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

Milwaukee Public SchoolsPACING GUIDE for

High School GEOMETRYFoundation Level

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


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 0GeometricArt

0.1 Geometry in Art and Nature

0.2 Line Designs

0.3 Circle Designs

0.4 Op Art

0.6 Islamic Tiles

CHAPTER 0LT2*: 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 02.2* 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



FeedbackReflection



Time Lesson/ Activity

MPS Learning TargetsLT1: 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 1IntroducingGeometry

1.1 Building Blocks of Geometry

Algebra ReviewMidpoint

1.2 Poolroom Math

1.3 Widgets


LT8*: Use the two-dimensional coordinate planeto analyze, generalize and represent algebraic properties in mathematical and real-world applications.

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

CHAPTER 12.3* 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 ReflectionWeek 2






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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.

18.8Make 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



FeedbackReflectionWeek 3






District Model CABS


Chapter1:continued1.9 Pictures

Exploration: GeometricProbabilityReviewAssessment

Chapter 2Reasoning in Geometry

2.1 Inductive Reasoning

2.2 Nth Term

Chapter 1: Learning Targets Covered:LT12 – Lines and AnglesLT 13 – Classify PolygonsLT 14 – Analyze PolygonsLT 15 – Congruence and SimilarityLT 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






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.


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






District Model CABS


Chapter 2: continuedAlgebraReview: SlopeReviewAssessment

Chapter 3:Using Tools ofGeometry

3.1 Duplicating Segments and Angles

3.2 ConstructPerpendicular. Bisectors

Learning Targets Covered: Chapter 2LT 12 – Lines and AnglesLT 14 – Analyze PolygonsLT 19 – Proofs


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 32.2* 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 geometricconstructions.

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



Feedback ReflectionWeek 6






District Model CABS


Chapter 3:continued

3.3 Construct Perpendicular. Lines

Assessment

3.4 Angle Bisectors

3.5 Parallel Lines

AlgebraReview 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.


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





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 3:continued

3.6 Constructions

Assessment

Exploration: Perspective Drawing

3.7 Concurrency

3.8 Centroid

ReviewAssessment

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 3LT 12 – Lines and AnglesLT 16 – TransformationsLT 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







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 InequalitiesAssessment

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


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

CHAPTER 412.7* 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.

18.5Compare perimeters and areas of similar 2-dimensionalfigures using proportions.

Equation







District Model CABS


Chapter 4, continued4.4 Congruence Shortcuts

4.5 Congruence Shortcuts

4.6 Congruence Shortcuts

4.7 Flow Charts

4.8 Extra Triangle Proofs



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).15.4Solve 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 modelsand geometric figures.

Inequality







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ReviewAssessment

AlgebraReview:Systems of Equations

WKCE Prep

Learning Targets Covered in Chapter 4:

LT12 – Lines and AnglesLT 14 – Analyze PolygonsLT 15 – Congruency and SimilarityLT 18 – Geometric FormulasLT 19 - Proofs







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.







District Model CABS


Chapter 5:Discovering and Proving Polygon Properties

5.1 Polygon SumConjecture

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.


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.14.5 Find 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



FeedbackReflection: Week 13



Time Lesson/ Activity MPS Learning TargetsLT1: 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 5, continued

5.3 Kite and Trapezoid Properties

5.4 Properties of Midsegments

5.5 Properties of Parallelograms

ASSESSMENT

5.6 Special Parallelograms

AlgebraReview: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 usingcharacteristics, postulates andtheorems of geometric figures

9.8 Solve linear equations, inequalities, quadratic equations and systems of linearequations related to real-world applications.

Midsegment, InterceptPerpendicularParallel



Feedback and Reflection:Week 14





District Model CABS


Chapter 5: continued

5.7 Proving Quadrilateral Properties

ReviewChapter 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 AnglesLT13 – Classify PolygonsLT14 – Analyze PolygonsLT19 - 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.FeedbackReflectionWeek 15





District Model CABS


CHAPTER 6Discovering 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 measuresof angles formed by chords, secants, and tangents.17.5 Calculate lengths of chord, tangent and secant segments.






District Model CABS



6.4 Proving Circle Conjectures

6.5 Circles and Diameter



17.1 Determine circumference and area of a circle.17.5 Calculate lengths of chord, tangent and secant segments.17.7 Solve real-worldapplications 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



6.6 Around the WorldAlgebra Review: Systems of Equations6.7 Arc length



Learning Targets Covered in Chapter 6:LT12 – Lines and AnglesLT17 – CirclesLT19 - 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

SuggestedVocabulary

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 definitionsrelated 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.



FeedbackReflection:

Semester 1






District Model CABS


Chapter 7:Transformations and Tesselations

7.1 Transformations/ Symmetry

7.2 Properties of Isometrics

7.3 Compositions of Transformations

Assessment

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

CHAPTER 716.2 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

Feedback andReflectionWeek 20





District Model CABS



7.4 Tessellations of regular polygons7.5 Tessellations of non-regular polygonsAssessment7.6 Tessellations with translations7.7 Tessellations with rotations

Exploration: Tessellating with Conway Criterion



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

Feedback and Reflection:Week 21




Benchmarks Embedded in Chapter Lesson

District Model CABS


Chapter 8: Area

8.1 Area of rectangles and parallelograms8.2 Area of kites, trapezoids and triangles

Assessment

8.3 Area ProblemsAlgebra Review: Products, factors, quadratic equations8.4 Area of regular polygonsExploration: Pick’s formula for area

CHAPTER 8


CHAPTER 8

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

Area, kite trapezoid






District Model CABS



8.5 Area of circlesAssessment

8.6 Any Way you Slice it: Area of Circle segmentsExploration: Geometric Probability

8.7 Surface Area

Chapter 8 Assessment



Learning Targets covered in Chapter 8:LT 17: CirclesLT 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 Pythagoras9.2 The Converse of the Pythagorean Theorem

Algebra Review: Radical Expressions

9.3 Two Special Right Triangles9.4 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



Assessment

9.5 Distance in a Coordinate Plane

Exploration: Ladder Climb

9.6 Circles and the Pythagorean Theorem

Review


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 TheoremLT 12: Classify polygonsLT 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


LT12: Classify and describe polygons and 3-dimensional figures.


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



Reflection and Feedback: Week 26





District Model CABS



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



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



Time Lesson/ Activity MPS Learning TargetsLT1: 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



Algebra: Solving for any variable

Assessment

Exploration Sherlock Holmes and Forms of Reasoning

Review



Learning Targets covered in Chapter 10:12: Classify Polygons13: Analyze Polygons18: Circles19: Proofs

19.2 Translate short verbal arguments into symbolic form

Negation

Feedback and Reflection Week 28

19.3



Time Lesson/ Activity MPS Learning Targets LT1: The student will communicate mathematical ideasand 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 11: Similarity

Algebra Skills: Proportion

11.1 Similar polygons

11.2 Similar triangles

Assessment

Exploration: Constructing a Dilation Design

CHAPTER 11




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



Time Lesson/ Activity MPS Learning TargetsLT1: The student will communicate mathematical ideasand 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



11.3 Indirect measurement with similar triangles11.4 Corresponding parts of similar triangles

Assessment

11.5 Proportions with area11.6 Proportions with volume

Exploration: Why Elephants Have Big Ears


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



11.7 Proportion and parallel lines

Exploration: Two more forms of Valid Reasoning

Review


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 PolygonsLT14: Analyze PolygonsLT15: Congruence and SimilarityLT18: FormulasLT19: 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




Time Lesson/ Activity MPS Learning Targets Benchmarks Embedded District Suggested Developed by the Milwaukee Mathematics Partnership with support by the National Science Foundation under Grant No. 0314898.

Draft 10/05/08


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

in Chapter Lessons Model CABS

vocabulary

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.

11.4Use trigonometric ratios to find the angle of elevation or the angle of depression in real world applications

Trigonometry functions, clinometer

Reflection and Feedback:Week 32





District Model CABS



12.5 Problem solving with Trigonometry

Assessment

Exploration: Trigonometric Ratios and the Unit Circle

Algebra Skills: Transforming Functions

Exploration: Three Types of Proof

Review

Chapter 12: Assessment

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.


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

Learning Targets covered in Chapter 12:LT11: Pythagorean TheoremLT16: TransformationsLT19: Proofs

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 characteristics and properties of algebraic models and geometric figures.



Reflection and Feedback: Week 33



Time Lesson/ Activity MPS Learning Targets LT1: The student will communicate mathematical ideasand 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 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.


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



13.5 Indirect Proof

13.6 Circle Proofs

13.7 Similarity Proofs

Algebra Skills: Coordinate Proof

Review

Chapter 13: Assessment


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

Learning Targets covered in Chapter 13:LT14: Analyze PolygonsLT15: Congruence and SimilarityLT19: 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.





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 311LT1: CommunicationLT2: MeasurementLT11: Right TrianglesLT15: Congruence and SimilarityLT16: TransformationsLT18: Geometric FormulasLT19: Proofs

Learning Targets Supported in Semester 2: MA 311:

LT12: Lines and AnglesLT13: Classify PolygonsLT14: Analyze Polygons

Final Reflection Semester Two MA 311


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