Download first quarter - Peoria Public Schools

GEOMETRY 1-2 ENRICHED
FIRST QUARTER
Geometry: For Enjoyment and Challenge, McDougal Littell (1991) ISBN 0-86609-965-4
While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following
topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, binomial
expansion, graphing equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, and solving systems
of equations and inequalities, and coordinates.
CCSS
Specific Topic
Algebra Review (1 week)
 Solving linear equations
 Graphing linear equations
 Equations of lines
 Systems of equations
G.CO.1
G.CO.12
G.GPE.6
G.CO.2
G.CO.3
G.CO.4
G.CO.5
G.CO.6
G.CO.7
G.CO.8
G.CO.12
Introduction to Geometry
 Define basic geometric terms and symbols
 Apply deductive reasoning
 Define structure of postulates, theorems,
and definitions
 Introduce format of 2-column and paragraph
proofs
 Define complementary and supplementary
angle relationships
Congruence and Transformational
Geometry
 Recognize, use, and compute
transformations of rigid motion; including
reflections, translations, and rotations.
 Recognize, use, and compute
transformations of rigid motion
 Transformations (Reflections, Translations,
Rotations)
 Input-output functions for translations,
rotations, reflections
 Composite transformations to map figures
onto other figures
 Use of translations, rotations, reflections to
establish triangle congruency
 Apply definitions, postulates, and theorems
to establish triangle congruence using
side/angle criteria (SSS, SAS, ASA, AAS)
 Utilize congruent triangles to expand on
theorems including CPCTC, overlapping
triangles, medians and altitudes, etc.
Teacher Resources
Measurements &
Constructions
Algebra Review
Chapter 13: 13.1-13.3
Chapter 1: 1.1 – 1.2
Chapter 2: All sections
Segment lengths
Angle measures
Segment Bisectors
Angle Bisectors
Perpendicular Lines
 Solve linear
equations
Chapter 14: 14.4
Congruent segments
Congruent Angles
Chapter 14
Median
Chapter 3: All sections
Altitude
Concurrence lines
(14.3):
Centroid
(Medians)
Orthocenter
(Altitudes)
Incenter
(Angle Bisectors)
 Solving equations
from CPCTC
 Coordinate plane
Properties of Triangles
 Classify triangles based on side lengths and
angle measures.
G.CO.10
G.CO.13
Properties of Triangles
 Apply triangle theorems involving angles,
exterior angles, and side lengths.
o
Triangle Sum Theorem
o
Isosceles Triangle Theorems
Chapter 4: 4.2,4.3
 Solve linear
equations
Chapter 3: 7.1
Chapter 3: 5.2,5.3
Common Core State Standards for Mathematics
STANDARDS FOR MATHEMATICAL PRACTICE
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and express regularity in repeated reasoning.
8 Look for and make use of structure.
Check the district website for additional math resources and information:
www.psd150.org
June 2013
GEOMETRY 1-2 ENRICHED
SECOND QUARTER
While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following
topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, binomial
expansion, graphing equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, and solving systems
of equations and inequalities.
CCSS
G.CO.10
G.CO.13
G.CO.1
G.CO.8
G.CO.9
G.CO.12
G.GPE.5
G.CO.3
G.CO.11
G.GPE.4
G.GPE.5
Specific Topic
Properties of Triangles
 Apply triangle theorems involving angles,
exterior angles, and side lengths.
o
Exterior Angle Theorem
o
Triangle Inequality a+b>c
 Construct and locate the perpendicular
bisector of a segment
 Apply theorem stating points on the
perpendicular bisector of a segment are
equidistant from the endpoints
Parallel and Perpendicular Line
Relationships
 Define relationship between slopes and
angle measures of parallel and
perpendicular lines.
 Apply transversals and parallel lines to find
associated angle pairs including AIA, AEA,
Corresponding, SSI, & SSE.
Properties of Polygons
 Classify quadrilaterals based on
distinguishing characteristics.
 Prove theorems about sides, angles, and
diagonals of quadrilaterals.
 Classify polygons by # of sides,
regular/irregular, and concave / convex.
 Calculate interior and exterior angle
measures.
Teacher Resources
Chapter 4: 4.2-4.4
Chapter 7: 7.1
Chapter 15: 15.2
Chapter 5: 5.2,5.3
Chapter 5: 5.4-5.7
Chapter 7: 7.3-7.4
Measurements &
Constructions
Algebra Review
Perpendicular
Bisector
Concurrence lines
(14.3):
Circumcenter
(Perp. Bisectors)
Parallel Lines
 Solve linear
equations
 Systems of
equations
 Many algebra
applications with
equations
established in
these theorems
 Create equations
for diagonals
bisecting each
other, diagonals
that are congruent
or perpendicular
legs in isosceles
trapezoid
congruent
 Use formulas
 Linear equations
Common Core State Standards for Mathematics
STANDARDS FOR MATHEMATICAL PRACTICE
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and express regularity in repeated reasoning.
8 Look for and make use of structure.
Check the district website for additional math resources and information:
www.psd150.org
June 2013
GEOMETRY 1-2 ENRICHED
THIRD QUARTER
While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following
topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, binomial
expansion, graphing equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, and solving systems
of equations and inequalities.
CCSS
G.CO.2
G.CO.10
G.SRT.1
G.SRT.2
G.SRT.3
G.SRT.4
G.SRT.5
G.SRT.5
G.SRT.6
G.SRT.7
G.SRT.8
G.SRT.10*
G.SRT.11*
G.GPE.7
G.CO.1
G.CO.13
G.C.1
G.C.2
G.C.3
G.C.4*
G.C.5
G.GPE.1
G.GPE.4
Specific Topic
Teacher Resources
Measurements &
Constructions
Algebra Review
Similarity
 Definitions
 Utilize dilations and reductions to establish
similarity
 Solve problems involving similar shapes and
proportions
 Apply similarity theorems including Midline
Theorem, Side-splitter Theorem, 3+ parallel
lines divided proportionally
Chapter 8: All sections
 Properties of ratio
and proportion
 Cross product
property
 Proportions
Right Triangles
 Apply similarity in right triangles to utilize the
altitude on hypotenuse theorems.
 Use Pythagorean Theorem, special right
triangles, and trigonometric ratios to solve
right triangles.
 Apply the distance formula to find lengths of
segments.
 *Calculate measures of missing sides and
angles of non-right triangles using the Law
of Sines and Law of Cosines
Chapter 9: All sections
 Solving quadratic
equations
 Simplify radicals
 Distance formula
 Geometric mean
Circles
 Identify and calculate measures of parts of
circles; including radii, diameters,
circumference, arc length, area, and sector
area.
 Define and solve problems involving
inscribed and circumscribed polygons.
 Determine measures of angles and arcs;
including minor arcs, major arcs,
semicircles, central angles, inscribed angles,
and angles related to tangents, chords, and
secants.
 Determine lengths of segments related to
tangents, chords, and secants.
Chapter 10: All sections
Chapter 13: 13.6 (Equations)
*Construct a tangent
to a circle from an
exterior point.
 Equations of circle
in coordinate
plane
 Using Formulas
Common Core State Standards for Mathematics
STANDARDS FOR MATHEMATICAL PRACTICE
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and express regularity in repeated reasoning.
8 Look for and make use of structure.
Check the district website for additional math resources and information:
www.psd150.org
June 2013
GEOMETRY 1-2 ENRICHED
FOURTH QUARTER
While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following
topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, graphing linear
equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, binomial expansion, and solving systems
of equations and inequalities.
CCSS
Specific Topic
Teacher Resources
Measurements &
Constructions
Algebra Review
Circles Continued (Be more specific)
G.GPE.7
G.SRT.9*
G.GMD.3
2-D Figures
 Calculate areas of individual and composite
2-D figures including triangles,
quadrilaterals, and regular polygons
 *Find area of non-right triangles using
formula A=(1/2) ab sin (c)
 Determine ratios of perimeters and areas of
similar figures.
Chapter 11: All sections
 Formulas
 Solving Equations
3-D Figures
 Calculate surface area and volume of right
prisms, regular pyramids, cylinders, cones,
and spheres.
 Determine ratios of volumes of similar
figures.
Chapter 12: All sections
 Using formulas
Common Core State Standards for Mathematics
STANDARDS FOR MATHEMATICAL PRACTICE
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and express regularity in repeated reasoning.
8 Look for and make use of structure.
Check the district website for additional math resources and information:
www.psd150.org
June 2013
GEOMETRY 1-2 ENRICHED
Additional Content (Temp collection area)
While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following
topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, graphing linear
equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, binomial expansion, and solving systems
of equations and inequalities.
CCSS
Specific Topic
Teacher Resources
Measurement
s&
Construction
s
Algebra
Review
Translate between the geometric description and the equation for a
conic section
G.GPE.2. Derive the equation of a parabola given a focus and directrix.
G.GPE.3. (+) Derive the equations of ellipses and hyperbolas given the foci,
using the fact that the sum or difference of distances from the foci is constant.
G.GPE.2*
G.GPE.3*
G.GMD.1*
G.GMD.2*
G.GMD.4*
G.MG.1*
G.MG.2*
G.MG.3*
Explain volume formulas and use them to solve problems
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.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.
Apply geometric concepts in modeling situations
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.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).
Chapter 13
13.1-Graphing Equations
13.2-Equations of lines with parallel and perp
13.3-Systems of equations
13.4-Graphing linear inequalities
13.5-3D Graphing w/ distance formula & reflections
13.6-Equations of Circles
13.7-General Coordinate Geometry
14.3 – Orthocenter, incenter, orthocenter, centroid
Chapter 14
14.1-Locus
14.2-Compound Locus
14.3-Concurrence Theorems
14.4-Basic Constructions
14.5-Applications of Constructions
14.6-Triangle Constructions
14.4 – Constructions
1. Segment Copy
2. Angle Copy
3. Angle Bisector
4. Perpendicular Bisector
5. Erecting Perp
6. Dropping a Perp
14.5 – Applications of Constructions
1. Parallels
2. Segment Divisions
3. Mean proportional
4. Fourth proportional
Common Core State Standards for Mathematics
STANDARDS FOR MATHEMATICAL PRACTICE
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and express regularity in repeated reasoning.
8 Look for and make use of structure.
Check the district website for additional math resources and information:
www.psd150.org
June 2013