Download Geometry Curriculum Map/Pacing Guide

CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
# of Blocks
CP
HN
121
77.5
Unit 1: Tools of
Geometry
15
9
How do you find length, area?
2
1
What are the basic tools and
concepts of geometry?
ow do we measure line segments and
angles?
1
3
2
1
0
0.5
How do we use the Distance
Formula?
ow do we use the Midpoint
Formula?
How do we identify parallel and
perpendicular lines?
page 1 of 16
Students will be able to...
Totals Always Include 2 blocks for Review & Test
book
Geometry
PH 2004
Geometry Activity binder, District Google
Documents site
• find area/perimeter of rectangles, triangles,
1.7
circles, composites.
1.2, 1.3
• identify and define the basic tools of geometry
(Line, point, plane, etc.)
1.4, 1.5
• measure & construct segments, angles,
triangles, bisectors
• measure figures, and find midpoint and distance
1.6
on the coordinate plane
• complete PSAT, MCAS MCQs/SAQs/ORQs
• complete PSAT, MCAS MCQs/SAQs/ORQs
2
0.5
• identify and define parallel and perpendicular
lines
• use slope to determine whether lines are
parallel or perpendicular
3.5, 3.6
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
Resources/Assessments
other
# of Blocks
CP
HN
page 2 of 16
Students will be able to...
book
Resources/Assessments
other
Unit 1: Tools of
Geometry (continued)
Geometry
PH 2004
2
2
1
2
How do we prove that lines are
parallel?
How do we determine angle measure
when parallel lines are cut by a
transversal?
• plan and write paragraph, flow chart and two
column proofs, distinguishing between properties, 2.1 - 2.5
postulates and theorems
• write conditional statements & their converses
• write proofs using the Alternate Interior Angles,
3.2, 3.2
Alternate Exterior Angles, & Corresponding
Angle Theorems
• determine angle measure when parallel lines
3.1, 3.2
are cut by a transversal
• explain the relationship between the types of
angles created when parallel lines are cut by a
transversal
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
# of Blocks
CP
HN
Unit 2: Triangles
25
How do we classify triangles by sides
and angle?
1
What are the relationships between
the sides and angles of a triangle?
What is the Triangle Inequality
postulate?
10
0.5
0.5
2
1
page 3 of 16
Students will be able to...
Totals Always Include 2 blocks for Review & Test
• define, identify, and classify triangles by sides
(scalene, isosceles, equilateral) and angles
(acute, equiangular, obtuse).
• understand the Side-Angle Postulate
• justify the Side-Angle Postulate in informal
proofs
• solve problems involving the Triangle Inequality
Postulate
book
Geometry
PH 2004
3.3
5.5
Resources/Assessments
other
Geometry Activity binder, District Google
Documents site
What is the Triangle Inequality
postulate?
What are the special segments within
a triangle?
What are the relationships between
the special segments within
triangles?
How do we determine if triangles are
congruent?
4
0.5
1
0.5
5
2
• justify the Triangle Inequality Postulate in
informal proofs
• identify and solve problems involving
midsegments, altitudes, and medians
• identify and solve problems involving incenter,
orthocenter, circumcenter, and centroid.
(Centroid-CP, all else Honors)
• understand the “shortcuts” for determining
congruency in triangles (ASA/SAA/SAS)
• complete PSAT, MCAS MCQs/SAQs/ORQs
5.1 - 5.3
5.3
4.1 - 4.3,
4.6
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
# of Blocks
CP
HN
page 4 of 16
Students will be able to...
Unit 2: Triangles
(continued)
How do we prove that triangles are
congruent?
book
Geometry
PH 2004
3
2
7
1
How do we determine if triangles are
similar?
• write proofs using the congruency postulates
• identify similar triangles, and solve problems
involving proportion
• identify minimum information to know if
triangles are similar (AA, SSS~, SAS~)
4.4, 4.5,
4.7
8.1 - 8.5
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
Resources/Assessments
other
# of Blocks
CP
HN
page 5 of 16
Students will be able to...
book
Resources/Assessments
other
Unit 3: Similarity &
Trigonometry
13
9
What are the special properties of
right triangles?
How can we use the Pythagorean
Theorem & its converse?
4
2
Totals Always Include 2 blocks for Review & Test
Geometry
PH 2004
• use geometric mean/similarity to solve problems
8.4
• solve with Pythagorean Theorem
•
deduce obtuse,acute,right with Pythagorean
Thoerem
7.2
Geometry Activity binder, District Google
Documents site
GSP Demos Ch 09
• use 3,4,5 and 5,12,13 Pythagorean Triples
1
0.5
1
0.5
5
4
What are special right triangles?
What are the 3 Trigonometric
Ratios?
• complete PSAT, MCAS MCQs/SAQs/ORQs
• solve problems involving 45-45-90 and 30-607.3
90 triangles
• apply the properties of special right & similar
7.3
triangles to determine the missing side of a given
triangle
• solve problems with trigonometry & use trig
tables & calculators for ratios
• connect 9.1 - 9.3
tangent ratio to slope of lines
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
Unit 4: Polygons
How can a polygon be classified?
How can the sum of a polygon's
interior angles be determined when
only the number of sides is known?
# of Blocks
CP
HN
16
10
1
0.5
2
1
Trig Ratio Tables p731
IMP 1: Return of the Tree
page 195 EGwGSP
page 6 of 16
Students will be able to...
Totals Always Include 2 blocks for Review & Test
• classify polygons based on number of sides
(quadrilateral, triangle, etc.) concave/convex,
regular/irregular
• determine the sum of the interior and exterior
angles of a polygon
book
Resources/Assessments
other
Geometry
PH 2004
Geometry Activity binder, District Google
Documents site
3.4
Ch5 Discovering Geometry
3.4
GSP Demos Ch 5
How can the sum of a polygon's
interior angles be determined when
only the number of sides is known?
How can it be determined if two
polygons are similar?
How can quadrilaterals be classified
using properties of sides, angles and
diagonals?
2
4
1
1
• decompose polygon into triangles
• solve problems using the formulas for interior
and exterior angles of polygons to determine the
measure of missing angles
• apply properties of similar figures to determine
8.2
if two polygons are similar
• apply properties of similar figures to determine
the length of missing sides and the measure of
missing angles in similar polygons using
proportions
• use knowledge of angles, sides and diagonals in
6.1, 6.2
order to classify quadrilaterals
• complete PSAT, MCAS MCQs/SAQs/ORQs
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
# of Blocks
CP
HN
Students will be able to...
book
Geometry
PH 2004
1
1
0.5
1
1
What makes a good definition?
EGwGSP page 112-113
Golden Ratio applies to credit cards, business
cards
GSP Demos Ch 01
CH 4 of EGwGSP
page 104-105 EGwGSP,
http://www.keymath.com/x19428.xml
page 7 of 16
Unit 4: Polygons
(continued)
1
http://www.keymath.com/x19426.xml
• use properties of quadrilaterals (sides,
diagonals, angles, and diagonals) to solve
problems involving squares, rectangles,
parallelograms, etc.
• define classes of quadrilaterals with biconditionals
• justify postulates about the special
quadrilaterals using informal proof
6.2 - 6.5
Resources/Assessments
other
How do we prove a conjecture?
2
2
• write proofs of quadrilateral theorems using the
properties of congruence, and angle postulates
Geometry Midterm Review
are the essential elements of
2What
blocks
4
3
• complete practice review problems that
summarize the terms’ work
Geometry?
6.3
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
# of Blocks
CP
HN
Unit 5: Circles
10
What types of lines and line segments
are associated with circles?
1
What are the special ratios of
circles?
1
3
What relationships exist among the
measures of central and inscribed
angles and arcs?
8.5
1
0.5
2
page 8 of 16
Students will be able to...
Totals Always Include 2 blocks for Review & Test
• classify special segments of circles (radius,
diameter, chord, secant, tangent, arc)
• demonstrate an understanding of circle ratios:
radius-diameter, diameter-circumference, pi
• solve problems for the circumference, diameter,
and radii of circles
• solve problems relating inscribed angles,
intercepted arcs, radii, tangent segments, secant
segments, chords*
• apply proportions to chords, tangents,
secants,radii*
• demonstrate understanding of the relationships
between the measures of central and inscribed
angles and arcs
book
Geometry
PH 2004
7.6
7.6
11.1 11.4
Resources/Assessments
other
Geometry Activity binder, District Google
Documents site
What relationships exist among the
measures of central and inscribed
angles and arcs?
• apply mean to vertical angles between
intercepted arcs
• complete PSAT, MCAS MCQs/SAQs/ORQs
11.1 11.4
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
# of Blocks
CP
HN
page 9 of 16
Students will be able to...
Unit 5: Circles
(continued)
How can the relationship between
arcs and angles be used to find the
length or measure of arcs?
How do we prove circle conjectures?
book
Geometry
PH 2004
2
1
1
2
• solve problems for the measurements of central
and inscribed angles, arc angles, the
measurements of angles and arcs formed by
secants and tangents
• write indirect proofs in paragraph and twocolumn format to prove theorems of circles,
involving conjectures, tangents, inscribed angles,
and parallel lines
11.1 11.4
11.1 11.4
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
Unit 6: Measuring 2D
Figures
How are triangles measured using
properties to deduce missing
information?
Resources/Assessments
other
# of Blocks
CP
HN
page 10 of 16
Students will be able to...
8
7
Totals Always Include 2 blocks for Review & Test
2
1
• differentiate between perimeter and area
book
Geometry
PH 2004
Resources/Assessments
other
Geometry Activity binder, District Google
Documents site
• deduce altitude of equilateral triangle
How are triangles measured using
properties to deduce missing
information?
• solve for the perimeter and area of triangles
using triangle formulas (i.e. area, Pythagoras,
Special Right Triangles, Trig)
2
3
How are quadrilaterals measured
using properties to deduce missing
information?
How are perimeter and/or area of
regular polygons found?
How are circles measured using
properties to deduce missing
information?
1
0.5
1
0.5
• differentiate between perimeter and area
• solve for the perimeter and area of
quadrilaterals (parallelograms vs. trapezoids)
using area formulas
• connect mean to trapezoid area formula
• complete PSAT, MCAS MCQs/SAQs/ORQs
• solve problems using the lengths of segments
and apothems to solve for the perimeter and/or
area of regular polygons
• solve problems for the circumference and area
of circles andcalculate the arc length and area of
sectors with proportions
• complete PSAT, MCAS MCQs/SAQs/ORQs
7.1 - 7.4
7.4
7.5
7.6, 7.7
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
Unit 7: Measurement in
Space
# of Blocks
CP
HN
10
6
What does 3-D mean?
1
How can polyhedrons be named?
0.5
page 11 of 16
Students will be able to...
Totals Always Include 2 blocks for Review & Test
• differentiate between 2D and 3D figures.
identify appropriate measurement units (i.e.
units², units³)
•
differentiate between bases and faces of prisms
• explore net diagrams
book
Geometry
PH 2004
10.1, 10.2
Resources/Assessments
other
Geometry Activity binder, District Google
Documents site
How is the lateral surface area of an
object found?
2
1.5
What are the formulas used to solve
for it?
How is the total surface area of an
object found?
• demonstrate understanding of lateral
• surface area as total surface area minus the
base area(s)
• solve for 10.3, 10.4
the total lateral area of objects in space using
lateral surface area formulas
• complete real-world modeling problems
2
0.5
What are the formulas used to solve
for it?
• differentiate between total surface area and
lateral surface area of an object
• solve for the total surface area of objects in
space using surface area formulas
• identify and calculate slant height
complete real-world modeling problems
10.7
10.3, 10.4
10.7
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
# of Blocks
CP
HN
page 12 of 16
Resources/Assessments
Students will be able to...
Unit 7: Measurement in
Space (continued)
How does one measure the space
inside 3D figures?
Geometry
PH 2004
1
1
What is volume?
What are the relationships between
perimeter scale factors and
area/volume ratios?
book
2
0.5
• demonstrate understanding of volume as a
measurement in cubic units
• select
10.5, 10.6
and differentiate between the volume formulas
necessary to solve problems
10.7
• complete real-world modeling problems
• identify scale factors for given polyhedrons
based on perimeter calculations (units)
• use the scale factor to calculate the area and
volume ratios (units², units³)
10.8
other
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
# of Blocks
CP
HN
page 13 of 16
Students will be able to...
book
Geometry
PH 2004
Unit 8: Transformations
7
5
What is a transformation?
2
0.5
• understand the basic concepts of
transformations, including image/pre-image,
isometry
0.5
• identify and define translation, reflection, and
rotation on and off the coordinate plane
12.2, 12.3
0.5
• complete PSAT, MCAS MCQs/SAQs/ORQs
• understand dilation and apply the concept of
scale factor to figures
• complete real-world modeling problems
12.7
What is an isometry?
When do we use dilation?
1
Totals Always Include 2 blocks for Review & Test
Resources/Assessments
other
Geometry Activity binder, District Google
Documents site
12.1
******MCAS Review******
1
0.5
• understand the concept of composition
• identify multiply transformations, including
glide reflections, reflections over parallel lines
(translation), and reflections over intersecting
lines (rotations)
How are composite transformations
created?
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
12.4
# of Blocks
page 14 of 16
Resources/Assessments
Essential Questions
CP
HN
Students will be able to...
Unit 8: Transformations
(continued)
book
other
Geometry
PH 2004
1
1
When are tessellations useful?
• identify when tessellations are used in the real
world
• create tessellations using chosen transformation
12.6
• identify the vertex arrangements of
tessellations, note sum of degrees
************NOTE: Alternative Assessment: Tessellation Drawing Project, Geometer's Sketchpad Kaleidoscope (pg 661)***************
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
Unit 9: Statistics &
Geometric Probability
# of Blocks
CP
HN
8
6
Why do we look at data? How can it
best be represented?
1
1
page 15 of 16
Students will be able to...
Totals Always Include 2 blocks for Review & Test
• classify different methods of data collection and
graphic representation such as frequency tables,
box-and-whisker, and stem-leaf plots, scatterplots
book
Resources/Assessments
other
Geometry
PH 2004
Geometry Activity binder, District Google
Documents site
7.6
Skills Handbook
1
1
• classify different methods of data collection and
pp. 712 graphic representation such as frequency tables,
714
box-and-whisker, and stem-leaf plots, scatterplots
1
• demonstrate understanding of mean, median,
mode, and range of data by solving central
tendency problems
• select
appropriate measures of central tendency to
adequately interpret data
What are some of the ways
quantitative data can be
represented?
How can one interpret quantitative
data?
2
What is a measure of central
tendency?
What generalizations can you draw
from a given set of data?
8.4
• complete PSAT, MCAS MCQs/SAQs/ORQs
1
0.5
• demonstrate understanding of weighted
frequency and line-of-best-fit with graphic
representations
3.5
• complete PSAT, MCAS MCQs/SAQs/ORQs
CRLS Mathematics Department
Geometry Curriculum Map/Pacing Guide
Understanding Goals/
Essential Questions
# of Blocks
CP
HN
page 16 of 16
Resources/Assessments
Students will be able to...
Unit 9: Statistics &
Geometric Probability
(continued)
What is the likelihood that an
outcome will occur?
book
Geometry
PH 2004
2
1.5
• use lengths, areas to calculate probability
pp 723 724
other
• find P(dart in bull's eye)
• solve problems for the probability of an event
occurring
Geometry Final Review
What are the essential elements of
Geometry?
5
4
• complete practice review problems that
summarize the year/semesters’ work
7.8