Download Geometry - Detroit Public Safety Academy

Curriculum Overview Map
Detroit Public Safety Academy 2015-2016
Course/Subject: Geometry
Grade:
10
Quarter: 1st
Essential Questions-Units-Chapters-Concepts
UNIT 1 LANGUAGE OF GEOMETRY: How can the coordinate system, constructions, and
precise language help us explore and justify geometric relationships?
 How can coordinates be used to describe attributes of geometric objects? (e.g. slope, midpoint,
length, parallelism, and perpendicularity, and equations of lines)
 In what ways can two or more lines intersect? How can the relationship between the lines and the
angle formed be represented and justified?
 What is the difference between inductive and deductive reasoning? What are the value and
limitations of each type of reasoning?
 How are geometric constructions useful tools for representing and reasoning about geometric
figures?
UNIT 2 TRANSFORMATIONAL GEOMETRY: What impact does each type of transformation
(reflection, rotation, translation, and dilation) have on the location, size, and orientation of
geometric objects?)
 How does the value of the scale factor in a dilation influence the size of the image?
 How can geometric transformations be represented algebraically?
Resources (include websites)
Atlas Rubicon Oakland Schools (2015). https://oaklandk12public.rubiconatlas.org/Atlas/Browse/Vie
w/Calendars
Pearson Education(2015). www.pearsonsuccess.net
(2012). Geometry
Curriculum Crafterhttps://curriculumcrafter.org/login.aspx
Sims. (2015). Algebra Housewww.algebrahouse.com
Kuta Software (2015). https://www.kutasoftware.com/freeia2.ht
ml
Khan Academy, 2015.
https://www.khanacademy.org/
Teacher Tube, 2015
www.teachertube.com
Learning Focused, 2013.
Higher Order Thinking
Learning Focused Lessons
http://www.learningfocused.com/index.p
hp/page/lfs-engaged
Standards-CCSS/GLCEs/HSCEs-KC4
Unit 1: G.CO.A.1, G.CO.D.12, G.CO.D.13, G.GPE.B.5, G.GPE.B.6, G.GPE.B.7
Unit 2: G.CO.A.1, G.CO.A.2, G.CO.A.3, G.CO.A.4, G.CO.A.5, G.CO.B.6, G.CO.D.12, G.SRT.A.1, G.SRT.A.1a, G.SRT.A.1b, G.SRT.A.2
Vocabulary/Key Concepts
Assessments/Projects
Unit 1: Bisector, angle bisector, segment bisector, perpendicular Standard Based Assessment: Interpreting Data through charts, tables and graphs.
bisector, conditional statements, if-then statements, inverse,
(Pre/Post x 2)
converse, contrapositive, constructions, coordinate geometry,
counterexample, definition, distance between two points,
Unit 1 Assessments (pre/post)
hypothesis, conclusion, midpoint, perpendicular and parallel line
relationships, reasoning, inductive, deductive,
STEM Cross Curricular Projects
Unit 2: Angle of rotation, center of dilations, center of rotations,
composition/sequence of two or more transformations,
M-STEP & SAT Prep
congruence, dilation, geometric constructions, image, preimage, lines of dilation, reflection, rotation, scale factor,
magnitude of dilation, similarity, similarity transformations,
symmetry (rotational and reflectional), transformation,
translation, triangle similarity
Curriculum Overview Map
Detroit Public Safety Academy 2015-2016
Course/Subject: Geometry
Grade:
10
Quarter: 2nd
Essential Questions-Units-Chapters-Concepts
UNIT 2 TRANSFORMATIONAL GEOMETRY: What impact does each type of
transformation (reflection, rotation, translation, and dilation) have on the location, size,
and orientation of geometric objects?)
 What impact does changing the center of dilation have on the location of the image?
 Which transformations preserve distance? Shape? Orientation? Angle?
 How might you investigate the composition of two or more transformations to
determine which combinations are commutative?
Resources (include websites)
Atlas Rubicon Oakland Schools- https://oaklandk12public.rubiconatlas.org/Atlas/Browse/View/Calendars
UNIT 3 TRIANGLES: What conditions must be met to show similarity or congruence
of triangles? What are the properties of medians, altitudes, angle bisectors, and
perpendicular bisectors of the sides of a triangle?
 What are the similarities and differences between similar and congruent triangles?
 Use a geometry software program or compass and straightedge to construct the
medians, altitudes, perpendicular bisectors, and angle bisectors of a triangle. Make
conjectures about their intersection points and any additional characteristics. Include
the effect of changing the type of triangle from acute to obtuse.
Pearson. (2012). Geometry
UNIT 4 QUADRILATERALS: How are various quadrilaterals related and what are
properties of their sides, angles, diagonals, and areas?
 How are properties of triangles used to justify properties of quadrilaterals (e.g., angle
sums, diagonal lengths)?
Pearson- www.pearsonsuccess.net
Curriculum Crafterhttps://curriculumcrafter.org/login.aspx
Sims. (2015). Algebra Housewww.algebrahouse.com
Kuta Software (2015). https://www.kutasoftware.com/freeia2.html
Khan Academy, 2015.
https://www.khanacademy.org/
Teacher Tube, 2015
www.teachertube.com
Learning Focused, 2013.
Higher Order Thinking
Learning Focused Lessons
http://www.learningfocused.com/index.php/page/lfsengaged
Standards-CCSS/GLCEs/HSCEs-KC4
Unit 2: G.CO.A.1, G.CO.A.2, G.CO.A.3, G.CO.A.4, G.CO.A.5, G.CO.B.6, G.CO.D.12, G.SRT.A.1, G.SRT.A.1a, G.SRT.A.1b, G.SRT.A.2
Unit 3: A.APR.C.4, G.CO.B.6, G.CO.B.7, G.CO.B.8, G.CO.B.10, G.SRT.A.2, G.SRT.A.3, G.SRT.B.4, G.SRT.B.5, G.C.A.3, G.GPE.B.4,
G.GPE.B.7, G.MG.A.3
Unit 4:G.CO.C.11, G.MG.A.1, G.MG.A.3
Vocabulary/Key Concepts
Unit 2: Angle of rotation, center of dilations, center of rotations,
composition/sequence of two or more transformations,
congruence, dilation, geometric constructions, image, pre-image,
lines of dilation, reflection, rotation, scale factor, magnitude of
dilation, similarity, similarity transformations, symmetry
(rotational and reflectional), transformation, translation, triangle
similarity
Assessments/Projects
Standard Based Assessment: Interpreting Data through charts, tables and graphs.
(Pre/Post x 2)
Unit 3: Altitude, angle bisectors, base angles, centroid,
circumcenter, corresponding parts, hypotenuse, incenter, leg,
medians, orthocenter, perpendicular bisectors, Pythagorean
Theorem, Triangle congruence (SSS, SAS, AAS, ASA, HL),
triangle similarity (SSS, SAS, AA), vertex angles, coordinate
proofs
M-STEP & SAT Prep
Unit 4: Coordinate proofs, definitions of quadrilaterals, geometric
modeling, measurement attributes of quadrilaterals (area, side
length, angle measure, diagonal length, perimeter), necessary and
sufficient conditions, properties of quadrilaterals (kite,
parallelogram, rectangle, rhombus, square, trapezoid),
Quadrilateral classification
Unit 2 & 3 Assessments (pre/post)
STEM Cross Curricular Projects
Final Exam Semester 1
Curriculum Overview Map
Detroit Public Safety Academy 2015-2016
Course/Subject: Geometry
Grade:
10
Quarter: 3rd
Essential Questions-Units-Chapters-Concepts
UNIT 4 QUADRILATERALS: How are various quadrilaterals related and what are properties
of their sides, angles, diagonals, and areas?
 How can sufficient conditions for quadrilaterals be used to guide and/or justify their
constructions?
 How do the properties of quadrilaterals help to make sense of and reason about real life
objects?
 What are the sufficient and/or necessary conditions for trapezoids, isosceles trapezoids,
parallelograms, rhombi, rectangles, squares and kites?
 How can coordinates, transformations, and properties of quadrilaterals be used in the process
of classifying quadrilaterals?
UNIT 5 RIGHT TRIANGLE TRIGONOMETRY: How can the unknown measures of the
angles or sides of a triangle be found? How can trigonometry help find these missing parts in
many real-world situations?
 What is the relationship between the side lengths of a right triangle and the sine, cosine, and
tangent ratios?
 Why do trigonometric ratios yield the same values for different sizes of right triangles?
 What is the relationship between the sides in a 45-45-90 triangle? In a 30-60-90 triangle?
 When is it appropriate to use the Law of Sines to solve a problem? The Law of Cosines?
Resources (include websites)
Atlas Rubicon Oakland Schoolshttps://oaklandk12public.rubiconatlas.org/Atlas/Browse/View
/Calendars
Pearson- www.pearsonsuccess.net
Curriculum Crafterhttps://curriculumcrafter.org/login.aspx
Pearson. (2012). Geometry
Sims. (2015). Algebra Housewww.algebrahouse.com
Kuta Software (2015). https://www.kutasoftware.com/freeia2.htm
l
Khan Academy, 2015.
https://www.khanacademy.org/
Teacher Tube, 2015
www.teachertube.com
Learning Focused, 2013.
Higher Order Thinking
Learning Focused Lessons
http://www.learningfocused.com/index.ph
p/page/lfs-engaged
Standards-CCSS/GLCEs/HSCEs-KC4
Unit 4: G.CO.B.6, G.CO.C.11, G.CO.C12, G.GPE.B.4, G.MG.A.1, G.GM.A.3
Unit 5: F.T.F.A.3, G.SRT.C.6, G.SRT.C.7, G.SRT.C.8, G.SRT.D.9, G.SRT.D.10, G.SRT.D.11
Vocabulary/Key Concepts
Unit 4: Coordinate proofs, definitions of quadrilaterals, geometric
modeling, measurement attributes of quadrilaterals (area, side
length, angle measure, diagonal length, perimeter), necessary and
sufficient conditions, properties of quadrilaterals (kite,
parallelogram, rectangle, rhombus, square, trapezoid),
Quadrilateral classification
Assessments/Projects
Standard Based Assessment: Interpreting Data through charts, tables and
graphs. (Pre/Post x 2)
Unit 4 & 5 Assessments (pre/post)
STEM Cross Curricular Projects
Unit 5: 30-60-90 triangles, 45-45-90 triangles, area of triangle
using trig, cosine, Law of Cosines, Law of Sines, sine, tangent
M-STEP & SAT
Curriculum Overview Map
Detroit Public Safety Academy 2015-2016
Course/Subject: Geometry
Grade:
10
Quarter: 4th
Essential Questions-Units-Chapters-Concepts
UNIT 6 CIRCLES: What are the properties and representations of special liens, segments, and angle
as they relate to a circle and how can these properties be used to solve problems?
 How is pi related to the parts of a circle?
 Why is the measure of an inscribed angle half of the measure of a central angle inscribed in the same
arc?
 What is the relationship of the area of a sector of a circle to the area of that circle?
 What is the relationship between the arc length on a circle and the circumference e of that circle?
 Give an example of an equation of a circle whose center is at the origin. How can you transform this
equations to the size is the same, but the center is not at the origin?
UNIT 7 MODELING WITH 3-DIMENSIONAL FIGURES: What are the connections between twodimensional and three-dimensional figures?
 How are pyramids like prims? How are they different? How are cones like cylinders? How are they
different?
 What characteristics of a three dimensional object are necessary to draw a sketch of the object?
Draw the object.
 Given a three-dimensional geometric object, how can you draw a two-dimensional net that represent
this object?
 What are the possible cross sections of various polyhedral?
 Given a two-dimensional figure, sketch the result of rotating the figure about a line.
 What is the relationship between the volume of a prism and a pyramid with congruent baes and
heights? What is the relationship between the volume of a cylinder and ac one with congruent bases
and heights?
Resources (include websites)
Atlas Rubicon Oakland Schoolshttps://oaklandk12public.rubiconatlas.org/Atlas/Browse/
View/Calendars
Pearson- www.pearsonsuccess.net
Curriculum Crafterhttps://curriculumcrafter.org/login.asp
x
Pearson. (2012). Geometry
Sims. (2015). Algebra Housewww.algebrahouse.com
Kuta Software (2015). https://www.kutasoftware.com/freeia2.
html
Khan Academy, 2015.
https://www.khanacademy.org/
Teacher Tube, 2015
www.teachertube.com
Learning Focused, 2013.
Higher Order Thinking
Learning Focused Lessons
http://www.learningfocused.com/index
.php/page/lfs-engaged
Standards-CCSS/GLCEs/HSCEs-KC4
Unit 6: F.TF.A.1, G.C.A.1, G.C.A.2, G.C.A.3, G.C.A.4, G.C.B.5, G.GPE.A.1
Unit 7: G.GMD.A.1, G.GMD.A.2, G.GMD.A.3, G.GMD.B.4, G.MG.A.1, G.MG.A.2, G.MG.A.3
Vocabulary/Key Concepts
Unit 6: Radius, diameter, center, chord, central angle, inscribed
angle, circumscribed angle, tangent, point of tangency, secant,
equation of a circle, arc, arc length, locus, degree and radian
measures and connections, circumference, area, sector, area of a
sector
Assessments/Projects
Standard Based Assessment: Interpreting Data through charts, tables and graphs.
(Pre/Post x 2)
Unit 7: Altitude, appropriate use of units in area and volume
calculations, cones, cross section, cylinders, faces, impact of
scale factor on the surface area and volume of a figure, isometry,
net, orthographic, planes of symmetry, polyhedron, prisms,
pyramids, relationship between the volumes of prisms and
pyramids; cylinders and cones, rotational symmetry of a 3-D
figure, slant height, solids of revolution, spheres, surface area
and volume of figures, vertex
STEM Cross Curricular Projects
Unit 6 & 7 Assessments (pre/post)
Final Exam Semester 2