curriculum design template content area - pennsville … · 2015-09-11 · curriculum design...

Curriculum Design Template

Content Area: Mathematics

Course Title: Geometry HN Grade Level: 9-10

Tools of Geometry

Reasoning and Proof

Parallel and Perpendicular Lines

Marking Period 1

Congruent Triangles

Relationships within Triangles

Polygons and Quadrilaterals

Marking Period 2

Similarity

Right Triangles and Trigonometry

Transformations

Marking Period 3

Area

Surface Area and Volume

Circles

Marking Period 4

Date Created: June 2014

Board Approved on: August 25, 2014

Geometry Honors 2014

Course Title: Honors Geometry Grade Level: 9 and 10

Overarching Essential Questions

What are the building blocks of geometry?

How is reasoning used in geometry?

What types of angle relationships occur in geometry?

How can you show triangle congruence and how is it used to help solve other problems?

What are the properties of polygons in regards to angles and sides?

What are the properties of circles?

What types of transformations occur in geometry and how do we create them? Which

transformations are rigid.

What are the different properties of right triangles including the Pythagorean Theorem

and trigonometric ratios?

What are similar figures and how to we use them in calculations?

How do we calculate surface areas and volumes of prisms, cylinders, pyramids, cones,

spheres, and combination solids?

Course Description

Honors Geometry is a rigorous look at how geometry evolves from basic building blocks. It

emphasizes logical reasoning, connecting ideas, and applying knowledge of concepts to solve

real-world problems. Students will explore concepts through investigation and learn to verify

conclusions using logical reasoning in the form of a proof. The Geometer’s Sketchpad software

will be vital to student exploration and learning.

Tools of Geometry(Chapter 1)

Essential Questions

What are building blocks of geometry?

How can you represent a 3-D figure with a 2-D drawing?

How can you describe the attributes of a segment or angle?

Key Terms

Point, line, plane, collinear, coplanar, segment, congruent, midpoint, bisect, ray, angle, side,

vertex, reflex measure, protractor, counterexample, skew, right angle, acute angle, obtuse angle,

complementary, supplementary, vertical angles, linear pair, polygon, diagonal, convex, concave,

perimeter, equilateral, equiangular, regular, scalene, isosceles, trapezoid, kite, parallelogram,

rhombus, rectangle, square, circle, radius, chord, diameter, tangent, concentric, minor arc, major

arc, semicircle, central angle, isometric drawing, cylinder, cone, pyramid, prism, sphere,

hemisphere, net

Objectives

Students will be able to:

Make nets and drawings of 3-D figures.

Identify and use basic terms and postulates of geometry.

Find and compare lengths of segments.

Find and compare measures of angles.

Identify special angle pairs and use their relationships to find angle measures.

Find the midpoint of a segment

Find the distance between two points in the coordinate plane.

Find the perimeter or circumference of basic shapes.

Find the area of basic shapes.

Standards associate with objectives

G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line

segment, based on the undefined notions of point, line, distance along a line, and distance

around a circular arc.

G.GPE.6 Find the point on a directed line segment between two given points that partitions

the segment in a given ratio.

G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.

G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and

rectangles, e.g., using the distance formula.★

N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step

problems; choose and interpret units consistently in formulas; choose and interpret the scale

and the origin in graphs and data displays Suggested Lesson Activities

Pre-assessment test

Group work on lessons based on individual pre-assessment results

Essential problems for each section as listed in the book.

Performance tasks (pg 69).

Standardized test prep in each section Enrichment worksheets as needed Activities, games, and puzzles worksheets as needed

Differentiation /Customizing learning (strategies)

Allow students to work in groups.

Allow for multiple representations of solutions.

Use varying degrees of difficulty.

Offer choice on assessments.

Assign Challenge Problems for the more advanced students.

Reasoning and Proof (Chapter 2) Essential Questions

How can you make a conjecture and prove that it is true?

Key Terms

Inductive reasoning, deductive reasoning, converse, counterexample, proof, and theorem

Objectives


Use inductive reasoning to make conjectures

Use deductive reasoning to prove and apply theorems about angles

Write logical arguments using deductive reasoning.

Discover relationships between special pairs of angles

Standards associated with objectives

G.CO.9 Prove theorems about lines and angles.

G.CO.10 Prove theorems about triangles

G.CO.11 Prove theorems about parallelograms

Suggested Lesson Activities



Standardized test prep in each section Mixed review problems in each section Puzzling Patterns Enrichment worksheets Activities, games, and puzzles worksheets Research other patterns on internet using ipads





Offer choice on assessments


Parallel and Perpendicular Lines (Chapter 3)

Essential Questions

How do you prove that two lines are parallel?

What is the sum of the measures of the angles of a triangle?

Key Terms

Alternate interior or exterior angles, corresponding angles, parallel lines, perpendicular lines,

skew lines, transversal, remote interior angles, exterior angle of a polygon, same-side interior

angles.

Objectives


Identify relationships between figures in space

Identify angles formed by two lines and a transversal

Prove theorems about parallel lines.

Use properties of parallel lines to find angle measures

Determine if two lines are parallel.

Relate parallel and perpendicular lines

Use parallel lines to prove a theorem about triangles.

Find measures of angles of a triangle

Construct parallel and perpendicular lines.


G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and

line segment, based on the undefined notions of point, line, distance along a line, and

distance around a circular arc

G.CO.9 Prove theorems about lines and angles.

G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or

structure to satisfy physical constraints or minimize cost; working with typographic grid

systems based on ratios)


G.CO.12 Make formal geometric constructions with a variety of tools and methods

(compass and straightedge, string, reflective devices, paper folding, dynamic geometric

software, etc.)

G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a

circle.




Standardized test prep in each section Mixed review problems in each section Enrichment worksheets Activities, games, and puzzles worksheets Concept Byte: Exploring Spherical Geometry

Internet activities using ipads







Congruent Triangles (Chapter 4)

Essential Questions

How do you identify corresponding parts of congruent triangles?

How do you show that two triangles are congruent?

How can you tell whether a triangle is isosceles or equilateral?

Key Terms

Base, base angles, congruent polygons, corollary, hypotenuse, legs of an isosceles or right

triangle, vertex angle.

Objectives


Recognize congruent figures and their corresponding parts.

Prove two triangles congruent using SSS and SAS Postulates

Prove two triangles congruent using ASA and AAS Postulates

Use triangle congruence and corresponding parts to prove that parts of two triangles are

congruent.

Use and apply properties of isosceles and equilateral triangles.

Prove right triangles are congruent using H-L Theorem.

Identify congruent overlapping triangles

Prove two triangles congruent using other congruent triangles.


G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to

prove relationships in geometric figures.



software, etc.).

G.CO.10 Prove theorems about triangles.


circle.


Getting Ready (pg 215)



Standardized test prep in each section Mixed review problems in each section Puzzling Patterns Enrichment worksheets Activities, games, and puzzles worksheets Internet research and activity on Sierpinski’s Triangle using ipads







Relationships Within Triangles (Chapter 5)

Essential Questions

How do we use coordinate geometry to find relationships within triangles? How do you solve problems that involve measurements of triangles?

Key Terms

Altitude, centroid, circumcenter, concurrent, circumscribed, equidistant, incenter, inscribed,

median, midsegment, orthocenter, point of concurrency

Objectives

Students will be able to

Use properties of midsegments to solve problems.

Use properties of perpendicular bisectors, and angle bisectors.

Identify properties of perpendicular bisectors and angle bisectors.

Identify properties of medians and altitudes of a triangle.

Use inequalities involving angles and sides of a triangle.

Apply inequalities in two triangles.

.





software, etc.)



G.CO.9 Prove theorems about lines and angles

G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties

of angles for a quadrilateral inscribed in a circle.





Standardized test prep in each section Mixed review problems in each section Enrichment worksheets Activities, games, and puzzles worksheets Internet activities on powergeometry.com using ipads. Concept Byte: Paper Folding Bisectors (pg 300)

Concept Byte: Special Segments in Triangles (pg 308) – requires geometry software.




Use varying degrees of difficulty. Offer choice on assessments. Assign Challenge Problems for the more advanced students.

Polygons and Quadrilaterals (Chapter 6)

Essential Questions

How can you find the sum of the measures of the angles of a polygon?

How can you classify quadrilaterals?

How can you use coordinate geometry to prove general relationships?

Key Terms

Base/base angles/leg of a trapezoid, consecutive angles, equiangular/equilateral polygon,

isosceles trapezoid, kite, opposite angles/sides, parallelogram, rectangle, regular polygon,

rhombus, square, trapezoid.

Objectives


Find the sum of the measures of the interior or exterior angles of a polygon.

Use relationships among sides and angles of a parallelogram.

Use relationships among diagonals of a parallelogram.

Determine whether a quadrilateral is a parallelogram.

Define and classify special types of parallelograms.

Use properties of diagonals of rhombuses and rectangles.

Determine whether a parallelogram is a rhombus or rectangle.

Verify and use properties of trapezoids and kites.

Classify polygons in the coordinate plane.

Prove theorems using figures in the coordinate plane.

Standards associate with objectives.



G.CO.11 Prove theorems about parallelograms


rectangles, e.g., using the distance formula.

G.GPE.4 Use coordinates to prove simple geometric theorems algebraically





Standardized test prep in each section Mixed review problems in each section Enrichment worksheets

Activities, games, and puzzles worksheets Internet activities on powergeometry.com using ipads. Concept Byte: Exterior Angles of a Polygon (pg 352) – requires geometry software. Concept Byte: Quadrilaterals in Quadrilaterals (pg 413) – requires geometry

software.







Similarity (Chapter 7) Essential Questions

How do you use proportions to find side lengths in similar polygons?

How do you show two triangles are similar?

How do you identify corresponding parts of similar triangles?

Key Terms

Extremes, means, geometric mean, indirect measurement, proportion, ratio, scale factor, scale

drawing, similar.

Objectives


Write and solve proportions

Identify and apply similar polygons.

Use the AA, SAS, and SSS Similarity Postulates/Theorems

Use similarity to find indirect measurements.

Find and use relationships in similar triangles.

Use the Side-Splitter Theorem and the Triangle-Angle-Bisector Theorem.



prove relationships in geometric figures

G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve

geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line

that passes through a given point).

G.SRT.4 Prove theorems about triangles



software, etc.)





Standardized test prep in each section Mixed review problems in each section Enrichment worksheets Activities, games, and puzzles worksheets Internet activities on powergeometry.com using ipads. Concept Byte: Fractals (pg 448)

Concept Byte: Exploring Proportions in Triangles (pg 470) – requires geometry software.







Right Triangles and Trigonometry (Chapter 8) Essential Questions

How do you find a side length or angle measure in a right triangle?

How do trigonometric ratios relate to similar right triangles?

Key Terms

Angle of depression/elevation, cosine, sine, tangent, Pythagorean triple

Objectives


Use the Pythagorean Theorem and its converse.

Use properties of 45-45-90 and 30-60-90 triangles.

Use sine, cosine, and tangent ratios to solve problems.

Use angles of elevation/depression to solve problems.


G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in

applied problems

G.SRT.4 Prove theorems about triangles

G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g.,

modeling a tree trunk or a human torso as a cylinder)

G.SRT.7 Explain and use the relationship between the sine and cosine of complementary

angles





Standardized test prep in each section Mixed review problems in each section Enrichment worksheets Activities, games, and puzzles worksheets Internet activities on powergeometry.com using ipads. Concept Byte: Measuring From Afar (pg 515)

Concept Byte: Exploring Trigonometric Ratios (pg 506) – requires geometry software. .





Offer choice in assessments.


Suggested Formative Assessments:

Homework, practice problems, quizzes

Suggested Summative Assessments:

Tests, Exams, Projects

Transformations (Chapter 9)

Essential Questions

How can you change a figures position without changing its size and shape?

How can you change a figures size without changing its shape?

How can you represent a transformation in the coordinate plane?

How do you recognize congruence and similarity in figures?

Key Terms

Congruence transformation, dilation, image, isometry, preimage, reflection, rigid motion,

rotation, similarity transformation, translation.

Objectives


Identify rigid motions

Identify translation images of figures.

Find reflection images of figures.

Draw and identify rotation images of figures.

Find the composition of isometries.

Identify congruence transformations.

Draw dilation images of figures


G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry

software; describe transformations as functions that take points in the plane as inputs and

give other points as outputs. Compare transformations that preserve distance and angle to

those that do not (e.g., translation versus horizontal stretch).

G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles,

circles, perpendicular lines, parallel lines, and line segments.

G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the

effect of a given rigid motion on a given figure; given two figures, use the definition of

congruence in terms of rigid motions to decide if they are congruent

G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the

transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a

sequence of transformations that will carry a given figure onto another

G.CO.7 Use the definition of congruence in terms of rigid motions to show that two

triangles are congruent if and only if corresponding pairs of sides and corresponding pairs

of angles are congruent

G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from

the definition of congruence in terms of rigid motions.

G.SRT.1a Verify experimentally the properties of dilations given by a center and a scale

factor:

a. A dilation takes a line not passing through the center of the dilation to a parallel line, and

leaves a line passing through the center unchanged.

b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G.SRT.2 Given two figures, use the definition of similarity in terms of similarity

transformations to decide if they are similar; explain using similarity transformations the

meaning of similarity for triangles as the equality of all corresponding pairs of angles and

the proportionality of all corresponding pairs of sides.





Standardized test prep in each section Mixed review problems in each section Enrichment worksheets Activities, games, and puzzles worksheets Internet activities on powergeometry.com using ipads. Concept Byte: Tracing Paper Transformations (pg 544)

Concept Byte: Paper Folding Reflections (pg 553) Concept Byte: Exploring Dilations (pg 586)







Area (Chapter 10)

Essential Questions

How do you find the area of a polygon or find the circumference and area of a circle?

How do perimeters and areas of similar polygons compare?

Key Terms

Apothem, arc length, central angle, concentric circles, diameter, minor/major arc, radius, sector.

Objectives


Find the area of parallelograms and triangles.

Find the area of trapezoids, rhombuses, and kites.

Find the area of regular polygons.

Find perimeters and areas of similar figures.

Find areas of regular polygons and triangles using trigonometry.

Find measures of central angles and arcs

Find the circumference and arc length of circles.

Find areas of circles, sectors, and segments of circles.


G.MG.1 Use geometric shapes, their measures, and their properties to describe objects

(e.g., modeling a tree trunk or a human torso as a cylinder).★


rectangles, e.g., using the distance formula


circle.

G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve

problems

G.SRT.9 Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an

auxiliary line from a vertex perpendicular to the opposite side.

G.C.1 Prove that all circles are similar.

G.C.2 Identify and describe relationships among inscribed angles, radii, and chords.

G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is

proportional to the radius, and define the radian measure of the angle as the constant of

proportionality; derive the formula for the area of a sector





Standardized test prep in each section Mixed review problems in each section Enrichment worksheets Activities, games, and puzzles worksheets Internet activities on powergeometry.com using ipads. Concept Byte: Transforming to Find Area (pg 614)

Concept Byte: Inscribed and Circumscribed Figures (pg 667)







Surface Area and Volume (Chapter 11)

Essential Questions

How do you find the surface area and volume of a solid?

How do surface areas and volumes of similar solids compare?

Key Terms

Cone, cross-section, cylinder, prism, pyramid, sphere, lateral area, surface area, slant height,

height, volume.

Objectives


Find the surface area of a prism and cylinder

Find the surface area of a pyramid and cone

Find the volume of a prism and cylinder

Find the volume of a pyramid or cone

Find the surface area and volume of a sphere

Compare and find the surface areas and volumes of similar solids

Standards associated with objectives

G.MG.1 Use geometric shapes, their measures, and their properties to describe objects

(e.g., modeling a tree trunk or a human torso as a cylinder).

G.GMD.1 Give an informal argument for the formulas for the circumference of a circle,

area of a circle, volume of a cylinder, pyramid, and cone.

G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve

problems.

G.GMD.2 Give an informal argument using Cavalier’s principle for the formulas for the

volume of a sphere and other solid figures.

G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g.,

persons per square mile, BTUs per cubic foot)





Standardized test prep in each section Mixed review problems in each section Enrichment worksheets Activities, games, and puzzles worksheets Internet activities on powergeometry.com using ipads. Concept Byte: Finding Volume (pg 725)

Concept Byte: Exploring Similar Solids (pg 741) - Ipad







Circles (Chapter 12) Essential Questions

How can you prove relationships between angles and arcs in a circle?

When lines intersect a circle or within a circle, how do you find the measures of resulting

angles, arcs, and segments?

How do you find the equation of a circle in the coordinate plane?

Key Terms

Chord, inscribed angle, intercepted arc, secant, tangent.

Objectives


Use properties of a tangent to a circle.

Use congruent chords, arcs, and central angles.

Use perpendicular bisectors of chords.

Find the measure of an inscribed angle.

Find the measure of angle formed by a tangent and a chord

Find the measures of angles formed by chords, secants, and tangents

Find the lengths of segments associated with circles.

Write the equation of a circle of a circle.

Find the center and radius of a circle.


G.C.2 Identify and describe relationships among inscribed angles, radii, and chords

G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove

properties of angles for a quadrilateral inscribed in a circle

G.C.4 Construct a tangent line from a point outside a given circle to the circle

G.GPE.1 Derive the equation of a circle of given center and radius using the

Pythagorean Theorem; complete the square to find the center and radius of a circle given

by an equation.





Standardized test prep in each section Mixed review problems in each section Enrichment worksheets Activities, games, and puzzles worksheets Internet activities on powergeometry.com using ipads. Concept Byte: Paper Folding With Circles (pg 770)

Concept Byte: Exploring Chords and Secants (pg 789) – requires geometry software.







curriculum design template content area - pennsville … · 2015-09-11 · curriculum design...

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