Download Geometry Scope and Sequence 2012-13

GEOMETRY
Scope and Sequence 2012-13
To make relative emphases in the standards more transparent and useful, SBAC designates clusters of standards as Major (M), Supporting (S), and
Additional (A) for coherence. Major clusters are areas of intensive focus, where students need fluent understanding and are able to apply the core
concepts. Supporting clusters are areas that should link to the core concepts in the major clusters and apply them. Additional clusters expose
students to other subsequent, higher level math ideas. The Common Core assessment will mirror the relative importance of these clusters. Within
geometry, only one cluster is identified as being Major: Prove geometric theorems. The standards within this cluster are CO-9: Prove theorems about
lines and angles; CO-10: Prove theorems about triangles; CO-11: Prove theorems about parallelograms. These standards have been bolded within the
scope and sequence below.
Each unit has an anticipated number of teaching days, excluding the review and summative assessment. Based on those numbers, semester one
would be completed after Unit 4. This includes 35 days for the units and a day for final exam review. The remaining units cover approximately 38 –
44 days, not including any review for the final exam. It is unlikely all of this would be covered in the 2012-2013 school year.
NCSD Geometry Scope and Sequence – 2012-13
6/2012
SEMESTER ONE
Unit 1: Building Blocks (9 content days)
Key Idea
Standard
Targets. I can…
G.CO.1
1. Basic Vocabulary and
Notation
Pre-req
G.CO.2
G.CO.4
2. Introduction to
Coordinate Geometry
(Transformation)
G.CO.5
G.CO.6
G.GPE.5
G.GPE.6
Pre-req
3. Angle Relationships
NCSD Geometry Scope and Sequence – 2012-13
• Define point, line, plane, line segment, angle, parallel and perpendicular
lines, and congruence
• Use proper notation to name figures and show relationships (i.e.
congruence)
• Find the distance between two points, graphically.
• Find the midpoint of two points forming a line segment, with an emphasis
on the graph.
• Find the slope of a line or line segment, graphically and/or algebraically
(i.e. from two points).
• Use ordered pair rules to transform figures.
• Define rotations, reflections, and translations, using specific geometric
vocabulary.
• Draw a specific transformation (rotation, reflection, or translation).
Emphasize using polygons on a coordinate plane.
• Identify a sequence of transformations that moved a figure.
• Determine if two figures are congruent based on the definition of
congruence. Use coordinate geometry as a means to prove congruence.
• Determine transformations that preserve congruence.
• Identify whether two lines are parallel, perpendicular, or neither,
graphically and algebraically.
• (Time permitting) write equations of lines that are parallel and
perpendicular.
• Find the point that divides a line segment into a given ratio (not necessarily
in half).
• Measure an angle using a protractor and categorize them as acute, obtuse,
right, supplementary, complementary, vertical angles, linear pair.
• Parallel line properties.
• Graph parallel and perpendicular lines and use them to find angles.
Pacing
Section/Notes
1 day
Section 1.1
1 day
Section 9.5, UYAS 1, UYAS 2
½ day
1½ days
Section 7.2
Section 7.1, 7.2, 7.3
1½ days
Section 1.4, supplement
1 day
UYAS 3 and 4
½ day
Supplement
2 days
Section 1.2, 1.3, 2.5, 2.6,
supplements
6/2012
Unit 2: Triangles (10 content days)
Key Idea
Standard
Targets. I can…
Pre-req
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G.CO.9
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1. Logic and Formal
Proof
G.GPE.7
•
Identify an if-then statement
State the converse of an if-then statement
Give a counterexample to an if-then statement
I can structure an argument using at least one of the following: paragraph
proof, two-column proof, or flowchart proof.
Prove theorems about lines and angles.
Prove that vertical angles are congruent
Prove that when two parallel lines are cut by a transversal, the
corresponding angles are congruent, the AIAs are congruent, and the
AEAs are congruent.
Use the distance formula to determine the distance between two points on
a coordinate grid
Use the coordinates of the vertices of a triangle graphed in the coordinate
plane and use the distance formula to compute the perimeter.
Use the coordinates of the vertices of a triangle graphed in the coordinate
plane and use the distance formula to classify the triangle (scalene,
isosceles, equilateral)
Use coordinates to prove simple geometric theorems algebraically.
•
Prove theorems about triangles.
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•
•
•
Define triangle congruence as preserving distances and angle measures
Connect triangle congruence in terms of rigid motions
Identify corresponding sides/angles of congruent triangles
Use triangle shortcuts (SAS, AAS, SSS, ASA) to determine congruency
•
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2. Properties and Proofs
G.GPE.4
G.CO.10
3. Triangle Congruence
G.CO7
G.CO.8
NCSD Geometry Scope and Sequence – 2012-13
Pacing
Section/Notes
2 days
Section 1.3, 2.1, 2.2, 2.5,
supplement
2 days
Section 2.5, 2.6, 3.2, supplement
Other examples include:
o Prove a point on a perpendicular
bisector is equidistant to the
segment’s endpoints
1 day
Section 9.5, supplement
1 day
Section 3.8
Possible examples include:
o
Prove the midsegment of a
triangle is parallel to the side.
o Prove a segment in a triangle is a
median by determining if it
bisects a side.
2 days
Section 4.1, 4.2
Possible examples include:
o
Prove the triangle sum theorem.
o
Prove the base angles of
isosceles triangles are congruent.
o Prove two triangles are
congruent (using shortcuts).
Problems could include
checking SSS on a coordinate
plane.
2 days
Section 1.4, 4.4, 4.5, 4.6,
supplement
6/2012
Unit 3: Polygons (4½ content days)
Key Idea
Standard
Targets. I can…
1. Vocabulary
G.CO.1
2. Transformations
G.CO.3
•
G.GPE.5
•
G.GPE.7
G.CO.11
G.GPE.4
•
•
•
G.MG.1
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•
Pacing
Section/Notes
1½ days
Section 1.4, 1.5
Describe the reflections and rotations that carry a given polygon onto itself
½ day
Use properties of slope (parallel and perpendicular) and distance on a
coordinate grid to prove properties of polygons
Calculate the perimeter of a polygon given the coordinates of the vertices
Prove theorems about parallelograms
Use coordinates to prove simple geometric theorems algebraically.
2 days
Is this just reflectional and
rotational symmetry?
Section 5.3, 5.4, 5.5, 5.6,
supplement
Supplement
Section 5.5, 5.6
Describe real-world objects as geometric figures and solve problems
related to perimeter
½ day
Precisely define polygons: convex, concave, regular, n-gon...
o Precisely define types of quadrilaterals by their characteristics
Possible examples include:
o
Prove four points on a
coordinate plane form a
rectangle.
o Determine if a quadrilateral on
a coordinate plane is a
parallelogram.
Supplement
Unit 4: Circles (5½ - 6½ content days)
Key Idea
1. Properties
Standard
Targets. I can…
Section/Notes
Section 6.1, 6.2, 6.3
•
Identify and describe circle properties related to inscribed angles, radii,
chords, and tangents
2 days
•
•
•
•
•
Find the circumference of a circle
Informally argue the circumference formula
Find the length of an arc on a circle
Introduction to radians as a ratio of arc length to the radius of a circle?
Describe real-world objects as geometric figures and solve problems
related to circumference
Derive the equation of a circle given the center and radius.
Write an equation for a circle given its center and radius.
(Time permitting) complete the square to find the center and radius of a
circle given by an equation.
½ day
Section 6.5
1 day
Section 6.7, supplement
1 day
Section 6.5, 6.6
1-2 days
Section 9.5, supplement
Properties include:
o
Relationships between central,
inscribed, and circumscribed
angles
o
Inscribed angles on a diameter
are right angles
o Radii are perpendicular to
tangents
G.C.2
G.GMD.1
2. Circumference and
Arc Length
Pacing
G.C.5
G.MG.1
G.GPE.1
3. Equation of a Circle
NCSD Geometry Scope and Sequence – 2012-13
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6/2012
SEMESTER TWO
Unit 5: Area (7 content days)
Key Idea
Standard
Targets. I can…
Pre-Req.
1. Circles
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•
G.GMD.1
G.C.5
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G.MG.1
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G.MG.2
2. Applications
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Use formulas to calculate the area of basic shapes
Find the area of an inscribed regular polygon using congruent triangles
Use and explain how to generate the formula for area of a regular polygon
Explain how the formula for the area of a circle can be generated using the
idea that a circle is equivalent to a regular polygon with an infinite number
of sides
Calculate the area of a sector of a circle
Describe real-world objects as geometric figures and solve problems
related to area
Convert units of measure (square feet to square miles)
Break composite figures into manageable figures
Apply area to the application of density problems (like people per square
mile)
Apply geometric methods to solve design problems
Pacing
Section/Notes
1 day
3 days
Section 8.1, 8.2
Section 8.4, 8.5
2 days
Section 8.6
Throughout Chapter 8
Supplement
Supplement
An example would be to minimize cost to
satisfy physical constraints
G.MG.3
3. Coordinate Geometry
S.CP.2
G.GPE.7
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•
Use area formulas to calculate geometric probability
Calculate the area of a geometric figure given the coordinates of the
vertices
1 day
Supplement, p. 442
Supplement
Pacing
Section/Notes
4-5 days
Section 10.1, 10.2, 10.3, 10.6
Section 8.7, 10.7
2-3 days
Section 10.4, 10.5, and throughout
Chapter 10
Unit 6: Volume and Surface Area (6 – 8 content days)
Key Idea
Standard
Targets. I can…
1. Review Vocabulary
and Basic Formulas
Pre-Req.
•
•
•
2. Informally Prove
Volume Formulas
G.GMD.1
•
G.MG.1
•
G.GMD.3
G.GMD.4
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3. Applications
NCSD Geometry Scope and Sequence – 2012-13
Name and sketch 3-d solids (prisms, pyramids, cones, cylinders, spheres)
Calculate the volume of prisms, pyramids, cylinders, cones, and spheres
Calculate the surface area for prisms, pyramids, cylinders, cones, and
spheres
Develop the volume formulas for a cylinder, pyramid, and cone using
dissection arguments, Cavalieri’s principle, and informal limit arguments
Describe real-world objects as geometric figures and solve problems
related to volume and surface area
Use formulas for cylinders, pyramids, cones and spheres to solve problems
Identify 2-dimensional shapes of cross-sections of 3-dimensional objects
Identify the 3-dimensional solid generated when a 2-dimensional object is
rotated about a line
Supplement
6/2012
Unit 7: Similarity and Trigonometry (7 – 8½ content days)
Key Idea
Standard
Targets. I can…
•
Define what it means for two figures to be similar
Draw two similar figures given a scale factor
Determine how the perimeter of a similar figure is related to the scale
factor
Graph similar figures given an order pair rule
Use the definition of similarity to determine if two figures are similar
Explain what it means for two triangles to be similar
Explain why the AA shortcut applies to similar triangles
Apply triangle similarity to solve problems, including indirect
measurements such as the shadow method
Prove triangle theorems using similarity.
G.C.1
•
Prove all circles are similar
G.SRT.6
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•
Use similar triangles to introduce the trigonometric ratios
Explain the relationship between the sine and cosine of complementary
angles
Use trigonometric ratios and the Pythagorean Theorem to solve right
triangle applications
Derive the area formula A=1/2ab sin (C)
Prove the Law of Sines and Cosines and use them to solve problems
Apply the Law of Sines and Cosines in context
G.SRT.1
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G.SRT.2
G.SRT.3
G.SRT.5
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1. Similarity as a
Transformation
Pacing
Section/Notes
1 day
Section 11.1, supplement
2 day
Section 11.1, 11.2, 11.3
1 days
Section 11.6
Examples include:
o A line parallel to one side of
a triangle divides the other
two proportionally
o Pythagorean theorem
Share ideas with colleagues
because this standard seems silly.
Section 12.1, supplement
Supplement
G.SRT.4
2. Proofs
3. Trigonometric Ratios
4. Applications
G.SRT.7
G.SRT.8
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G.SRT.9*
G.SRT.10*
G.SRT.11*
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NCSD Geometry Scope and Sequence – 2012-13
1½ days
1½
without
laws
Section 12.1, 12.2, 12.3, 12.4, 12.5
*These are not assessable.
3 days
with
laws
6/2012
Unit 8: Probability (6 content days)
Key Idea
Standard
Targets. I can…
•
Pre-Req.
•
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•
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1. Review and Set
Theory Vocabulary
S.CP.1
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S.CP.2
S.CP.3
S.CP.4
2. Compound and
Conditional
Probability
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S.CP.5
S.CP.6
S.CP.7
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S.CP.8*
S.CP.9*
Explain the difference between experimental and theoretical probability
and compare the two given an experiment
Calculate the probability of a simple event
List possible outcomes in an organized list or a tree diagram
Define event and sample space
Establish events as subsets of a sample space
Define union, intersection, and complement
Establish events as subsets of a sample space based on the union,
intersection, and/or complement of other events
Define and identify independent events
Explain and provide an example to illustrate that for two independent
events A and B, P(A and B) = P(A)*P(B)
Find the conditional probability of event A assuming B happened;
introduce notation P(A|B)
Create 2-way frequency tables (see notes) and use them to decide if events
are independent and to approximate conditional probabilities
Recognize and explain the concepts of conditional probability and
independence in everyday language and everyday situations
Calculate conditional probability of real-world models
Apply addition rule P(A or B) = P(A) + P(B) – P(A and B)
Apply the general Multiplication Rule, P(A and B) = P(A)*P(B|A)
Use permutations and combinations to compute probabilities
Pacing
Section/Notes
1 day
Introduce notation (∪, ∩)
1½ days
1½ days
2-way frequency table:
2 days
*These are not assessable.
Unit 9: Constructions/Conics (4 – 6 content days)
Key Idea
Standard
Targets. I can…
•
G.CO.12
1. Constructions
G.CO.13
G.C.3
2. Conics
G.GPE.2
NCSD Geometry Scope and Sequence – 2012-13
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Use a variety of tools to make formal constructions including:
◦ Copy a segment or angle.
◦ Bisect a segment or angle
◦ Construct perpendicular lines and bisectors.
Construct parallel line through a point not on the line
Construct an equilateral triangle inscribed in a circle
Construct a square inscribed in a circle
Construct a regular hexagon inscribed in a circle
Construct inscribed and circumscribed circles of a triangle
Derive the equation of a parabola given focus and directrix
Pacing
Section/Notes
3-5 days
Section 3.1, 3.2, 3.3, 3.4, 3.5
Supplement
1 day
Supplement
Supplement
Directrix should be parallel to a
coordinate axis
6/2012