Download Standards Learning Targets - Jefferson City Public Schools

Geometry
Conceptual Category(s)
Domain
Cluster
Alignments:
CCSS: See below
Performance: 1.10, 3.5, 3.3
Knowledge: (MA) 5
MACLE: See below
NETS: 2d; 4b
DOK: 1-3
•
•
•
•
•
Geometry
Congruence (G-CO)
Experiment with transformations in the plane (G-CO.1)
Prove geometric theorems (G-CO.9)
Make geometric constructions (G-CO.12)
Standards
Learning Targets
G-CO.1, 9, 12
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
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 segments endpoints
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; 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
Unit A: Basic Geometry: Learn definitions of basic geometric principles,
prove and apply theorems about special angles, and create formal geometric
constructions
•
•
•
Apply the concepts of point, line and plane
Apply the definition of segment, congruent, midpoint, and bisect
Apply the definition of perpendicular, parallel and ray
CCSS: G-CO.1
MACLE: GSR.1
•
Copy a segment and bisect a segment using a compass and straightedge
CCSS: G-CO.12
MACLE: GSR.1
•
Construct perpendicular lines, the perpendicular bisector of a segment,
and a line parallel to a given line through a point not on the line using a
compass and straightedge
CCSS: G-CO.12
MACLE: N/A
Approved 7-15-13
Revised 2013
1
Geometry
•
Use the segment addition postulate to find the length of segments
CCSS: G-CO.1
MACLE: NO.2.D
•
Apply the definition of angle and angle bisector, and use the angle
addition postulate to find the measure of an angle
CCSS: G-CO.1
MACLE: M.2.B
•
Copy an angle and bisect an angle using a compass and a straightedge
CCSS: G-CO.12
MACLE: N/A
•
Identify types of angles including linear pair, supplements,
complements, vertical, adjacent, to prove and apply theorems about
angles
CCSS: G-CO.1
MACLE: GSR.1.A
•
Apply the definition of transversal and identify types of angles
including alternate interior, alternate exterior, same-side interior, sameside exterior and corresponding to prove and apply theorems about
angles
•
Prove and use properties of parallel lines cut by a transversal
CCSS: G-CO.9
MACLE: M.2.B
Approved 7-15-13
Revised 2013
2
Geometry
Instructional Strategies
•
•
•
•
•
Lecture enhanced with:
• SMART Notebook
• PowerPoint
• the Internet
Drill and guided practice
Demonstrations on constructions
Reflective discussion
Class discussion
Assessments/Evaluations
The students will be assessed on the concepts taught using a variety of modalities:
• Direct teacher observations
• Projects w/ scoring guides:
• Design a City Map: Using this real-world application, the students will work in small groups to design a city based on the terms and
theorems learned in this unit (under development)
• Quizzes
• Homework assignments
• Formal common assessment – Unit A test
Mastery Level: 80%
Instructional Resources/Tools
Textbook(s): Pearson Geometry Common Core
Website(s):
• How to construct a line parallel to a given line through a given point: http://www.youtube.com/watch?v=WWvkS-IGjtM
• How to construct a perpendicular line through a point not on the line: http://www.youtube.com/watch?v=R6YltpN8QIU
• Scientific calculator
•
•
Approved 7-15-13
Revised 2013
3
Geometry
Conceptual Category(s)
Domain
Cluster
•
•
•
•
Geometry
Congruence (G-CO)
Experiment with transformations in the plane (G-CO.2-5)
Understand congruence in terms of rigid motions (G-CO.6)
Alignments:
CCSS: See below
Performance: 1.10, 3.3
Knowledge: (MA) 2
MACLE: See below
NETS: 1b; 3a; 4d
DOK: 1-3
Standards
G-CO.2-6
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)
3. Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself
4. Develop definitions of rotations, reflections, and translations in
terms of angles, circles, perpendicular lines, parallel lines, and line
segments
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
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
Learning Targets
Unit B: Transformations: Represent, compare, perform and describe
transformations in the plane
•
Identify isometries (e.g., basic rigid transformations – reflections,
translations, and rotations)
CCSS: G-CO.2,4,6
MACLE: GSR.3.A
•
•
•
Perform and use reflections in the plane in terms of the given definition
Perform and use translations in the plane in terms of the given definition
Perform and use rotations in the plane in terms of the given definition
CCSS: G-CO.2,4,5
MACLE: GSR.3.A
•
Identify and use types of 2-D symmetry (line and rotational symmetry)
and 3-D symmetry (plane and axis symmetry) on a given figure/object
CCSS: G-CO.3,4
MACLE: GSR.3.C
Approved 7-15-13
Revised 2013
4
Geometry
•
Represent transformations as compositions of simpler transformations
CCSS: G-CO.5,6
MACLE: GSR.3.A
Instructional Strategies
•
•
•
•
•
Lecture enhanced with:
• SMART Notebook
• PowerPoint
• the Internet
Drill and guided practice
Demonstrations of various transformations on:
• Geogebra
• Geometer’s Sketchpad
• wax paper
Reflective discussion
Class discussion
Assessments/Evaluations
The students will be assessed on the concepts taught using a variety of modalities:
• Direct teacher observations
• Quizzes
• Homework assignments
• Formal common assessment – Unit B test
Mastery Level: 80%
Instructional Resources/Tools
•
•
•
•
Textbook(s): Bass et al., Prentice Hall Mathematics Geometry. Boston: Pearson/Prentice Hall, 2004.
Website(s): www.geogebra.org
Software:
• Geometer’s Sketchpad
• Geogebra
Scientific calculator
Approved 7-15-13
Revised 2013
5
Geometry
Conceptual Category(s)
Domain
• Geometry
• Expressing Geometric Properties with Equations (G-GPE)
• Congruence (G-CO)
Cluster
• Use Coordinates to prove simple geometric theorems algebraically (G-GPE.4-7)
• Prove Geometric Theorems (G-CO.11)
Alignments:
CCSS: See below
Performance: 1.6, 1.10, 3.4, 3.5
Knowledge: (MA) 2,4
MACLE: See below
NETS: 3d; 4c; 6b
DOK: 1-3
Standards
G-GPE.4-7
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)
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)
6. Find the point on a directed line segment between two given
points that partitions the segment in a given ratio
7. Use coordinates to compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the distance formula
Learning Targets
Unit C: Coordinate Geometry: Apply properties of parallel and
perpendicular lines to write equations of lines. Use the distance and
midpoint formulas and theorems about special parallelograms to prove
conjectures or classify shapes
•
•
Find the slope of a line, given the coordinates or a graph
Find the point on a directed line segment between two given points that
partitions the segment in a given ratio
CCSS: G-GPE.6
MACLE: N/A
•
G-CO.11
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
Approved 7-15-13
Write equations of lines in slope-intercept and point-slope form
CCSS: G-GPE.4
MACLE: AR.4.A
Write equations of parallel and perpendicular lines
CCSS: G-GPE.5
MACLE: AR.4.A
Revised 2013
6
Geometry
•
•
•
Use the distance and/or midpoint formula to find the length and/or
midpoint of a segment
Prove the classification of a polygon on the coordinate grid
Use coordinates to find the perimeters and/or areas of polygons
CCSS: G-GPE.4,5,7
MACLE: M.2.B; GSR.2.A
•
•
•
•
•
•
•
•
Apply theorems about parallelograms
Use coordinates to prove a quadrilateral is a parallelogram
Prove if a quadrilateral is a parallelogram by applying theorems about
parallelograms
Prove if a quadrilateral is a parallelogram using coordinates
Apply theorems about special parallelograms
Use coordinates to prove if a quadrilateral is a special parallelogram and
compute the perimeter
Use properties of trapezoids and kites
Use coordinates to classify quadrilaterals and compute perimeters
CCSS: G-GPE.4; G-CO.11
MACLE: GSR.1.A; GSR.2.A
Instructional Strategies
•
•
•
•
Lecture enhanced with:
• SMART Notebook
• PowerPoint
• the Internet
Drill and guided practice
Reflective discussion
Class discussion
Approved 7-15-13
Revised 2013
7
Geometry
Assessments/Evaluations
The students will be assessed on the concepts taught using a variety of modalities:
• Direct teacher observations
• Quizzes
• Homework assignments
• Formal common assessment – Unit C test
Mastery Level: 80%
Instructional Resources/Tools
Textbook(s): Bass et al., Prentice Hall Mathematics Geometry. Boston: Pearson/Prentice Hall, 2004.
Website(s):
• www.ixl.com
• www.khanacademy.org
• Scientific calculator
•
•
Approved 7-15-13
Revised 2013
8
Geometry
Conceptual Category(s)
Domain
• Geometry
• Congruence (G-CO)
• Similarity, Right Triangles, and Trigonometry (G-SRT)
Cluster
• Understand congruence in terms of rigid motion (G-CO.7, 8)
• Prove geometric theorems (G-CO.9, 10)
• Prove theorems involving similarity (G-SRT.5)
Alignments:
CCSS: See below
Performance: 1.10, 3.5, 4.1
Knowledge: (MA) 2
MACLE: See below
NETS: 1a; 4c
DOK: 1-3
Standards
G-CO.7-10
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
8. Explain how the criteria for triangle congruence (ASA, SAS, and
SSS) follow from the definition of congruence in terms of rigid
motions
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
segment are exactly those equidistant from the segments endpoints
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
Learning Targets
Unit D: Triangle Congruence & Properties and Attributes of Triangles:
Understand congruence in terms of rigid motions, prove geometric
theorems, and prove theorems involving similarity as they apply to triangles
•
•
•
•
•
Classify triangles by their angle measures and side lengths
Use triangle classifications to find angle measures and side lengths
Prove and use Triangle-Angle Sum Theorem
Prove and use the Isosceles Triangle Theorem and its converse
Prove and use the Equilateral and Equiangular Triangle Corollaries
CCSS: G-CO.10
MACLE: M.2.B; GSR.4.B
•
•
Apply a rigid transformation to a polygon and prove the polygon
remains congruent to the pre-image
Prove two polygons are congruent if and only if all the corresponding
pairs of sides and corresponding pairs of angles are congruent
CCSS: G-CO.7
MACLE: M.2.B
Approved 7-15-13
Revised 2013
9
Geometry
G-SRT.5
5. Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures
•
Apply and prove triangle congruence with the following postulates or
theorems: SSS, SAS, ASA, AAS and HL
CCSS: G-CO.8; G-SRT.5
MACLE: M.2.B
•
Prove corresponding parts of congruent triangles are congruent
(CPCTC) and use to solve problems
CCSS: G-SRT.5
MACLE: M.2.B
•
•
•
Locate perpendicular bisectors, angle bisectors, medians, and altitudes
of a triangle and identify the name of the point created by their
respective intersections
Prove the Mid-segment Theorem
Prove points on a perpendicular bisector are exactly those equidistant
from the segments endpoints
CCSS: G-CO.9,10
MACLE: M.2.B; NO.2.D
•
•
Prove the sum of any two side lengths of a triangle is greater than the
third side length
Reason and prove angle-side relationships in triangles. (i.e., The longest
side of a triangle is opposite the largest angle)
CCSS: G-CO.10
MACLE: M.2.B; NO.2.D
Approved 7-15-13
Revised 2013
10
Geometry
Instructional Strategies
•
•
•
•
•
•
•
Lecture enhanced with:
• SMART Notebook
• PowerPoint
• the Internet
Drill and guided practice: e.g., “Speed Dating”/Flash Card activity over recognizing which postulate or theorem proves a pair of triangles
congruent
Demonstrations such as modeling the constructions of:
• circumcenter
• incenter
• centroid
• orthocenter
Problem solving: e.g., Proof Card-Sorting activities
Class discussion
Technology enhanced such as online:
• instructional videos
• practices that give immediate feedback to students:
• www.ixl.com
• www.khanacademy.org)
Literacy such as:
• written explanations of how to prove triangles congruent
• how parts of congruent triangles are congruent – paragraph proofs
Approved 7-15-13
Revised 2013
11
Geometry
Assessments/Evaluations
The students will be assessed on the concepts taught using a variety of modalities:
• Direct teacher observations
• Concept checkpoints such as:
• starters
• entrance/exit passes
• target tickets
• homework quizzes
• Quizzes
• Homework assignments
• Formal common assessment – Unit D Test
Master Level: 80%
Instructional Resources/Tools
Textbook(s):
• Pearson Geometry
• Holt McDougal Geometry
• Website(s):
• www.ixl.com
• www.khanacademy.org
• Scientific calculator
•
Approved 7-15-13
Revised 2013
12
Geometry
Conceptual Category(s)
Domain
Cluster
Alignments:
CCSS: See below
Performance: 1.6
Knowledge: (MA) 2,4
MACLE: See below
NETS: 1c; 2d; 4a
DOK: 1-3
•
•
•
•
•
•
Geometry
Similarity, Right Triangles, and Trigonometry (G-SRT)
Circles (G-C)
Understand similarity in terms of similarity transformations (G-SRT.1)
Prove theorems involving similarity (G-SRT.4, 5)
Understand and apply theorems about circles (G-C.1)
Standards
G-SRT.1-4
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
b. The dilation of a line segment is longer or shorter in the ratio
given by the scale factor
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
proportionality of all corresponding pairs of sides
3. Use the properties of similarity transformations to establish the AA
criterion for two triangles to be similar
4. Prove theorems about triangles. Theorems include: a line parallel
to one side of a triangle divides the other two sides proportionally,
and conversely; the Pythagorean Theorem proved using triangle
similarity
Learning Targets
Unit E: Similarity: Use similarity to analyze and solve problems
•
•
•
Write ratios and solve proportions
Define similarity as a composition of rigid motions followed by
dilations in which angle measure is preserved and side length is
proportional
Demonstrate that in a pair of similar triangles or in a pair of similar
figures, corresponding angles are congruent and corresponding sides are
proportional
CCSS: G-SRT.2
MACLE: NO.3.E; M.2.B; GSR.1.A; GSR.3.A
•
Use triangle similarity theorems (AA~, SAS~, SSS~) to prove triangles
are similar
CCSS: G-SRT.3
MACLE: GSR.1.A
Approved 7-15-13
Revised 2013
13
Geometry
G-C.1
1. Prove that all circles are similar
G-SRT.5
5. Use congruence and similarity criteria for triangles to solve
problems and to prove relationships in geometric figures
•
Use theorems, postulates, or definitions to prove theorems about
triangles, including the Side Splitter Theorem and its converse
CCSS: G-SRT.4
MACLE: GSR.1.A; M.2.B
•
Prove that all circles are similar by showing that for a dilation centered
at the center of a circle, the preimage and the image have equal central
angle measures
CCSS: G-C.1
MACLE: GSR.1.A
•
•
•
•
Perform dilation with a given center and scale factor on a figure in the
coordinate plane
Verify that when a side passes through the center of dilation, the side
and its image lie on the same line
Verify that corresponding sides of the preimage and image are parallel
Identify if a scale factor reduces or enlarges an image
CCSS: G-SRT.1
MACLE: GSR.1.A; GSR.3.A
•
•
Use triangle similarity to solve problems (indirect measure, missing
sides/angle measures, side splitting)
Use similarity ratios for sides, perimeters, and areas to find missing
measures
CCSS: G-SRT.5
MACLE: GSR.1.A
Approved 7-15-13
Revised 2013
14
Geometry
Instructional Strategies
•
•
•
•
•
Lecture enhanced with:
• SMART Notebook
• PowerPoint
• the Internet
Drill and guided practice
Reflective discussion
Class discussion
Game: Jeopardy game on:
• congruence
• similarity
• dilations (under development)
Assessments/Evaluations
The students will be assessed on the concepts taught using a variety of modalities:
• Direct teacher observations
• Projects with scoring guides:
• The students will design a scale-down version of a new high school for the Jefferson City Public Schools
• The teacher will provide an entry document that will provide the necessary information to students to get started on their project (under
development)
• Quizzes
• Homework assignments
• Formal common assessment – Unit E test
Mastery Level: 80%
Approved 7-15-13
Revised 2013
15
Geometry
Instructional Resources/Tools
•
•
•
•
Textbook(s): Bass et al., Prentice Hall Mathematics Geometry. Boston: Pearson/Prentice Hall, 2004.
Website(s): www.khanacademy.org
Scientific calculator
Computer simulation software:
• Congruence
• Similarity
apps, if available
Approved 7-15-13
Revised 2013
16
Geometry
Conceptual Category(s)
Domain
Cluster
Alignments:
CCSS: See below
Performance: 1.6, 1.10, 3.4
Knowledge: (MA) 2,4
MACLE: See below
NETS: 3d; 4c; 6b
DOK: 1-3
•
•
•
•
Geometry
Similarity, Right Triangles, and Trigonometry (G-SRT)
Prove theorems involving similarity (G-SRT.4)
Define trigonometric ratios and solve problems involving right triangles (G-SRT.6-8)
Standards
G-SRT.4, 6-8
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
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
7. Explain and use the relationship between the sine and cosine of
complementary angles
8. Use trigonometric ratios and the Pythagorean Theorem to solve
right triangles in applied problems
Learning Targets
Unit F: Right Triangle Trigonometry: Solve problems involving right
triangles using the Pythagorean Theorem and its converse, geometric mean,
or trigonometric ratios
•
•
•
Prove the Pythagorean using triangle similarity
Use the Pythagorean Theorem to find the missing length of a right
triangle
Use the Converse of the Pythagorean Theorem to determine if a triangle
is right, acute or obtuse
CCSS: G-SRT.4,8
MACLE: GSR.1.A
•
Use the properties of 45-45-90 and 30-60-90 triangles to determine
missing sides of a triangle
CCSS: G-SRT.6
MACLE: M.2.B
•
Use the concept of geometric mean to find missing lengths in right
triangles
CCSS: G-SRT.6
MACLE: M.1
Approved 7-15-13
Revised 2013
17
Geometry
•
•
Use sine, cosine and tangent ratios to determine side lengths and angles
in right triangles
Use angles of elevation/depression to solve problems
CCSS: G-SRT.7
MACLE: GSR.1.A
Instructional Strategies
•
•
•
•
•
•
•
•
Lecture enhanced with:
• SMART Notebook
• PowerPoint
• the Internet
• Applets
• Geometer’s Sketchpad (or similar software)
Guided and independent practice
Demonstrations: e.g., Proving the Pythagorean Theorem using similarity and areas – see the website
Problem solving: e.g., Finding the height of a flag pole, or other structure on school grounds, using trigonometric ratios
Reflective discussion
Class discussion
Computer assisted instruction (may be used with Geometer’s Sketchpad or similar software)
Station review
Assessments/Evaluations
The students will be assessed on the concepts taught using a variety of modalities:
• Direct teacher observations
• Project with scoring guides: “Light for All Seasons” project – adapted from: Discovering Geometry, Key Curriculum Press, Serra, 2008
(under development)
• Quizzes
• Homework assignments: see pacing guide
• Formal common assessment – Unit F test
Mastery Level: 80%
Approved 7-15-13
Revised 2013
18
Geometry
Instructional Resources/Tools
•
•
•
Textbook: Bass et al., Prentice Hall Mathematics Geometry. Boston: Pearson/Prentice Hall, 2004.
Website(s):
• Similar right triangles and the geometric mean applet (2013)
• http://www.mathwarehouse.com/geometry/similar/triangles/geometric-mean.php
• Proof of the Pythagorean Theorem with animation (2013)
• http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.html
• Trigonometry angles of elevation/depression practice (2013)
• http://illuminations.nctm.org/LessonDetail.aspx?id=L383
Scientific calculator
Approved 7-15-13
Revised 2013
19
Geometry
Conceptual Category(s)
Domain
Cluster
Alignments:
CCSS: See below
Performance: 1.10, 1.6
Knowledge: (MA) 2
MACLE: See below
NETS: 3d; 4c; 6b
DOK: 1-4
•
•
•
•
•
•
Geometry
Geometric Measurement and Dimension (G-GMD)
Modeling with Geometry (G-MG)
Explain volume formulas and use them to solve problems (G-GMD.3)
Visualize relationships between two-dimensional and three-dimensional objects (G-GMD.4)
Apply geometric concepts in modeling situations (G-MG.1-3)
Standards
G-GMD.3, 4:
3. Use volume formulas for cylinders, pyramids, cones and spheres
to solve problems
4. Identify the shapes of two-dimensional cross-sections of threedimensional objects and identify three-dimensional objects
generated by rotations of two-dimensional objects
G-MG.1-3:
1. Use geometric shapes, their measures, and their properties to
describe objects
2. Apply concepts of density based on area and volume in modeling
situations
3. Apply geometric methods to solve design problems
Learning Targets
Unit G: Area, Surface Area, and Volume: Find and apply area, surface
area and volume of various two and three-dimensional figures
•
Find and apply the area of triangles, quadrilaterals and regular
polygons
CCSS: G-MG.2
MACLE: M.2.C
•
•
Identify the cross sections of three-dimensional objects
Identify the three-dimensional figure whose cross section is given
CCSS: G-GMD.4
MACLE: M.2.C
•
Find and use surface area and volume of spheres, prisms, cylinders,
pyramids and cones
CCSS: G-GMD.3
MACLE: M.2.C
Approved 7-15-13
Revised 2013
20
Geometry
•
Approximate surface area and volume of real-world objects
CCSS: G-MG.1
MACLE: M.2.C
Instructional Strategies
•
•
•
•
•
Lecture enhanced with:
• SMART Notebook
• PowerPoint
• internet practice
Drill and guided practice
Demonstrations:
• Net Packaging Explorer (in SMART Notebook)
• Three-dimensional manipulatives
Reflective discussion
Class discussion
Assessments/Evaluations
The students will be assessed on the concepts taught using a variety of modalities:
• Direct teacher observations
• Quizzes
• Homework assignments
• Formal common assessment – Unit G test
Mastery Level: 80%
Approved 7-15-13
Revised 2013
21
Geometry
Instructional Resources/Tools
Textbook(s): Bass et al., Prentice Hall Mathematics Geometry. Boston: Pearson/Prentice Hall, 2004.
Website(s):
• http://www.wisc-online.com/Objects/ViewObject.aspx?ID=GEM1304
• http://www.regentsprep.org/Regents/math/ALGEBRA/AS2/PracSol.htm
• http://www.ixl.com/math/geometry/surface-area-of-prisms-and-cylinders
• http://www.ixl.com/math/geometry/surface-area-of-pyramids-and-cones
• http://www.ixl.com/math/geometry/volume-of-prisms-and-cylinders
• http://www.ixl.com/math/geometry/volume-of-pyramids-and-cones
• http://www.ixl.com/math/geometry/surface-area-and-volume-of-spheres
• http://www.ixl.com/math/geometry/surface-area-and-volume-of-similar-solids
• Scientific calculator
•
•
Approved 7-15-13
Revised 2013
22
Geometry
Conceptual Category(s)
Domain
Cluster
Alignments:
CCSS: See below
Performance: 1.6, 3.4
Knowledge: (MA) 2
MACLE: See below
NETS: 1a; 4b
DOK: 1-3
•
•
•
•
•
•
Geometry
Circles (G-C)
Congruence (G-CO)
Understand and apply theorems about circles (G-C.2-5)
Experiment with transformations in the plane (G-CO.1)
Make geometric constructions (G-CO.13)
Standards
G-C.2-5
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
3. Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle
4. (+) Construct a tangent line from a point outside a given circle to
the circle
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-CO.1, 13
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
13. Construct an equilateral triangle, a square, and a regular hexagon
inscribed in a circle
Approved 7-15-13
Learning Targets
Unit H: Circles: Understand and apply theorems about circles
•
•
•
•
Recall definitions of center, diameter, radius, and circumference
Review measures of central angles, inscribed angles, and angles
formed by two tangents or a tangent and a chord
Find the measures of angles formed by two chords
Understand and use the properties of chords
CCSS: G-C.2
MACLE: M.2.B
•
•
•
•
Understand the definitions of tangent and secant
Find the measures of angles formed by tangent lines and secant lines
Find the measures of angles formed by two secant lines
Construct a line tangent to a circle from a point outside the circles
CCSS: G-C.2,4
MACLE: M.2.B
Revised 2013
23
Geometry
•
•
Circumscribe a circle about a triangle
Inscribe a circle in a triangle
CCSS: G-C.3
MACLE: M.2.B
•
•
•
Understand the properties of quadrilaterals inscribed in a circle
Construct a square inscribed in a circle
Construct a regular hexagon inscribed in a circle
CCSS: G-C.3; G-CO.13
MACLE: M.2.B
•
•
Understand and find the length of an arc of a circle
Construct an equilateral triangle in a circle
CCSS: G-CO.1; G-CO.13
MACLE: M.2.B
•
Understand and find the areas of sectors and segments of a circle
CCSS: G-C.5
MACLE: M.2.C
Instructional Strategies
Lecture enhanced with:
• SMART Notebook
• PowerPoint
• Drill and guided practice
• Reflective discussion
• Class discussion
•
Approved 7-15-13
Revised 2013
24
Geometry
Assessments/Evaluations
The students will be assessed on the concepts taught using a variety of modalities:
• Direct teacher observation
• Quizzes
• Homework assignments
• Formal common assessment – Unit H test
Mastery Level: 80%
Instructional Resources/Tools
•
•
•
Textbook: Bass et al., Prentice Hall Mathematics Geometry. Boston: Pearson/Prentice Hall, 2004.
Website: http://www.mathwarehouse.com/geometry/circle/index.php
Scientific calculator
Approved 7-15-13
Revised 2013
25