Download 2015 Geometry Curriculum Map

Updated Spring 2015
Curriculum Map Geometry
Month:
Unit:
Core Standards:
Text Book Sections:
August
Chapter 1: Tools of Geometry
G.CO.1, G.C0.12
1-2: Points, Lines, and Planes
1-3: Measuring Segments
1-4: Measuring Angles
1-5: Exploring Angle Pairs
1-6: Basic Constructions
1-7: Midpoint and Distance in the Coordinate Plane
1-8: Perimeter, Circumference, and Area
Skills/Understanding/
Student
Demonstrators:
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.12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line
parallel to a given line through a point not on the line.
Literacy Standards: Tier Three Word and Content Learning.
Critical Vocabulary:
Instructional
Strategies:
Learning Targets:
Assessments:
Angle bisector, congruent segments, construction, linear pair, perpendicular bisector, postulate, segment bisector, supplementary angles, vertical angles
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Calculator Use, and Constructions using tools(compass, ruler,
protractor)
I can:
1.) Describe the undefined terms of Geometry.
2.) Find multiple names for geometric objects.
3.) Use the undefined terms to define other terms.
4.) Identify planes, lines, segments, and rays on a diagram.
5.) Apply Postulates 1-1, 1-2, 1-3, 1-4, 1-5, and 1-6.
6.) Compare the lengths of segments.
7.) Name, measure, and classify angles.
8.) Apply the Angle Addition Postulate.
9.) Apply the Linear Pair Postulate.
10.) Solve problems involving angle bisectors.
11.)Make basic constructions using a straightedge and ruler.
12.)Find the midpoint of a segment.
13.)Find the distance between two points in the coordinate plane.
14.)Find the perimeter and area of basic shapes.
Bell work, Daily Classwork, Homework, Quizzes, Tests
Updated Spring 2015
Month:
Unit:
Core Standards:
TextBook Sections:
Skills and
Student
Demonstrators:
September
Chapter 2: Reasoning &Proof
Chapter 3: Parallel and Perpendicular Lines
G.CO.1 ,G.CO.9, G.C0.10, G.CO.11, G.CO.12, G.MG.3
2-5: Reasoning in Algebra and Geometry
2-6: Proving Angles Congruent
3-1: Lines and Angles
3-2: Properties of Parallel Lines
3-3: Proving Lines Parallel
3-5: 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. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
G-CO.10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the
segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G-CO.11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each
other, and conversely, rectangles are parallelograms with congruent diagonals.
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.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line
segment; and constructing a line parallel to a given line through a point not on the line.
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).★
Critical Vocabulary:
Instructional
Strategies:
Learning Targets:
Literacy Standards: R.CCR .4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how
specific word choices shape meaning or tone. W.CCR .5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
Parallel lines, skew lines, parallel planes, transversal, alternate interior angles, same-side interior angles, corresponding angles, alternate interior angles
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Test Reviews, Calculator Use, and
Constructions using tools(compass, ruler, protractor)
I can:
1.) Use the properties of equality and congruence to construct a two-column proof.
2.) Prove and apply theorems about angles.
3.) Identify parallel and skew lines and planes.
4.) Identify angle pairs formed by a transversal.
5.) Use the properties of parallel lines to find angle measures.
6.) Prove theorems about parallel lines.
7.) Apply the Triangle Angle Sum Theorem and the Triangle Exterior Angle Theorem.
Updated Spring 2015
Month:
Unit:
Core Standards:
Text Book Sections:
Skills and
Student
Demonstrators:
October
Chapter 3: Parallel and Perpendicular Lines (continued)
Chapter 4: Congruent Triangles
G.CO.1, G.CO.9, G.CO.10, G.CO.12, G.GPE.5, G.MG.3
3-7: Equations of Lines in the Coordinate Plane
3-8: Slopes of Parallel and Perpendicular Lines
4-1: Congruent Figures
4-2: Triangle Congruence by SSS and SAS
4-3: Triangle Congruence by ASA and AAS
4-4: Using Corresponding Parts of Congruent Triangles
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. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
G-CO.10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the
segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
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.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular
bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
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-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).★
Critical Vocabulary:
Instructional
Strategies:
Learning Targets:
Assessments:
Literacy Standards: R.CCR .4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how
specific word choices shape meaning or tone. W.CCR .5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
Slope, slope-intercept form, point-slope form, congruent polygons, congruent triangles
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Test Reviews ,Calculator Use, and
Constructions using tools(compass, ruler)
I can:
1.) Find the slope of a line.
2.) Graph a line.
3.) Write the equation of a line (both point-slope and slope intercept forms).
4.) Determine if two lines are parallel.
5.) Determine if two lines are perpendicular.
6.) Recognize congruent figures and their corresponding parts.
7.) Prove two triangles are congruent using the SSS Postulate.
8.) Prove two triangles are congruent using the SAS Postulate.
Bell work, Daily Homework, Constructions, Quizzes, Tests (summative and formative), Projects
Updated Spring 2015
Month:
Unit:
Core Standards:
Text Book Sections:
Skills and
Student
Demonstrators:
November
Chapter 4: Congruent Triangles (continued)
Chapter 5: Relationships within Triangles
G.CO. 9, G.SRT.5, G.C.3, G.CO.10
4-5: Isosceles and Equilateral Triangles
4-6: Congruence in Right Triangles
5-1: Midsegments of Triangles
5-2: Perpendicular and Angle Bisectors
5-3: Bisectors in Triangles
5-4: Medians and Altitudes
G-CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
G-CO.10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints
of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G-C.3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Critical Vocabulary:
Instructional
Strategies:
Learning Targets:
Assessments:
Literacy Standards: R.CCR .4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices
shape meaning or tone. W.CCR .5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
Legs & base of an isosceles triangle, vertex and base angles of an isosceles triangle, corollary, hypotenuse, legs of a right triangle, altitude of a triangle, centroid, circumcenter, concurrent,
equidistant
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Test Reviews ,Calculator Use
I can:

Apply properties of isosceles and equilateral triangles

Prove right triangles congruent using the Hypotenuse-Leg Theorem

Identify congruent overlapping triangles

Prove two triangles congruent using congruent triangles

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 triangles
Bell work, Daily Homework, Constructions, Quizzes ,Tests (summative and formative), Projects
Updated Spring 2015
Month:
Unit:
Core Standards:
Text Book Sections:
December
Chapter 6: Polygons and Quadrilaterals
G.SRT.5, G.CO.11, G.GPE.7, G.GPE.4
6-1: The Polygon-Angle Sum Theorem
6-2: Properties of Parallelograms
6-3: Proving that a Quadrilateral is a Parallelogram
6-4: Properties of Rhombuses, Rectangles, and Squares
6-6: Trapezoids and Kites
6-9: Proofs Using Coordinate Geometry
Skills and
Student
Demonstrators:
G-CO.11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and
conversely, rectangles are parallelograms with congruent diagonals.
G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G-GPE.4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove
or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
G-GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.★
Critical Vocabulary:
Instructional
Strategies:
Learning Targets:
Assessments:
Literacy Standards: R.CCR .4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices
shape meaning or tone. W.CCR .5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
Equilateral polygon, equiangular polygon, regular polygon, parallelogram, opposite sides and angles, consecutive angles, rhombus,
rectangle, square, trapezoid, base, leg, base angle, isosceles triangle, midsegment of a trapezoid, kite, distance formula
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Test Reviews ,Calculator Use
I can:

Find the sum of the measures of the interior angels of a polygon

Find the sum of the measures of the exterior angles of a polygon

Use relationships among sides and angles of parallelograms

Use relationships among diagonals of parallelograms

Determine whether a quadrilateral is a parallelogram

Determine 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

Use the distance formula to determine the distance between two coordinate points

Prove theorems using figures in the coordinate plane
Bell work, Daily Homework, Constructions, Quizzes ,Tests (summative and formative), Projects
Updated Spring 2015
Month:
Unit:
Core Standards:
Text Book Sections:
Skills and
Student
Demonstrators:
January
Chapter 7: Similarity
Chapter 8: Right Triangles and Trigonometry
G.SRT.4, G.SRT.5, G.SRT.6 G.SRT.7, G.SRT.8, G.SRT.10, G.SRT.11, G.GPE.4, G.GPE.5, G.MG.1
7-2: Similar Polygons
7-3: Proving Triangles Similar
7-4: Similarity in Right Triangles
7-5: Proportions in Triangles
8-1: The Pythagorean Theorem and its Converse
8-2: Special Right Triangles
8-3: Trigonometry
8-4: Angles of Elevation and Depression
8-5: Law of Sines
8-6: Law of Cosines
G-SRT.4. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using
triangle similarity.
G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles.
G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
G-SRT.10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G-SRT.11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
G-GPE.4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove
or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
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-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).★
Critical Vocabulary:
Instructional
Strategies:
Learning Targets:
Literacy Standards: R.CCR .4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices
shape meaning or tone. W.CCR .5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
Ratio, extended ratio, proportion, similar figures, similar polygons, extended proportion, scale factor, indirect measurement, geometric mean, Pythagorean triple, trigonometric ratios, sine,
cosine, tangent, angle of elevation, Angle of depression, Law of Sines, Law of Cosines
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Test Reviews ,Calculator Use
I can:
Updated Spring 2015
Assessments:

Write ratios and solve proportions

Identify and apply similar polygons

Use the AA~ postulate and the SAS~ and SSS~ theorems

Use similarity to find indirect measurements

Find and use relationships in similar triangles

Use the triangle-angle-bisector theorem

Use the Pythagorean theorem and its converse

Use the properties of the special right triangles

Use the sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles

Use angles of elevation and depression to solve problems

Apply the Law of Sines

Apply the Law of Cosines
Bell work, Daily Homework, Constructions, Quizzes ,Tests (summative and formative), Projects
Updated Spring 2015
Month:
Unit:
Core Standards:
Text Book Sections:
February
Chapter 9: Transformations
G.CO.2, G.CO.3, G.CO.4, G.CO.5, G.CO.6, G.CO.7, G.CO.8, G.SRT.1a, G.SRT.1b, G.SRT.2, G.SRT.3
9-1: Translations
9-2: Reflections
9-3: Rotations
9-4: Composition of Isometries
9-5: Congruence Transformations
9-6: Dilations
9-7: Similarity Transformations
Skills and
Student
Demonstrators:
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.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G-CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
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.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.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.1. Verify experimentally the properties of dilations given by a center and a scale factor:

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.

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.
G-SRT.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Literacy Standards: Informational/Explanatory Writing and Tier Three Words and Content Learning
Critical Vocabulary:
Congruence transformation, dilation, image, isometry, preimage, reflection, rigid motion, rotation, similarity transformation,
translation
Instructional
Strategies:
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Test Reviews ,Calculator Use, and
Updated Spring 2015
Learning Targets:
Assessments:
I can:

Find translations of images of figures

Find the reflection images of figures

Draw and identify rotation images of figures

Find composition of isometries, including glide reflections

Identify congruence transformations

Prove triangle congruence using isometries

Understand dilation images of figures

Identify similarity transformations and verify properties of similarity
Bell work, Daily Homework, Constructions, Quizzes ,Tests (summative and formative), Projects
Updated Spring 2015
Month:
Unit:
Core Standards:
Text Book Sections:
March
Chapter 10: Area
G.C.1, G.C.5, G.MG.1, G.MD.1, G.GMD.3
10-1: Areas of Parallelograms and Triangles
10-2: Areas of Trapezoids, Rhombuses, and Kites
10-3: Areas of Regular Polygons
10-4: Perimeters and Areas of Similar Figures
10-5: Trigonometry and Area
10-6: Circles and Arcs
10-7: Areas of Circles and Sectors
Skills and
Student
Demonstrators:
G-C.1. Prove that all circles are similar.
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.
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. Use dissection arguments, Cavalieri’s principle,
and informal limit arguments.
G-GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★
Literacy Standards: R.CCR .4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices
shape meaning or tone. W.CCR .5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
Critical Vocabulary:
Base of a parallelogram, altitude of a parallelogram, height of a parallelogram, base of a triangle, height of a triangle, height of
A trapezoid, radius of a regular polygon, apothem, circle, center, diameter, radius, congruent circles, semicircle, minor arc,
Major arc, adjacent arcs, circumference, pi, concentric circles, arc length, sector of a circle, segment of a circle, polyhedron, face, edge, vertex, cross section, prism, right
prism, oblique prism, cylinder, right cylinder, oblique cylinder, pyramid, regular pyramid, cone, right cone, volume,
Composite space figure, sphere, center of a sphere, radius of a sphere, diameter of a sphere, circumference of a sphere, great circle,
Hemisphere, similar solids
Instructional
Strategies:
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Test Reviews ,Calculator Use, and
Learning Targets:
I can:













Find the area of parallelograms and triangles
Find the area of a trapezoid, rhombus and kite
Find the area of a regular polygon
Find the perimeters and areas of similar polygons
Find areas of regular polygons and triangles using trigonometry
Find measures of central angles and arcs
Find the circumference and arc length
Find the areas of circles, sectors, and segments of circles
Recognize polyhedron and their parts
Visualize cross sections of space figures
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 the volume of a cylinder
Updated Spring 2015
Assessments:

Find the volume of a pyramid and cone

Find the surface area and volume of a sphere

Find and compare the areas and volumes of similar solids
Bell work, Daily Homework, Constructions, Quizzes ,Tests (summative and formative), Projects
Updated Spring 2015
Month:
Unit:
Core Standards:
Text Book Sections:
April
Chapter 11: Surface Area & Volume
G.MG.1, G.MG.2, G.GMD.1, G.GMD.2, G.GMD.3, G.GMD.4
11-1: Space Figures and Cross Sections
11-2: Surface Areas of Prisms and Cylinders
11-3: Surface Areas of Pyramids and Cones
11-4: Volumes of Prisms and Cylinders
11-5: Volumes of Pyramids and Cones
11-6: Surface Areas and Volume of Spheres
11-7: Areas and Volumes of Similar Solids
Skills and
Student
Demonstrators:
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-MG.2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).★
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. Use dissection arguments, Cavalieri’s principle,
and informal limit arguments.
G-GMD.2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
G-GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★
G-GMD.4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Literacy Standards: Argumentative and Informational/Explanatory Writing. R.CCR .4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and
figurative meanings, and analyze how specific word choices shape meaning or tone. W.CCR .5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new
approach.
Critical Vocabulary:
Base of a parallelogram, altitude of a parallelogram, height of a parallelogram, base of a triangle, height of a triangle, height of
A trapezoid, radius of a regular polygon, apothem, circle, center, diameter, radius, congruent circles, semicircle, minor arc,
Major arc, adjacent arcs, circumference, pi, concentric circles, arc length, sector of a circle, segment of a circle, polyhedron, face, edge, vertex, cross section, prism, right
prism, oblique prism, cylinder, right cylinder, oblique cylinder, pyramid, regular pyramid, cone, right cone, volume,
Composite space figure, sphere, center of a sphere, radius of a sphere, diameter of a sphere, circumference of a sphere, great circle,
Hemisphere, similar solids
Instructional
Strategies:
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Test Reviews ,Calculator Use, and
Learning Targets:
I can:










Find the area of parallelograms and triangles
Find the area of a trapezoid, rhombus and kite
Find the area of a regular polygon
Find the perimeters and areas of similar polygons
Find areas of regular polygons and triangles using trigonometry
Find measures of central angles and arcs
Find the circumference and arc length
Find the areas of circles, sectors, and segments of circles
Recognize polyhedron and their parts
Visualize cross sections of space figures
Updated Spring 2015






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 the volume of a cylinder
Find the volume of a pyramid and cone
Find the surface area and volume of a sphere
Find and compare the areas and volumes of similar solids
Month:
Unit:
Core Standards:
Text Book Sections:
May
Circles
G.C.2, G.C.3, G.C.4, G.GPE.1, G.GMD.4
12-1: Tangent Lines
12-2: Chords and Arcs
12-3: Inscribed Angels
12-4: Angle Measure and Segment Length
12-5: Circles in the Coordinate Plane
12-6: Locus: A Set of Points
Skills and
Student
Demonstrators:
G-C.2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter
are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
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
G-GMD.4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Literacy Standards: R.CCR .4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices
shape meaning or tone. W.CCR .5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
Critical Vocabulary:
Chord, inscribed angle, intercepted arc, locus, point of tangency, secant, standard form of an equation of a circle,
Tangent to a circle, center and radius of a circle
Instructional
Strategies:
Model Presentations, Practice Worksheets, Board Work, Group Work Vocabulary, Class Discussion, Homework Review, Test Reviews ,Calculator Use, and
Learning Targets:
I can:
Assessments:

Use properties of a tangent to a circle

Use congruent chords, arcs and central angles

Use perpendicular bisectors to chords

Find the measures of an inscribed angle

Find the measure of an angle formed by a tangent and a chord

Find measures of angels formed by chords, secants and tangents

Find the lengths of segments associated with circles

Write the equation of a circle

Find the center and radius of a circle

Draw and describe a locus
Bell work, Daily Homework, Constructions, Quizzes ,Tests (summative and formative), Projects
Updated Spring 2015