Assessments/ Resources
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics
Date:
Standard/ Benchmarks
Essential Questions
Content / Unit of Study
Skills
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Standa rd/ Bench marks
Sept. G.CO.1 G.CO.9 G.GPE.4 G.GMD.4 G.CO.10 G.CO.11
Sept. into early Oct.
Essential Questions
1. What is Geometry? 2. What two things other than words are important to understand when reading a geometry text. What determines if a network is traversable?
If a conditional is true, must the converse be true? What is a good definition?
G
Content / Unit of Study
Skills
Chapter One: Points as Dots, Locations, ordered pairs & nodes. Drawing in perspective, The need for undefined terms Postulates for Euclidean Geometry Betweenness and Distance
1.01 Reason abstractly to distinguish between 4 concepts of a point & recognize differences in the geometries they lead to 1.02 Construct e network diagram of a given situation & determine if it is traversable 1.03 Apply the Betweenness Property to overlapping distance problems 1.04 Graph a line given: 2 pts, a point & the slope and of the form y=mx+b
Chapter Two: (Omit automatic drawer) The need for Definitions Conditional statements and Converses Union and intersections of figures Polygons The triangle inequality Conjectures
Assessments/ Resources
Notebook/ Ch. Test Quiz 1.1-1.3, 1.4-1.7 Board work, Home Work Projects related to Chapter One concepts
1.05 Drawing a box in perspective Write conditional statements and their converses Recognize whether conclusions drawn from a known conditional express regularity in reasoning Form the union and intersections of figures Form an accurate hierarchy diagram given a list of interrelated geometric figures Apply the triangle inequality postulate to determine the possible lengths of the sides of a triangle Determine if a polygon is convex
Use a protractor to estimate the
Quiz 2.1-2.3, 2.4-2.6 Ch. Test Home Work, Board Work Projects related to Chapter Two concepts (Latitude & Longitude, computer graphics, Perspective drawing etc.)
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Standa rd/ Bench marks
Essential Questions
Oct. What is the difference between arc length and arc measure? If two lines do not intersect must they be parallel?
Content / Unit of Study
Chapter Three Angles and Their Measures Arcs and Rotations Properties of Angles Algebra Properties Used in Geometry One-Step Proof Arguments Parallel Lines Perpendicular Lines Drawing Parallel and Perpendicular Lines
Skills
measure of an angle Solve algebraic examples applied to angle bisectors, angle addition property, complementary & supplementary angles, linear pairs, vertical angles Recognize valid /invalid characteristics and relationships implied in a given figure Rotate a given figure about a given point by a given magnitude Find measures of various arcs based on given information Understand the logic and support of a given proof Given two parallel lines cut by a transversal, identify related angles and compute their measures based on given information Calculate slopes of lines and determine when they are parallel or perpendicular to a given line by their equations. Attend to precision in using a ruler, protractor and compass to rotate a figure about a point
Assessments/ Resources
Quiz 3.1-3.3; 3.4-3.6 Ch. Test Projects related to chapter three concepts Home Work, Board Work
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Standa rd/ Bench marks
G.CO.2 G.CO.4 G.CO.5 G.CO.6 Nov
Essential Questions
How many points are needed to determine the reflection of an angle? How many bisectors does a segment have? An angle? How many perpendicular bisectors? When is a reflection a translation? a rotation?
Content / Unit of Study
Chapter Four Reflecting points and figures, transformation, orientation of a figure , composition, translation, rotation, vector, isometry, glide reflection, congruent figures, directly and oppositely congruent, concurrent lines. Miniature gold and billiards Composing reflections over parallel lines and intersecting lines
Skills
Reflect a given point or figure over a given line and in the coordinate plane and its axis Given a point & its reflection image, locate the line of reflection, when in the coordinate plane find its equation Identify the orientation of a figure Given a geometric figure and its position relative to a reflection line, identify the points that must be reflected to accurately determine the image Apply reflection to perform carom shots when playing billiard or miniature golf Given a figure and parallel lines accurately form the composite Identify the magnitude & direction of a translation Given a figure and its rotation image and the center of rotation , locate 2 intersecting reflection lines for the composition Given a figure and a vector, perform the translation of the figure in the open plane and the coordinate plane
Assessments/ Resources
Quiz 4.1 – 4.3, 4.4 – 4.7 Ch test Projects related to chapter 4 concept such as using reflections when playing billiard or miniature golf Compass, ruler, protractor Home work, board work
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Standa rd/ Bench marks
Essential Questions
Content / Unit of Study
Skills
Assessments/ Resources
Given a figure and its glide reflection image, locate the primary reflecting line and translation vector for the glide reflection Look for and make use of structure to identify which isometry maps a given figure onto its image using properties unique to each isometry
Dec. Does Euclidean geometry apply on the surface of the Earth? Why is it possible to draw a circle through any three points?
Chapter Five Corresponding parts of congruent figure (CPCF Thm.) Defining uniquely determined, auxiliary figures, circumcenter of a triangle One-step congruence proofs Proofs using transitivity and reflections Triangle sum of angles measure & polygons sum of he angle measure Proofs using reflections Theorems of angles formed by parallel lines and a trnsversal
Identify corresponding parts in given congruent figures Developing a paragraph proof by making viable arguments and critique the reasoning of others. Writing a one-step two column proof Locate the center of a given circle using the perpendicular bisector theorem Identify valid auxiliary figures when uniquely determined Apply the triangle angle sum theorem polygon sum theorem to compute the interior angles of polygons with given no. of sides
Quiz 5.1 – 5.4 Ch test Project on Non-Euclidean geometry
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Standa rd/ Bench marks
Essential Questions
Content / Unit of Study
Chapter 6 Dec & early Jan.
G.CO.3
Why do many companies choose logos that are reflection symmetric? Which special parallelograms have reflection symmetry? Rotation symmetry? Does an angle have a line of symmetry? What is it? Is an equilateral triangle isosceles? How many lines of symmetry do each have?
Definitions: Reflection Symmetric Figure & Rotation Symmetric Figure. Symmetry line of an isosceles triangle, Median & centroid of any triangle, Parallelogram, rhombus, trapezoid rectangle, kite, square. Center of rotation, regular polygons, equiangular figures, chord of a circle Theorems: Flip-Flop, Segment Symmetry, Angle Symmetry, side switching, Circle Symmetry, Isosceles Triangle Coincident lines, Isosceles Triangle Base Angles, Equilateral Triangle and ita Corollaries, Quadrilateral Hierarchy, Kite Symmetry, Kite diagonal, Rhombus Diagonal, Isosceles Trapezoid Symmetry, Rectangle Symmetry. Multiple Reflection-Symmetry Lines & Rotational Symmetry, Center of a Regular Polygon & Regular Polygon Symmetry Theorems Chapter Seven
Skills
Identify reflection-symmetric figures & the number of symmetry lines Accurately locate the symmetry line for reflection-symmetric figures Identify rotation-symmetric figures visually & by their characteristics Identify parts of an isosceles triangle; given one angle measure in an isosceles triangle, find all other possible angle measures Use algebra to solve problems about angles of an isosceles triangle Develop proofs using the theorems Compute values of angles and side lengths in kite, rhombuses, trapezoids, rectangles and squares using related theorems to calculate accurately and efficiently. Identify types of quadrilaterals by given characteristics Recognize relationships among quadrilaterals consistent with the Quadrilateral Hierarchy
Assessments/ Resources
Quiz 6.1-6.3 ; 6.4 – 6.7 Home Work, Board Work Chapter Test Related chapter projects
Home Work, Bd Work
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Standa rd/ Bench marks
Essential Questions
Content / Unit of Study
Jan If the angles of 2 Triangle are congruent must the triangles be congruent? Which conditions must be true for triangles to be congruent? How many regular polygons can tessellate a plane? What is true about the measure of the exterior angle of a regular polygon as the # of sides increases? About the measure of the interior angle?
Definitions: Hypotenuse and legs of a right triangle, distance between 2 parallel lines, ext angle of a polygon Theorems: no choice for3rd angle of triangles, SSS, SAS ASA, AAS, isosceles triangle base angle converse, HL, SsA Thm Properties of Parallelograms, distance between Parallel lines Thm, Sufficient conditions for a parallelogram Thm, Ext angle for a triangle, Ext angle inequality and unequal sides Thm.
Skills
Thm Recognize and apply theorems to determine triangle congruence Write proofs making conjectures and build a logical progression using the triangle congruence theorems for various situations and apply the Properties of parallelograms & sufficient conditions for a parallelogram Compute numerical values for angles & lengths in a //gram based on given information Use numerical relationships to determine if a given quadrilateral is a parallelogram Use exterior angle thms to find various angle measures in triangles attending to precision. Use unequal sides or the unequal angles Thm to order the side lengths or angle measures of a triangle or 2 adjacent triangles.
Assessments/ Resources
Quiz 7.1 – 7.4 Chapter test Related projects to material covered
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Jan.
Standa rd/ Bench marks
G.SRT.5 G.SRT.4 G.CO.7 G.CO.8 G.CO.10 G.CO.11 G.SRT.5 G.CPE.4
Essential Questions
Content / Unit of Study
Skills
What conditions must be true for triangles to be congruent?
Chapter Seven
Write proofs using the triangle congruence theorems applying the given information and the corresponding parts Write proofs applying the properties of parallelograms and sufficient conditions for a parallelogram by analyzing situations by breaking them down into cases. Determine the angle measure and segment lengths in a parallelogram based on given information Use numerical relationship to determine if a given quadrilateral is a parallelogram Use exterior angle thm to find angle measures in triangles Use the unequal sides and unequal angles thm to order the side lengths or angle measures of a triangle
Is it possible to find the angles of an isosceles triangle if one of measures is known? How is the distance between two parallel lines measured? How many regular polygons can tessellate a plane? How is the point of rotation symmetry found in a parallelogram?
Drawing triangle, Tessellations Definitions: Hypotenuse & legs of a right triangle, exterior angle of a polygon Theorems: Third angle for triangles, SSS, SAS, ASA, AAS, Isosceles triangle base angles converse, HL, SsA, Properties of parallelograms, Distance between parallel lines, Parallelogram symmetry, Sufficient conditions for a parallelogram, Exterior angle inequality, Unequal sides & Unequal angles Thm
Assessments/ Resources
Homework Quiz 7.1 – 7.3, 7.4 – 7.6 Chapter test Related chapter projects
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Jan. into Feb.
Standa rd/ Bench marks
G.SRT.4 G.SRT.5 N.Q.1 G.CPE.7 G.CO.13 G.MG.1 G.CO.1 G.CO.5
Essential Questions
Content / Unit of Study
If 2 polygons have the same perimeter must they be congruent? Must they have the same area?
Chapter Eight
If the areas are = must the polygons be congruent? If the circumference of a circle is known can the area be determined?
Definitions: Perimeter and area of a polygon, Pythagorean triples, circumference and arc length of a circle, area and sectors of a circles Area Postulate Theorems: Pythagorean and its Converse Formulas for perimeters and areas of: Equilateral triangle, trapezoid, triangle, parallelogram, circle
Skills
Calculate the perimeter of polygons Calculate areas of rectangles and of irregular regions that can be subdivided into rectangles being careful in using the right unit of measure. Strategically use estimation to find the area of irregular regions using gridding method Calculate various areas of regions including triangles, parallelograms, trapezoids & rhombuses Apply the Pythagorean Theorem to find missing side lengths Use the converse of the Pythagorean Thm to determine if a triangle is a right triangle Use the circle area formula to compute exact & approximate values for a circle’s area & sector area
Assessments/ Resources
Homework, Board work Chap. test, Quiz 8.1 – 8.3, 8.4 – 8.7 Related chapter projects
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Feb.
Standa rd/ Bench marks
G.CO.1 G.CO.12 G.MG.3
Essential Questions
How is the best route between two cities traveling by plane determined? If two lines do not intersect must they be parallel? Two planes? What must be true in order for a pyramid to be symmetrical? What plane figure is determined by the intersection of a plane and a cone?
Content / Unit of Study
Skills
Chapter Nine
Extend the 1 & 2 dimensional concept to 3 dimensional Recognize perpendicular and parallel planes in everyday life Distance between two parallel planes Develop a formula to find the diagonal of a rectangular solid Calculate accurately the height and slant height of a pyramid and a cone Sketch a three dimensional figure Recognize various plane sections of different solids Identify the major conic sections based on description of how they are formed.
Points, Lines, and Plane in Space Definitions: Parallel planes, line perpendicular to a plane, distance between parallel planes, distance from a point to a plane, dihedral angles, rectangular and cylindrical solids, right cylinder and prism, oblique cylinder and prism, regular prism, conic solids, cone pyramid, right pyramid, tight cone, axis of a cone, sphere, great circle, plane section, conic sections( parabola, ellipse, hyperbola) Height and slant height of solids Extension of the point line-plane postulate Line-plane perpendicular theorem. Four-color theorem
Assessments/ Resources
Homework, Board work Chapter test, Quiz 9.1 – 9.4, 9.5-9.7
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Early March
Standa rd/ Bench marks
N.Q.1 G.CMD.3 G.MG.1 G.GMD.2
Essential Questions
If the sides of rectangular solid are doubled what happens to its surface area? To its volume? If a jar is twice as tall but its diameter is half of another, which one will hold more? If the radius of s sphere is doubled what happens to the surface area? To its volume? If 2 cones are formed from the same circle with different central angles, which one is the tallest? Which one has the larger lateral area?
Content / Unit of Study
Skills
Chapter Ten
Calculate accurately lateral areas and surface areas of cylinders , prisms, pyramids and cones from appropriate lengths and apply the formulas to real situations Calculate volumes of rectangular prisms and cylinders from appropriate lengths and apply the formulas to real situations Determine what happens to the surface area and volume of a figure when its dimensions are multiplied by some number by reasoning abstractly and quantitatively Apply Cavalieri’s Principle under some given conditions Develop formulas for specific figures from more general formulas Calculate volumes of pyramids, cones and spheres from appropriate lengths and apply the respective formulas to real situations Calculate the surface area of a sphere and determine what happens to the surface area when its dimensions are multiplied by some number
Surface Areas and Volumes Formulas: Right Prism-Cylinder Lateral Area, Prism-Cylinder Surface Area, Pyramid-Cone Surface Area, Regular Pyramid-right Cone Lateral Area, Volume of a Cube, PrismCylinder Volume, Pyramid-Cone Volume, Sphere Volume, Sphere Surface Area, Volume of a Cube Definition: Cube root of a number Volume Postulates: Uniqueness, Congruence, Additive property, Cavalieri’s Principle
Assessments/ Resources
Quiz 10.1-10.3, 10.4-10.7 Chapter test, HW, Bd Wk
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
Second half of March
Standa rd/ Bench marks
G.CO.9 G.CO.10 C.CO.11 G.GPE.4 N.Q.1 G.CMD.3 G.MG.1
Essential Questions
If a conditional is true, is the converse true? The contrapositive? How can the distance formula be used to generate the equation of a circle?
Content / Unit of Study
Skills
Chapter Eleven
Follow the law of detachment, transitivity and contrapositive to make conclusions and apply the laws to real situations Formulate the converse, inverse or contrapositive of a conditional Follow the law of ruling out possibilities to make conclusions Follow the law of indirect reasoning to write indirect proofs constructing viable arguments Use coordinate geometry to deduce properties of figures and prove theorems Determine the length of a segment in the coordinate plane Derive and apply the Distance Formula Graph and write an equation for a circle given its center and radius Use the distance formula to find the equation of a circle when the coordinates of its center and a point on the circle are known Determine the coordinates of the midpoint of a segment in the coordinate plane Apply the midpoint connector theorem
Laws: Detachment, Transitivity, Contrapositive, Ruling out Possibilities, Indirect Reasoning Definitions: Negations, Inverses and Contrapositives of Conditionals , Contradictory Statements Formulas: Distance on the coordinate plane, Number Line Midpoint, Coordinate Plane Midpoint, Box Diagonal, Three Dimension Midpoint Equations; Circle & Sphere Theorem: Midpoint Connector
Assessments/ Resources
Quiz 11.1 – 11.3; 11.4- 11.6 Chapter test Transparencies on overhead
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
April
Standa rd/ Bench marks
G.SRT.5 G.CO.2
Essential Questions
Content / Unit of Study
Skills
How many points must be projected to perform a sizechange?
Chapter Twelve
Analyze size transformations on figures in the coordinate plane, draw size-transformation of images and apply properties of size transformation, use proportions to find missing parts in similar figures, use the fundamental Theorem of similarity to find lengths, perimeters, areas, and volumes in similar figures using definitions to formulate explanations
Are similar figures congruent? Are congruent figures similar?
Similarity Definitions: Size change, similar figures, similarity transformation, ratio of similitude Theorems: properties of size change,, size-change distance, size-change preservation, figure size-change, similar figures, fundamental thm of similarity
Assessments/ Resources
Quiz 12.1 -12.6 Home Work, Bd wk
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
May
Standa rd/ Bench marks N.Q.1 G.SRT.9 G.MG.1 G.SRT.10 G.SRT.6
Essential Questions
Can we find the area of a triangle if the altitude is not known? Must both legs of a right triangle be known to find the hypotenuse? Can we find the area of an equilateral triangle if we know the measure of one side? Why is the angle of depression equal the angle of elevation?
Content / Unit of Study
Chapter Thirteen Similar Triangles and Trigonometry Definitions: geometric mean, the tangent, cosine and sine ratios, Theorems: AA similarity, SAS similarity, side-splitting, sidesplitting converse, Geometric mean, right-triangle altitude, Isosceles right triangle, 30-60-90 triangle, SAS triangle area formula
Skills
.Determine whether or not triangles are similar using the AA and SAS Similarity Theorem, and apply it to find lengths and distances in real situations, find the lengths of the size of a right triangle and special right triangles using the Right-Triangle Altitude theorem or the trigonometric ratios, use trigonometry to find the area of a triangle, find the exact sine, cosine and tangent of special angles using the calculator to compute the trigonometric ratios
Assessments/ Resources
Quiz 13.1 – 13.3, 13.4 – 13.6 Chapter test,
In-class activity : ratios of legs in righ triangles. Ruler and protractor Ov. Proj.
Subject Area Pacing Guide Mathematics Department
Geometry Honors
CHAPTER REFERENCES ARE FROM: UCSMP – GEOMETRY Integrated Mathematics Date:
May into June
Standa rd/ Bench marks
G.C.2 G.C.3 G.C.4 G.C.5
Essential Questions
Content / Unit of Study
Chapter Fourteen What is the sum of the opposite angles of an inscribed quadrilateral? How can we find the length of a chord if we know the radius of a circle?
Work With Circles Definitions: Intercepted Arc, measure of the intercepted arc, inscribed angle, secant, tangent to a circle Theorems: Arc-Chord congruence, Chord-Center, Inscribed Angle Thm, Angle-Chord, Angle-Secant, RadiusTangent, Tangent-chord, TangentSecant, Secant Length, Tangent Square, Isoperimetric theorem *opt Isoperimetric Thm (three dimensional version)
Skills
Calculate accurately lengths of chords and arcs, make deductions from properties of radii and chords, and know sufficient conditions for radii to be perpendicular to them, calculate measure of inscribed angles and angles formed by intersecting chords or secants, locate the center of a circle given sufficient information, make deductions from properties of radii and tangents and know sufficient conditions for radii to be perpendicular to them, determine the maximum distance that can be seen from a particular elevation, calculate the distance to the horizon from an elevation, apply the secant length and tangent square theorems and to come up with short cuts to compute accurately their measures.
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Assessments/ Resources
Quiz 14.1 – 14.3, 14.4 – 14.7 Chapter test Protractor, compass, ruler Home Work, Board Work Overhead Projector.
