: Use and analyze geometric relationships and properties of polygons and 3-dimensional figures to solve mathematical and real-world applications. 1

CHAPTER 5

12.6 Prove statements about segments, lines, angles and angle relationships by using properties, postulates, and theorems. 13.1* Classify polygons by sides and angles. 14.4 Find the measures of each interior and exterior angle of a regular polygon. 14.5Find the sum of the measures of the interior and exterior angles of a convex polygon. 14.6 Solve problems involving real-world applications using the relationships between pairs of angles..

Exterior angles



Feedback Reflection: Week 13



Time Lesson/ Activity MPS Learning Targets



District Model CABS


Chapter 5, continued 5.3 Kite and Trapezoid Properties 5.4 Properties of Midsegments 5.5 Properties of Parallelograms ASSESSMENT 5.6 Special Parallelograms Algebra Review: Linear equations

LT2. Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately.

LT12*: Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions. LT13*: Classify and describe polygons and 3- dimensional figures. LT19* Use increased rigor in justifying conclusions to mathematical and real-world applications and in verifying the truth of geometric theorems. LT9. Model and solve mathematical and real- world applications that can be represented by linear equations and systems of equations, linear inequalities, and quadratic equations.

2.2* Measure lengths using a metric/English ruler (to the appropriate degree of tenths of cm and sixteenths of an inch). 2.3* Measure angles using a protractor (to appropriate degrees). 12.7* Perform basic geometric constructions. 13.4 Describe properties of a given polygon. 13.5 Describe properties of quadrilaterals. 13.6 Describe properties of other polygons. 19.3 Write conjectures using characteristics, postulates and theorems of geometric figures 9.8 Solve linear equations, inequalities, quadratic equations and systems of linear equations related to real-world applications.

Midsegment, Intercept Perpendicular Parallel






District Model CABS


Chapter 5: continued 5.7 Proving Quadrilateral Properties Review Chapter Assessment

LT19. Use increased rigor in justifying conclusions to mathematical and real-world applications and in verifying the truth of geometric theorems. Learning Targets Covered in Chapter 5: LT12 Lines and Angles LT13 – Classify Polygons LT14 – Analyze Polygons LT19 - Proofs

19.6 Use valid forms of inductive and deductive reasoning to draw conclusions and make conjectures. 19.7 Select and use various types of reasoning and methods to prove characteristics and properties of algebraic models

and geometric figures.







District Model CABS


CHAPTER 6 Discovering and Proving Circle Properties 6.1 Tangent 6.2 Chord Assessment 6.3 Arcs/Angles

CHAPTER 6 LT12. Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions.

LT17: Use properties of circles to solve mathematical and real-world applications.

CHAPTER 6 12.7 Perform basic geometric constructions. 17.2 Determine measures of inscribed and central angles. 17.3 Determine arc lengths and areas of sectors of circles. 17.4 Write and solve equations to find the measures of angles formed by chords, secants, and tangents. 17.5 Calculate lengths of chord, tangent and secant segments.







District Model CABS


Chapter 6, continued 6.4 Proving Circle Conjectures 6.5 Circles and Diameter

LT17: Use properties of circles to solve mathematical and real-world applications. LT19: Use increased rigor in justifying conclusions to mathematical and real-world applications and in verifying the truth of geometric theorems.

17.1 Determine circumference and area of a circle. 17.5 Calculate lengths of chord, tangent and secant segments. 17.7 Solve real-world applications of circles. 19. 7 Use valid forms of inductive and deductive reasoning to draw conclusions and make conjectures. 19.8 Select and use various types of reasoning and methods to prove characteristics and properties of algebraic models and geometric figures.







District Model CABS


Chapter 6, continued 6.6 Around the World Algebra Review: Systems of Equations 6.7 Arc length Review Chapter Assessment

LT17: Use properties of circles to solve mathematical and real-world applications. Learning Targets Covered in Chapter 6: LT12 – Lines and Angles LT17 – Circles LT19 - Proofs

17.1 Determine circumference and area of a circle.

17.3 Determine arc lengths and areas of sectors of circles.






MPS Learning Targets Supported in Semester One:

MA301

District Model CABS

Suggested Vocabulary

Review for Final Exam Final Exam

Semester One – MA 301

LT2. Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately. LT12*: Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions. LT13*: Classify and describe polygons and 3-dimensional figures. LT14: Use and analyze geometric relationships and properties of polygons and 3-dimensional figures to solve mathematical and real-world applications. LT15: Apply the basic theorems of congruence and similarity to solve mathematical and real-world problems. LT17: Use properties of circles to solve mathematical and real-world applications.

Semester One – MA 301

LT16 Apply transformations and their compositions to analyze geometric figures and create designs. LT18 Use perimeter, area, volume and surface area to solve real-world applications. LT19 Use increased rigor in justifying conclusions to mathematical and real-world applications and in verifying the truth of geometric

theorems.



Feedback Reflection: Semester 1



Time Lesson/




District Model CABS


Chapter 7: Transformations and Tesselations 7.1 Transformations/ Symmetry 7.2 Properties of Isometrics 7.3 Compositions of Transformations Assessment

CHAPTER 7 LT16: Apply transformations and their compositions to analyze geometric figures and create designs.

CHAPTER 7 16.2 Perform transformations using triangles in a coordinate plane. 16.3 Identify, given an image and pre-image, the transformation that has taken place as a reflection, rotation, or translation. 16.4 Determine whether a figure has point symmetry, line symmetry or neither. 16.5 Design a real-world application of transformations and communicate the process used in the design.

Central angles, inscribed angles






District Model CABS


Chapter 7, continued 7.4 Tessellations of regular polygons 7.5 Tessellations of non-regular polygons Assessment 7.6 Tessellations with translations 7.7 Tessellations with rotations Exploration: Tessellating with Conway Criterion Review Chapter Assessment

LT16: Apply transformations and their compositions to analyze geometric figures and create designs. Learning Target covered in Chapter 7: LT 16: Transformations

16.6 Identify tessellations in art, construction and nature. 16.7 Design a real-world application of transformations and communicate the process used in the design.

Systems of equations






Benchmarks Embedded in Chapter Lesson

District Model CABS


Chapter 8: Area 8.1 Area of rectangles and parallelograms 8.2 Area of kites, trapezoids and triangles Assessment 8.3 Area Problems Algebra Review: Products, factors, quadratic equations 8.4 Area of regular polygons Exploration: Pick’s formula for area

CHAPTER 8 LT18: Use perimeter, area, volume and surface area to solve real-world applications.

CHAPTER 8 18.1 Determine the perimeter/circumference and area of quadrilaterals, triangles and other polygons, using real-world applications.

Area, kite trapezoid




Time Lesson/ Activity MPS Learning Targets LT1: The student will communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways, e.g. using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.


District Model CABS


Chapter 8, continued 8.5 Area of circles Assessment 8.6 Any Way you Slice it: Area of Circle segments Exploration: Geometric Probability 8.7 Surface Area Chapter 8 Assessment

LT17: Use properties of circles to solve mathematical and real-world applications.

LT18: Use perimeter, area, volume and surface area to solve real-world applications.

Learning Targets covered in Chapter 8: LT 17: Circles LT 18: Formulas

17.1 Determine circumference and area of a circle. 17.3 Determine arc lengths and areas of sectors of circles. 18.1 Determine the perimeter/circumference and area of quadrilaterals, triangles and other polygons, using real-world applications.

Sector of a circle, segment of a circle, annulus







District Model CABS


Chapter 9: Pythagorean Theorem 9.1 The Theorem of Pythagoras 9.2 The Converse of the Pythagorean Theorem Algebra Review: Radical Expressions 9.3 Two Special Right Triangles 9.4 Story Problems

CHAPTER 9 LT11: Explain and use the Pythagorean Theorem and right triangle trigonometry as models to solve a variety of right triangle problems in real-world applications.

CHAPTER 9

11.1 Apply the Pythagorean Theorem to find side lengths of a right triangle in mathematical and real-world applications. 11.2 Determine if a triangle is right, obtuse or acute by using the Pythagorean Theorem.

Surface area, Pythagorean Formula







District Model CABS


Chapter 9, continued Assessment 9.5 Distance in a Coordinate Plane Exploration: Ladder Climb 9.6 Circles and the Pythagorean Theorem Review Chapter 9 Assessment

LT12: Classify and describe polygons and 3-dimensional figures. LT11: Explain and use the Pythagorean Theorem and right triangle trigonometry as models to solve a variety of right triangle problems in real-world applications. LT18: Use appropriate measurements such as perimeter, area, volume, surface area and degrees to solve real-world applications. Learning Targets covered in Chapter 9: LT 11: Pythagorean Theorem LT 12: Classify polygons LT 18: Formulas

12.7 Classify geometric properties by using the coordinate system (e.g. distance formula, slope). 11.1 Apply the Pythagorean Theorem to find side lengths of a right triangle in mathematical and real-world applications. 18.4 Solve real-world application problems for missing lengths in special right triangles.






District Model CABS


Chapter 10: Volume 10.1 Geometry of solids Exploration: Euler’s formula for polyhedra 10.2 Volume of Prisms and cylinders 10.3 Volume of pyramids and cones Assessment Exploration: The Five Platonic Solids

CHAPTER 10

LT18: Use perimeter, area, volume and surface area to solve real-world applications. LT12: Classify and describe polygons and 3- dimensional figures. LT13: Use and analyze geometric relationships and properties of polygons and 3-dimensional figures to solve mathematical and real-world applications.

CHAPTER 10

18.2 Determine the volume and lateral area and total surface area of spheres, prisms, pyramids, cylinders and cones. 18.3 Use volume, lateral area and surface area of 3-dimensional figures to solve real-world application problems. 18.8 Make a model of a 3- dimensional figure from a 2- dimensional drawing.

12.8 Identify 3-dimensional objects (e.g. prisms, pyramids, cones, cylinders and spheres).

13.7 Make a two- dimensional representation of a 3-dimensional object.

Volume, polyhedron, prism, pyramid, cone, sphere, lateral face, surface area, cylinder






District Model CABS


Chapter 10, continued 10.4 Volume 10.5 Displacement and Density Assessment Exploration Orthographic Drawing 10.6 Volume of a sphere 10.7 Surface area of a sphere

LT18: Use perimeter, area, volume and surface area to solve real-world applications. LT19: Use increased rigor in justifying conclusions to mathematical and real-world applications and in verifying the truth of geometric theorems.

18.2 Determine the volume and lateral area and total surface area of spheres, prisms, pyramids, cylinders and cones. 18.3 Use volume, lateral area and surface area of 3-dimensional figures to solve real-world application problems. 18.7 Solve real-world application problems using scale drawings, perspective drawings, blueprints, or computer drawings as models of 3-dimensional objects. 19.1 Identify the converse, inverse and contra positive of a conditional statement.

Displacement, density, orthographic drawing, isometric drawing

Reflection and Feedback Week 27




LT1: The student will communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways, e.g. using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models


District Model CABS


Chapter 10, continued Algebra: Solving for any variable Assessment Exploration Sherlock Holmes and Forms of Reasoning Review Chapter 10 Assessment

LT19: Use increased rigor in justifying conclusions to mathematical and real-world applications and in verifying the truth of geometric theorems. Learning Targets covered in Chapter 10: 12: Classify Polygons 13: Analyze Polygons 18: Circles 19: Proofs

19.2 Translate short verbal arguments into symbolic form

Negation


19.3






District Model CABS


Chapter 11: Similarity Algebra Skills: Proportion 11.1 Similar polygons 11.2 Similar triangles Assessment Exploration: Constructing a Dilation Design

CHAPTER 11 LT13: Use and analyze geometric relationships and properties of polygons and 3-dimensional figures to solve mathematical and real-world applications. LT15: Apply the basic theorems of congruence and similarity to solve mathematical and real- world problems. LT18: Use perimeter, area, volume and surface area to solve real-world applications.

CHAPTER 11 13.3 Find the measures of segments in similar polygons.

15.1 Identify congruent and similar polygons. 15.2 Justify congruency or similarity of polygons by using formal and informal proofs. 15.4 Solve real-world applications using the properties of congruency and similarity. 18.5 Compare perimeters and areas of similar 2-dimensional figures using proportions. 18.6 Describe how a change in one measurement affects other measurements of the object.

Proportion, ratio, similar, dilation, scale






District Model CABS


Chapter 11, continued 11.3 Indirect measurement with similar triangles 11.4 Corresponding parts of similar triangles Assessment 11.5 Proportions with area 11.6 Proportions with volume Exploration: Why Elephants Have Big Ears

LT15: Apply the basic theorems of congruence and similarity to solve mathematical and real- world problems. LT18: Use perimeter, area, volume and surface area to solve real-world applications. .

15.5 Solve real-world applications using the properties of congruency and similarity.

18.5 Compare perimeters and areas of similar 2-dimensional figures using proportions. 18.6 Describe how a change in one measurement affects other measurements of the object.







District Model CABS


Chapter 11, continued 11.7 Proportion and parallel lines Exploration: Two more forms of Valid Reasoning Review Chapter 11 Assessment

LT14: Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions. LT 19: Use reasoning and logic to draw conclusions to mathematical and real-world applications.

Learning Targets covered in Chapter 11: LT13: Classify Polygons LT14: Analyze Polygons LT15: Congruence and Similarity LT18: Formulas LT19: Proofs

14.3 Find the measures of segments in similar polygons.

19.5 Diagram conditional statements to solve logic puzzles. 19.7 Use valid forms of inductive and deductive reasoning to draw conclusions and make conjectures. 19.8 Select and use various types of reasoning and methods to prove characteristics and properties of algebraic models and geometric figures.

Converse, inverse, contrapositive





District Model CABS


Chapter 12: Trigonometry 12.1 Trigonometric ratios 12.2 Solving with right triangles Assessment Exploration: Indirect measurement 12.3 Law of Sines 12.4 Law of Cosines

LT11: Explain and use the Pythagorean Theorem and right triangle trigonometry as models to solve a variety of right triangle problems in real-world applications. .

11.3 Solve right triangle problems using trigonometric ratios. 11.4 Use trigonometric ratios to find the angle of elevation or the angle of depression in real world applications

Trigonometry functions, clinometer







District Model CABS


Chapter 12, continued 12.5 Problem solving with Trigonometry Assessment Exploration: Trigonometric Ratios and the Unit Circle Algebra Skills: Transforming Functions Exploration: Three Types of Proof Review

LT11: Explain and use the Pythagorean Theorem and right triangle trigonometry as models to solve a variety of right triangle problems in real-world applications. LT16: Apply transformations and their compositions to analyze geometric figures and create designs. LT19: Use reasoning and logic to draw conclusions to mathematical and real-world applications Learning Targets covered in Chapter 12:

11.3 Solve right triangle problems using trigonometric ratios. 11.4 Use trigonometric ratios to find the angle of elevation or the angle of depression in real world applications. 16.6 Design a real-world application of transformations and communicate the process used in the design. 19.5 Diagram conditional statements to solve logic puzzles. 19.6 Use valid forms of inductive and deductive reasoning to draw conclusions and make conjectures. 19.7 Select and use various types of reasoning and methods to prove



Chapter 12: Assessment

LT11: Pythagorean Theorem LT16: Transformations LT19: Proofs

characteristics and properties of algebraic models and geometric figures.







District Model CABS


Chapter 13: Geometry as a Mathematical System 13.1 The Premises of Geometry 13.2 Planning a Geometry Proof 13.3 Triangle proofs Assessment 13.4 Quadrilateral proofs

CHAPTER 13 LT14: Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions. LT15: Apply the basic theorems of congruence and similarity to solve mathematical and real- world problems.

LT19: Use reasoning and logic to draw conclusions to mathematical and real-world applications.

CHAPTER 13 14.6 Prove statements about segments, lines, angles and angle relationships by using properties, postulates, and theorems. 15.2 Justify congruency or similarity of polygons by using formal and informal proofs. 15.3 Prove two triangles are congruent using coordinate methods (e.g. distance and slope formulas). 19.4 Select and use various types of reasoning and methods to prove characteristics and properties of algebraic models and geometric figures.

Commutative property, associative property, transitivity, distributive property







District Model CABS


Chapter 13, continued 13.5 Indirect Proof 13.6 Circle Proofs 13.7 Similarity Proofs Algebra Skills: Coordinate Proof Review Chapter 13: Assessment

LT15: Apply the basic theorems of congruence and similarity to solve mathematical and real- world problems.

LT19: Use reasoning and logic to draw conclusions to mathematical and real-world applications.

Learning Targets covered in Chapter 13: LT14: Analyze Polygons LT15: Congruence and Similarity LT19: Proofs

15.3 Prove two triangles are congruent using coordinate methods

(e.g. distance and slope formulas).

19.3 Write conjectures using characteristics, postulates and theorems of geometric figures. 19.5 Select and use various types of reasoning and methods to prove characteristics and properties of algebraic models and geometric figures.




Time Lesson/

Activity MPS Learning Targets: Semester Two MPS Learning Targets Supported in

Semester 2: MA 311 District Model CABS


Final Review: Semester Two Final Assessment: Semester Two

Learning Targets Covered in Semester 2: MA 311 LT1: Communication LT2: Measurement LT11: Right Triangles LT15: Congruence and Similarity LT16: Transformations LT18: Geometric Formulas LT19: Proofs

Learning Targets Supported in Semester 2: MA 311: LT12: Lines and Angles LT13: Classify Polygons LT14: Analyze Polygons

Final Reflection Semester Two MA 311

geometry curriculum pacing guide draft · investigations – please make sure these are a definite...

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