Download 2016 – 2017 - Huntsville City Schools

Huntsville City Schools - Instructional Guide
2016 – 2017
Course: Geometry
Grades: 9-11
Color Clarifications:
Green has to do with pacing/timing/scheduling of materials.
Pink has to do with differentiating between Regular Geometry and Honors Geometry.
Yellow places emphasis on a particular portion of a standard pertinent to that teaching unit.
Blue signifies that the standard is a power standard.
Table of Contents:(If you are viewing this document in Microsoft Word, hold the “Control” key and click on the Unit you want to view in order to go directly to
that unit. If you are viewing the document as a PDF, just click on the link.)
Unit 1 - First 9-weeks .................................................................................................................................................................................................... 2
Unit 2 - First 9-weeks .................................................................................................................................................................................................. 10
Unit 3 - First 9-weeks .................................................................................................................................................................................................. 12
Unit 4 - Second 9-weeks .............................................................................................................................................................................................. 13
Unit 5 - Second 9-weeks .............................................................................................................................................................................................. 16
Unit 6a - Second 9-weeks ............................................................................................................................................................................................ 18
Unit 6b - Third 9-weeks ............................................................................................................................................................................................... 19
Unit 7 - Third 9-weeks ................................................................................................................................................................................................. 20
Unit 8 - Third 9-weeks ................................................................................................................................................................................................. 22
Unit 10a - Third 9-weeks ............................................................................................................................................................................................. 24
Unit 10b - Fourth 9-weeks ........................................................................................................................................................................................... 25
Unit 12 - Fourth 9-weeks ............................................................................................................................................................................................. 27
Unit 11 - Fourth 9-weeks ............................................................................................................................................................................................. 29
Unit 9 - Fourth 9-weeks ............................................................................................................................................................................................... 31
Geometry Vocabulary
CCRS Standard
1. [G-CO.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.
Vocabulary
∙Point ∙Line ∙Segment ∙Angle
∙Perpendicular line ∙Parallel line
∙Distance ∙Arc length ∙Ray ∙Vertex
∙Endpoint ∙Plane ∙Collinear ∙Coplanar
∙Skew
CCRS Standard
22. [G-SRT.10] (+) Prove the Laws of
Sines and Cosines and use them to
solve problems.
Vocabulary
∙Law of Sines ∙Law of Cosines
2. [G-CO.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).
∙Transformation ∙Reflection
∙Translation ∙Rotation ∙Dilation
∙Isometry ∙Composition ∙Horizontal
stretch ∙Vertical stretch ∙Horizontal
shrink ∙Vertical shrink ∙Clockwise
∙Counterclockwise ∙Symmetry
∙Preimage ∙Image
23. [G-SRT.11] (+) Understand and
apply the Law of Sines and the Law
of Cosines to find unknown
measurements in right and nonright triangles (e.g., surveying
problems, resultant forces).
∙Law of Sines ∙Law of Cosines
∙Transit ∙Resultant force
3. [G-CO.3] Given a rectangle,
parallelogram, trapezoid, or regular
polygon, describe the rotations and
reflections that carry it onto itself.
∙Transformation ∙reflection
∙translation ∙rotation ∙dilation
∙isometry ∙composition ∙horizontal
stretch ∙vertical stretch ∙horizontal
shrink ∙vertical shrink ∙clockwise
∙counterclockwise ∙symmetry
∙trapezoid ∙square ∙rectangle ∙regular
polygon ∙parallelogram ∙mapping
∙preimage ∙image
24. [G-C.1] Prove that all circles are
similar.
∙Diameter ∙Radius ∙Circle ∙Similar
4. [G-CO.4] Develop definitions of
rotations, reflections, and translations
in terms of angles, circles,
perpendicular lines, parallel lines, and
line segments.
∙Transformation ∙Reflection
∙Translation ∙Rotation ∙Dilation
∙Isometry ∙Composition ∙Clockwise
∙Counterclockwise ∙Preimage ∙Image
25. [G-C.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
∙Central angles ∙Inscribed angles
∙Circumscribed angles ∙Chord
∙Circumscribed ∙Tangent
∙Perpendicular
5. [G-CO.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.
∙Transformation ∙Reflection
∙Translation ∙Rotation ∙Dilation
6. [G-CO.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.
∙Rigid motions ∙Congruence
7. [G-CO.7] Use the definition of
∙Corresponding sides and angles ∙Rigid
congruence in terms of rigid motions to motions ∙If and only if
show that two triangles are congruent
if and only if corresponding pairs of
sides and corresponding pairs of angles
are congruent.
8. [G-CO.8] Explain how the criteria for
triangle congruence, angle-side-angle
(ASA), side-angle-side (SAS), and sideside-side (SSS), follow from the
definition of congruence in terms of
rigid motions.
∙Triangle congruence ∙Angle-SideAngle (ASA) ∙Side-Angle-Side (SAS)
∙Side-Side-Side (SSS)
perpendicular to the tangent where
the radius intersects the circle.
26. [G-C.3] Construct the inscribed
and circumscribed circles of a
triangle, and prove properties of
angles for a quadrilateral inscribed
in a circle.
27. [G-C.4] (+) Construct a tangent
line from a point outside a given
circle to the circle.
28. [G-C.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.
29. [G-GPE.1] Derive the equation of
a circle of given center and radius
using the Pythagorean Theorem;
complete the square to find the
center and radius of a circle given by
an equation.
∙Construct ∙Inscribed and
circumscribed circles of a triangle
∙Quadrilateral inscribed in a circle
∙Opposite angles ∙Consecutive
angles ∙Incenter ∙Circumcenter
∙Orthocenter ∙Angle bisector
∙Altitude ∙Median of a triangle
∙Centroid
∙Tangent line ∙Tangent ∙Point of
tangency ∙Perpendicular
∙Similarity ∙Constant of
proportionality ∙Sector ∙Arc ∙Derive
∙Arc length ∙Radian measure ∙Area of
sector ∙Central angle
∙Pythagorean theorem ∙Radius
9. [G-CO.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 segment's
endpoints.
∙Same side interior angle ∙Consecutive
interior angle ∙Vertical angles ∙Linear
pair ∙Adjacent angles ∙Complementary
angles ∙Supplementary angles
∙Perpendicular bisector ∙Equidistant
∙Theorem Proof ∙Prove ∙Transversal
∙Alternate interior angles
∙Corresponding angles
30. [G-GPE.4] Use coordinates to
prove simple geometric theorems
algebraically. 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).
∙Simple geometric theorems ∙Simple
geometric figures
10. [G-CO.10] Prove theorems about
triangles. Theorems include measures
of interior angles of a triangle sum to
180o, 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.
∙Interior angles of a triangle ∙Isosceles
triangles ∙Equilateral triangles ∙Base
angles ∙Median ∙Exterior angles
∙Remote interior angles ∙Centroid
31. [G-GPE.5] Prove the slope
∙Parallel lines ∙Perpendicular lines
criteria for parallel and
∙Slope
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).
11. [G-CO.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.
∙Parallelograms ∙Diagonals ∙Bisect
32. [G-GPE.6] Find the point on a
directed line segment between two
given points that partitions the
segment in a given ratio.
∙Directed line segment ∙Partitions
∙Dilation ∙Scale factor
12. [G-CO.12] Make formal geometric
constructions with a variety of tools
and methods such as compass and
straightedge, string, reflective devices,
paper folding, and dynamic geometric
software, etc. Constructions include
copying a segment; copying an angle;
bisecting a segment; bisecting an
angle; 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.
∙Construction ∙Compass
33. [G-GPE.7] Use coordinates to
compute perimeters of polygons
and areas of triangles and
rectangles, e.g., using the distance
formula.*
∙Coordinates ∙Cartesian coordinate
system ∙Perimeter ∙Area ∙Triangle
∙Rectangle
13. [G-CO.13] Construct an equilateral
triangle, a square, and a regular
hexagon inscribed in a circle.
∙Construct ∙Inscribed ∙Hexagon
∙Regular
34. [G-GMD.5] Determine areas and
perimeters of regular polygons,
including inscribed or circumscribed
polygons, given the coordinates of
vertices or other characteristics.
(Alabama)
14. [G-SRT.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. ∙The dilation of a
line segment is longer or shorter in the
ratio given by the scale factor.
∙Dilations ∙Center ∙Scale factor
35. [G-GMD.1] Give an informal
argument for the formulas for the
circumference of a circle; area of a
circle; and volume of a cylinder,
pyramid, and cone. Use dissection
arguments, Cavalieri's principle, and
informal limit arguments.
∙Area ∙Perimeter ∙Inscribed polygons
∙Circumscribed polygons ∙Regular
polygons ∙Apothem ∙Coordinates
∙Vertices ∙Height ∙Radius ∙Diameter
∙Perpendicular bisector ∙Distance
∙Midpoint ∙Slope ∙Classification of
polygons ∙Cartesian coordinate
system
∙Dissection arguments ∙Cavalieri's
Principle ∙Cylinder ∙Pyramid ∙Cone
∙Ratio ∙Circumference
∙Parallelogram ∙Limits ∙Conjecture
∙Cross-section
15. [G-SRT.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
the proportionality of all corresponding
pairs of sides. (Alabama)Example 1:
Image Given the two triangles above,
show that they are similar. 4/8 = 6/12
They are similar by SSS. The scale
factor is equivalent. Example 2: Image
Show that the two triangles are similar.
Two corresponding sides are
proportional and the included angle is
congruent. (SAS similarity)
∙Similarity transformation ∙Similarity
∙Proportionality ∙Corresponding pairs
of angles ∙Corresponding pairs of
sides
36. [G-GMD.3] Use volume formulas
for cylinders, pyramids, cones, and
spheres to solve problems.*
∙Cylinder ∙Pyramid ∙Cone ∙Sphere
16. [G-SRT.3] Use the properties of
similarity transformations to establish
the angle-angle (AA) criterion for two
triangles to be similar.
∙Angle-Angle (AA) criterion
37. [G-GMD.6] Determine the
relationship between surface areas
of similar figures and volumes of
similar figures. (Alabama) *
∙Volume ∙Surface area ∙Similar ∙Ratio
∙Dimensions
17. [G-SRT.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.
∙Theorem ∙Pythagorean Theorem
38. [G-GMD.4] Identify the shapes
of two-dimensional cross-sections
of three-dimensional objects, and
identify three-dimensional objects
generated by rotations of twodimensional objects.
∙Two-dimensional cross-sections
∙Two-dimensional objects ∙Threedimensional objects ∙Rotations
∙Conjecture
18. [G-SRT.5] Use congruence and
similarity criteria for triangles to solve
problems and to prove relationships in
geometric figures.
∙Congruence and similarity criteria for
triangles
39. [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).*
∙Model
19. [G-SRT.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.
∙Side ratios ∙Trigonometric ratios ∙Sine
∙Cosine ∙Tangent ∙Secant ∙Cosecant
∙Cotangent
40. [G-MG.2] Apply concepts of
density based on area and volume
in modeling situations (e.g., persons
per square mile, British Thermal
Units (BTUs) per cubic foot).*
∙Density
20. [G-SRT.7] Explain and use the
relationship between the sine and
cosine of complementary angles.
∙Sine ∙Cosine ∙Complementary angles
∙Geometric methods ∙Design
problems ∙Typographic grid system
21. [G-SRT.8] Use trigonometric ratios
and the Pythagorean Theorem to solve
right triangles in applied problems.*
∙Angle of elevation ∙Angle of
depression
41. [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).*
42. [S-MD.6] (+) Use probabilities to
make fair decisions (e.g., drawing by
lots, using a random number
generator).
43. [S-MD.7] (+) Analyze decisions
and strategies using probability
concepts (e.g., product testing,
medical testing, pulling a hockey
goalie at the end of a game).
(Alabama)Example: Image What is
the probability of tossing a penny
and having it land in the non-shaded
region? Geometric Probability is the
Non-Shaded Area divided by the
Total Area.
∙Fair decisions ∙Probability ∙Fair
decisions ∙Random
∙Probability
Unit 1 - First 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
First 9-weeks
Unit 1: Tools for Geometry
12 days
This unit corresponds well with Pearson Geometry Chapter 1, with the first portion of the unit giving emphasis to the building of proper vocabulary and
symbology, while the second portion is emphasizing the application points, lines, and planes, as well as the other learned vocabulary.
ALCOS #1. Know precise definitions of angle,
Pearson: 1.2-1.5
Throughout the
circle, perpendicular line, parallel line, and line
IXL:B.1,C.1,D.1
unit.
segment based on the undefined notions of point,
LTF:
5 days
line, distance along a line, and distance around a
circular arc. [G-CO1]
ALCOS #32. Find the point on a directed line
Pearson: 1.7 (Problem 46)
2 days
segment between two given points that partitions the
IXL:
segment in a given ratio. [G-GPE6]
LTF:
ALCOS #12. Make formal geometric constructions
Pearson: 1.6
1 day
with a variety of tools and methods such as compass
IXL:B.9,C.6,C.7
and straightedge, string, reflective devices, paper
LTF:
folding, and dynamic geometric software.
Constructions include copying a segment; copying an
angle; bisecting a segment; bisecting an angle;
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. [G-CO12]
ALCOS #30. Use coordinates to prove simple
Pearson:1.7
geometric theorems algebraically. [G-GPE4]
IXL:B.7
LTF:
ALCOS #33. Use coordinates to compute perimeters
Pearson: 1.7-1.8
of polygons and areas of triangles and rectangles,
IXL:
e.g., using the distance formula.* [G-GPE7]
LTF:
ALCOS #39. Use geometric shapes, their measures,
and their properties to describe objects (e.g.,
Pearson: 1.8
IXL:
2 days
modeling a tree trunk or a human torso as a
cylinder).* [G-MG1]
ALCOS #40. Apply concepts of density based on
area and volume in modeling situations (e.g., persons
per square mile, British Thermal Units (BTUs) per
cubic foot). [G-MG2]
(Quality Core) D.1.a
Identify and model plane figures, including collinear
and non-collinear points, lines, segments, rays, and
angles using appropriate mathematical symbols
(Quality Core) D.1.b
Identify vertical, adjacent, complimentary, and
supplementary angle pairs and use them to solve
problems (e.g., solve equations, use proofs)
(Quality Core) D.1.e
Locate, describe, and draw a locus in a plane or space
(Quality Core) D.1.f
Apply properties and theorems of parallel and
perpendicular lines to solve problems.
(Quality Core) G.1.b Apply the midpoint and
distance formulas to points and segments to find
midpoints, distances, and missing information.
(Quality Core) F.1.a
Find the perimeter and area of common plane
figures, including triangles, quadrilaterals, regular
polygons, and irregular figures, from given
information using appropriate units of measurement.
(Quality Core) F.1.b
Manipulate perimeter and area formulas to solve
problems (e.g., find missing length)
LTF: Infinity in Geometry (This lesson
shows the derivation of the area of a circle
based on the formula for circumference,
and cutting the circle into tiny sectors.)
Pearson: 1.8
IXL:
LTF:
Pearson: 1.2, 1.4
IXL:
LTF:
Pearson: 1.4, 1.5
IXL:
LTF:
Pearson: 1.2
IXL:
LTF:
Pearson: 1.7
IXL:
LTF:
Pearson: 1.8
IXL:
LTF:
Unit 2 - First 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
First 9-weeks
Unit 2: Reasoning and Proof
11 days
A primary resource for this Unit will be Pearson Geometry, in particular sections 2.2-2.6, though regular Geometry should consider reinforcing the concepts on
patterns and inductive reasoning from section 2.1.
ALCOS #9. Prove theorems about lines and angles.
Pearson: 2.6
Theorems include vertical angles are congruent;
IXL: C.1,2,3,4,8
when a transversal crosses parallel lines, alternate
LTF: Logical Reasoning (This lesson
interior angles are congruent and corresponding
gives students the opportunity to
angles are congruent; and points on a perpendicular
assign a true or false value to each of
bisector of a line segment are exactly those
10 “tricky” statements.)
equidistant from the segment’s endpoints. [G-CO9]
(Prepares for) ALCOS #10. Prove theorems about
Pearson: 2.2-2.6
triangles. Theorems include measures of interior
IXL:
angles of a triangle sum to 180º, base angles of
LTF:
isosceles triangles are congruent, the segment joining
midpoints of two sides of a triangle is parallel to the
third side and half the length, and the medians of a
triangle meet at a point. [G-CO10]
(Prepares for) ALCOS #11. Prove theorems about
Pearson: 2.2-2.6
parallelograms. Theorems include opposite sides are
IXL:
congruent, opposite angles are congruent; the
LTF:
diagonals of a parallelogram bisect each other; and
conversely, rectangles are parallelograms with
congruent diagonals. [G-CO11]
(Quality Core) C.1.a. Use definitions, basic
Pearson:
postulates, and theorems about points, segments,
2.2-2.6
lines, angles, and planes to write proofs and to solve
IXL: C.8
problems
LTF:
(Quality Core) C.1.b. Use inductive reasoning to
Pearson: 2.1
make conjectures and deductive reasoning to arrive
IXL:
at valid conclusions
LTF:
(Quality Core) C.1.c. Identify and write conditional and
Pearson: 2.2-2.4
biconditional statements along with the converse, inverse,
IXL: I.1,2,5,7,8
and contrapositive of a conditional statement; use these
statements to form conclusions
(Prepares for) (Quality Core) C.1.d. Use various
methods to prove that two lines are parallel or
perpendicular (e.g., using coordinates, angle
measures)
(Quality Core) C.1.e. Read and write different types
and formats of proofs including two-column,
flowchart, paragraph, and indirect proofs
Pearson: 2.2-2.6
IXL:
LTF:
Pearson: 2.4-2.6
IXL:
LTF:
Unit 3 - First 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
First 9-weeks
Unit 3: Parallel and Perpendicular Lines
15 days
The first part of this unit deals with angles formed by lines and a transversal, then extension is made to parallel lines cut by a transversal, and finally the
Triangle-Angle Sum Theorem. The second part of the unit is devoted to parallel and perpendicular lines, both from a construction and an algebraic standpoint.
The primary text resource here is Pearson Geometry (3.1-3.8).
ALCOS #1. Know precise definitions of angle,
Pearson: 3.4
circle, perpendicular line, parallel line, and line
IXL: D.1
segment based on the undefined notions of point,
LTF:
line, distance along a line, and distance around a
circular arc. [G-CO1]
ALCOS #12. Make formal geometric constructions
Pearson: 3.6
with a variety of tools and methods such as compass
IXL: D.2,5
and straightedge, string, reflective devices, paper
LTF:
folding, and dynamic geometric software.
Constructions include copying a segment; copying an
angle; bisecting a segment; bisecting an angle;
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. [G-CO12]
ALCOS #41. Apply geometric methods to solve
Pearson: 3.1-3.8
design problems (e.g., designing an object or
IXL:
structure to satisfy physical constraints or minimize
LTF:
cost, working with typographic grid systems based
on ratios).* [G-MG3]
ALCOS #10. Prove theorems about triangles.
Pearson: 3.5
Theorems include measures of interior angles of a
IXL: D.3,4; F.2,3
triangle sum to 180º, base angles of isosceles
LTF:
triangles are congruent, the segment joining
midpoints of two sides of a triangle is parallel to the
third side and half the length, and the medians of a
triangle meet at a point. [G-CO10]
ALCOS #31. 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). [G-GPE5]
(Quality Core) G.1.a
Use slope to distinguish between and write equations
for parallel and perpendicular lines.
(Quality Core) D.1.c
Identify corresponding, same-side interior, same-side
exterior, alternate interior, alternate exterior angle
pairs formed by a pair of parallel lines and a
transversal and use these special angle pairs to solve
problems (e.g., solve equations, use in proofs)
(Quality Core) C.1.d. Use various methods to prove
that two lines are parallel or perpendicular (e.g.,
using coordinates, angle measures)
(Quality Core) C.1.e. Read and write different types
and formats of proofs including two-column,
flowchart, paragraph, and indirect proofs
Pearson: 3.7-3.8
IXL: E.2 thru 6
LTF: Tangent Line Equations
(Teacher would need to briefly
explain the equation of a circle, but
this lesson does a good job driving
home an important situation where
we need a line perpendicular to a
given line through a given point.)
Pearson: 3.7
Pearson: 3.1-3.4
Pearson: 3.4,3.8
IXL: E.3,4,6,7
LTF:
Pearson: 3.3
IXL:
LTF:
Unit 4 - Second 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Second 9-weeks
Unit 4: Congruent Triangles
16 days
The first part of this chapter provides the basics for ways triangles can be proven to be congruent, while the second section provides methods specific to certain
triangle types (isosceles, equilateral, right, overlapping). The primary text resource for this unit is Pearson Geometry 4.1-4.6 for all levels, and Honors
Geometry also visiting concepts in section 4.7.
ALCOS #18. Use congruence and similarity criteria
Pearson: 4.1-4.7
for triangles to solve problems and to prove
IXL: J.1 thru 3
relationships in geometric figures. [G-SRT5]
LTF:
ALCOS #10. Prove theorems about triangles.
Pearson: 4.5
Theorems include measures of interior angles of a
IXL: K.8,9
triangle sum to 180º, base angles of isosceles
LTF:
triangles are congruent, the segment joining
midpoints of two sides of a triangle is parallel to the
third side and half the length, and the medians of a
triangle meet at a point. [G-CO10]
ALCOS #8. Explain how the criteria for triangle
Pearson: 4.1-4.3
IXL: K.1 thru 6
congruence, angle-side-angle (ASA), side-angle-side
LTF:
(SAS), and side-side-side (SSS), follow from the
definition of congruence in terms of rigid motions.
[G-CO8]
(Quality Core) C.1.e. Read and write different types
Pearson: 4.1-4.7
and formats of proofs including two-column,
IXL: K.2,4,6,7,9
flowchart, paragraph, and indirect proofs
LTF:
(Quality Core) C.1.f. Prove that two triangles are
congruent by applying the SSS, SAS, ASA, AAS,
and HL congruence statements
(Quality Core) C.1.g. Use the principle that
corresponding parts of congruent triangles are
congruent to solve problems
Pearson: 4.1-4.3,4.6
IXL: K.10
LTF:
Pearson: 4.4
IXL: K.7
LTF:
(Quality Core) D.2.a
Identify and classify triangles by their sides and
angle
(Quality Core) D.2.j
Apply the Isosceles Triangle Theorem and its
converse to triangles to solve mathematical and realworld problems
Pearson: 4.5
IXL:
LTF:
(Quality Core) E.1.b
Identify congruent figures and their corresponding
parts
Pearson: 4.1-4.4
IXL:
LTF:
Unit 5 - Second 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Second 9-weeks
Unit 5: Relationships Within Triangles
12 days
The main portion of this unit deals with concurrent lines in triangles, and the second part, which mostly pertains to Honors Geometry deals with indirect proof
and inequalities in triangles. The main text resource for this unit is Pearson Geometry (5.1-5.4, 5.6 for Regular and 5.1-5.7 for Honors).
ALCOS #10. Prove theorems about triangles.
Pearson: 5.1-5.4
Theorems include measures of interior angles of a
IXL: M.1 thru 4
triangle sum to 180º, base angles of isosceles
LTF:
triangles are congruent, the segment joining
midpoints of two sides of a triangle is parallel to the
third side and half the length, and the medians of a
triangle meet at a point. [G-CO10]
ALCOS #18. Use congruence and similarity criteria
Pearson: 5.1-5.4
for triangles to solve problems and to prove
IXL: M.5
relationships in geometric figures. [G-SRT5]
LTF:
ALCOS #9. Prove theorems about lines and angles.
Pearson: 5.2
Theorems include vertical angles are congruent;
IXL: B.6
when a transversal crosses parallel lines, alternate
LTF:
interior angles are congruent and corresponding
angles are congruent; and points on a perpendicular
bisector of a line segment are exactly those
equidistant from the segment’s endpoints. [G-CO9]
ALCOS #12. Make formal geometric constructions
with a variety of tools and methods such as compass
and straightedge, string, reflective devices, paper
folding, and dynamic geometric software.
Constructions include copying a segment; copying an
angle; bisecting a segment; bisecting an angle;
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. [G-CO12]
Pearson: 5.1-5.4
IXL: M.6
LTF:
ALCOS #26. Construct the inscribed and
circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a
circle. [G-C3]
** Create equations and inequalities in one variable,
and use them to solve problems. Include equations
arising from linear and quadratic functions, and
simple rational and exponential functions. [A-CED]
** Alg I Objectives – Review.
(Quality Core) D.2.b
Identify medians, altitudes, perpendicular bisectors,
and angle bisectors of triangles and use their
properties to solve problems (e.g., find points of
concurrency, segment lengths, or angle measures)
(Quality Core) D.2.c
Apply the Triangle Inequality Theorem to determine
if a triangle exists and the order of sides and angles
Pearson: 5.2-5.3
IXL: M.6; U.16
LTF:
Pearson: 5.6-5.7
IXL:
LTF:
Pearson: 5.3-5.4
IXL:
LTF:
Pearson: 5.6
IXL:
LTF:
Unit 6a - Second 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Second 9-weeks
Unit 6a: Polygons and Quadrilaterals
10 days
The first part of this unit is devoted to the general polygon-angle sum theorem, then emphasis is given to the various types of special quadrilaterals. The
primary text resource is Pearson Geometry 6.1-6.6.
ALCOS #11. Prove theorems about parallelograms.
Pearson: 6.2-6.6
Theorems include opposite sides are congruent,
IXL: G.1 thru 4; N.1,2,4,5,6,7
opposite angles are congruent; the diagonals of a
LTF: Handshake Problem (goes
parallelogram bisect each other; and conversely,
alongside the idea of counting
rectangles are parallelograms with congruent
total diagonals – connecting two
diagonals. [G-CO11]
points instead of connecting two
people)
(Quality Core) C.1.i. Use properties of special
Pearson: 6.2-6.6
quadrilaterals in a proof
IXL: N.3,9,10
LTF:
(Quality Core) D.2.g
Pearson: 6.2-6.6
Identify and classify quadrilateral, including
IXL:
parallelograms, rectangles, rhombi, squares, kites,
LTF:
trapezoids, and isosceles trapezoids, using their
properties.
(Quality Core) D.2.h
Pearson: 6.1
Identify and classify regular and non-regular
IXL:
polygons (e.g., pentagons, hexagons, heptagons,
LTF:
octagons, nonagons, decagons, dodecagons) based on
the number of sides given angle measures, and to
solve real-world problems
(Quality Core) D.2.i
Apply the Angle Sum Theorem for triangles and
polygons to find interior and exterior angle measures
given the number of sides, to find the number sides
given angle measures, and to solve real-world
problems.
Unit 6b - Third 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Third 9-weeks
Unit 6b: Polygons and Quadrilaterals
5 days
This unit (or sub-unit) deals with analytic geometry, or coordinate geometry, where specific coordinates are used to verify criteria, and general coordinates are
used to prove theorems. The primary text resource is Pearson Geometry (6.7 for Regular Geometry, and 6.7-6.9 for Honors Geometry).
ALCOS #11. Prove theorems about parallelograms.
Pearson: 6.7
Theorems include opposite sides are congruent,
IXL: A.4; B.8
opposite angles are congruent; the diagonals of a
LTF:
parallelogram bisect each other; and conversely,
rectangles are parallelograms with congruent
diagonals. [G-CO11]
ALCOS #33. Use coordinates to compute perimeters
Pearson: 6.7
of polygons and areas of triangles and rectangles,
IXL:
e.g., using the distance formula.* [G-GPE7]
LTF:
ALCOS #30. Use coordinates to prove simple
Pearson: 6.7
geometric theorems algebraically. [G-GPE4]
IXL:
Example: Prove or disprove that a figure defined by
LTF: Coordinate Geometry and
four given points in the coordinate plane is a
Proofs (This problem is really just
rectangle; prove or disprove that the point (1, √3) lies
about using variable coordinates
on the circle centered at the origin and containing the
to verify properties of a geometric
point (0,2)
figure on the coordinate plane.)
(Quality Core) C.1.i. Use properties of special
Pearson: 6.7-6.9
quadrilaterals in a proof
IXL:N.3,9,10
LTF:
Unit 7 - Third 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Third 9-weeks
Unit 7: Similarity
10 days
Similar polygons are the focus! This means we will use a lot of ratios to solve problems. The primary text resource is Pearson Geometry (7.1-7.5). Honors
Geometry may consider whether 7.1 is helpful for your class, depending on the readiness of your students.
ALCOS #18. Use congruence and similarity criteria
Pearson: 7.1-7.5
for triangles to solve problems and to prove
IXL: A.1, P.1-7,11
relationships in geometric figures. [G-SRT5]
LTF:
(Algebra Standard for Review) Create equations and
inequalities in one variable, and use them to solve
problems. Include equations arising from linear and
quadratic functions, and simple rational and
exponential functions. [A-CED1]
Pearson: 7.4-7.5
IXL:
LTF:
ALCOS #17. Prove theorems about triangles.
Theorems include a line parallel to one side of a
triangle divides the other two proportionally, and
conversely; and the Pythagorean Theorem proved
using triangle similarity. [G-SRT4]
Pearson: 7.5
IXL: P.10
LTF:
(Quality Core) C.1.h. Use several methods, including
AA, SAS, and SSS, to prove that two triangles are
similar, corresponding sides are proportional, and
corresponding angles are congruent
Pearson: 7.3
IXL: M.8
LTF: Similar Triangles (This lesson
explores the relationship between
perimeters and areas of similar
triangles.)
Pearson: 7.4
IXL:
LTF:
(Quality Core) D.2.d
Solve problems involving the relationships formed
when the altitude to the hypotenuse of a right triangle
is drawn.
(Quality Core) E.1.g
Determine the geometric mean between two numbers
and use it to solve problems (e.g., find the lengths of
segments in right triangles)
(Quality Core) E.1.c
Identify similar figures and use ratios and proportions
to solve mathematical and real-world problems (e.g.,
finding the height of a tree using the shadow of the
tree and the height and shadow of a person.
Person: 7.3
IXL:
LTF:
(Quality Core) E.1.d
Use the definition of similarity to establish the
congruence of angles, proportionality of sides, and
scale factor of two similar polygons.
Pearson: 7.2
IXL:
LTF:
Unit 8 - Third 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation
/ Date(s) Taught
Third 9-weeks
Unit 8: Right Triangles and Trigonometry
12 days
This unit has some very important concepts for students moving on to more advanced math courses. These concepts include: Pythagorean Theorem,
Converse of the Pythagorean Theorem, Special Right Triangles, Basic Triangle Trigonometry, and for Honors – Law of Sines and Law of Cosines. The
primary text resource will be Pearson Geometry 8.1-8.4 for Regular Geometry and 8.1-8.6 for Honors.
ALCOS #17. Prove theorems about triangles.
Pearson: 8.1
IXL: Q.1,2
Theorems include a line parallel to one side of a
LTF: Pythagorean Theorem
triangle divides the other two proportionally, and
Applications (More involved
conversely; and the Pythagorean Theorem proved
problems combining algebra and the
using triangle similarity. [G-SRT4]
Pythagorean Theorem); Introduction
ALCOS #19. 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. [G-SRT6]
ALCOS #20. Explain and use the relationship between
the sine and cosine of complementary angles. [GSRT7]
ALCOS #21. Use trigonometric ratios and the
Pythagorean Theorem to solve right triangles in applied
problems.* [G-SRT8]
to Related Rates – Pythagorean
Theorem (Good for writing equations
for one side in terms of another side.)
Pearson: 8.2-8.4
IXL: Q.4; R.1,3,5 thru 10
LTF: Special Right Triangle
Applications (Lots of topics in the
applications – so it might be better
near the end of the year.); Trig. Ratios
with Special Right Triangles
(Explores trig. function values for
angles in special right triangles.)
Pearson: 8.3-8.4
IXL: R.4
LTF:
Pearson: 8.4
IXL: R.10
LTF: Vectors (Good word problems
dealing with vectors. You could also
share this with a Precalculus teacher.)
ALCOS #39. 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-MG1]
Pearson: 8.5
IXL: R.10
LTF:
(Honors Only) ALCOS #22. (+) Prove the Law of
Sines and the Law of Cosines and use them to solve
problems. [G-SRT10]
Pearson: 8.5-8.6
IXL: R.11 thru 13
LTF: Proof of Law of Sines (Guides
students through the proof of law of
sines.)
Pearson: 8.5-8.6
IXL: R.11 thru 13
LTF:
(Honors Only) ALCOS #23. (+) Understand and apply
the Law of Sines and the Law of Cosines to find
unknown measurements in right and non-right triangles
(e.g., surveying problems, resultant forces). [G-SRT11]
(Quality Core) D.2.e
Apply the Pythagorean Theorem and its converse to
triangles to solve mathematical and real-world
problems (e.g., shadows, poles, and ladders)
(Quality Core) D.2.f
Identify and use Pythagorean triples in right triangles
to find lengths of the unknown side
(Quality Core) H.1.a
Apply properties of 45-45-90 and 30-60-90 triangles to
determine lengths of sides of triangles
(Quality Core) H.1.b
Find the sine, cosine, and tangent ratios of acute angles
given the side lengths of right triangles
(Quality Core) H.1.c
Use trigonometric ratios to find the sides or angles of
right triangles and to solve real-world problems (e.g.,
use angles of elevation and depression to find missing
measures)
Pearson: 8.1
IXL:
LTF:
Pearson: 8.2
IXL:
LTF:
Pearson: 8.3
IXL:
LTF:
Pearson: 8.3-8.4
IXL:
LTF:
Unit 10a - Third 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Third 9-weeks
Unit 10a: Area
10 days
In this unit, we have several methods for finding areas of quadrilaterals and triangles, and we use trigonometry to find the area of a regular polygon. Then
we move on to finding arc length and sector areas for circles. Finally, we apply all of these concepts to calculate geometric probability. The primary text
for this unit is Pearson Geometry 10.1-10.7 for Regular Geometry, and 10.8 for Honors.
ALCOS #33. Use coordinates to compute perimeters of
Pearson: 10.1-10.5
IXL: S.1-6,8,11
polygons and areas of triangles and rectangles, e.g.,
LTF: Areas of Triangles (Many methods
using the distance formula.* [G-GPE7]
for finding areas of triangles. Even if you
don’t do all of them, students usually
enjoy the variety of methods here.)
ALCOS #39. Use geometric shapes, their measures,
Pearson: 10.1-10.5
IXL: S.8
and their properties to describe objects (e.g., modeling
LTF:
a tree trunk or a human torso as a cylinder).* [G-MG1]
ALCOS #41. Apply geometric methods to solve design
Pearson: 10.1-10.5
IXL:
problems (e.g., designing an object or structure to
LTF:
satisfy physical constraints or minimize cost, working
with typographic grid systems based on ratios).* [GMG3]
ALCOS #13. Construct an equilateral triangle, a
Pearson: 10.3,10.5
IXL:
square, and a regular hexagon inscribed in a circle. [GLTF:
CO13]
ALCOS #34. Determine areas and perimeters of
Pearson: 10.3,10.5
IXL:
regular polygons, including inscribed or circumscribed
LTF: Accumulation (Good review and/or
polygons, given the coordinates of vertices or other
application of area concepts to
characteristics. (Alabama only)
approximate the area of an irregular
region under a curve.)
(Quality Core) G.1.c
Pearson: 10.4
Use coordinate geometry to solve problems about
IXL:
geometric figures (e.g., segments, triangles,
LTF:
quadrilaterals)
Unit 10b - Fourth 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Fourth 9-weeks
Unit 10b: Area
ALCOS #33. Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g.,
using the distance formula.* [G-GPE7]
ALCOS #39. 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-MG1]
ALCOS #41. 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).* [GMG3]
ALCOS #13. Construct an equilateral triangle, a square,
and a regular hexagon inscribed in a circle. [G-CO13]
ALCOS #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. [G-CO1]
ALCOS #24. Prove that all circles are similar. [G-C1]
ALCOS #28. 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-C5]
5 days
Pearson: 10.8
IXL: S.12
LTF:
Pearson: 10.6-10.8
IXL:
LTF:
Pearson: 10.6-10.8
IXL:
LTF:
Pearson: 10.7-10.8
IXL: U.13,14,15
LTF:
Pearson: 10.6
IXL: S.7
LTF:
Pearson: 10.6-10.7
IXL: P.9
LTF:
Pearson: 10.6-10.7
IXL: S.7; U.3,4
LTF:
(Honors Only) ALCOS 42. (+) Use probabilities to
make fair decisions (e.g., drawing by lots, using a
random number generator). [S-MD6]
(Honors Only) ALCOS #43. (+) Analyze decisions and
strategies using probability concepts (e.g., product
testing, medical testing, pulling a hockey goalie at the
end of a game). [S-MD7]
(Quality Core) D.3.b
Determine the measure of central and inscribed angles
and their intercepted arcs
(Quality Core) F.1.d
Find arc lengths and circumference of circles from given
information (e.g., radius, diameters, coordinates)
(Quality Core) F.1.c
Use area to solve problems involving geometric
probability
(Quality Core) F.1.e
Find area of a circle and the area of a sector of a circle
from given information (e.g., radius, diameter,
coordinates)
Pearson: 10.8
IXL: S.8 thru 12; X.7
LTF: Geometric Probability (Good review
of some of the geometric probability
concepts.)
Pearson: 10.8
IXL:
LTF:
Pearson: 10.6
IXL:
LTF:
Pearson: 10.8
IXL:
LTF:
Pearson: 10.7
IXL:
LTF:
Unit 12 - Fourth 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Fourth 9-weeks
Unit 12: Circles
12 days
This unit deals with the interaction of tangent lines and secant lines with circles. We will find angle measures in several situations, as well as segment
lengths in those situations. Finally, we will work with equations of circles in the coordinate plane, and we will discuss what is meant by a “locus” of points.
The primary text resource will be Pearson Geometry 12.1-12.6.
ALCOS #25. Identify and describe relationships among
Pearson Geometry: 12.1-12.4
IXL: U.1 thru 11
inscribed angles, radii, and chords. Include the
LTF:
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. [G-C2]
ALCOS #29. Derive the equation of a circle of given
center and radius using the Pythagorean Theorem;
complete the square to find the center and radius of a
circle given by an equation. [G-GPE1]
Pearson Geometry: 12.5
IXL: V.1 thru 5
LTF:
(Honors Only) ALCOS #27. (+) Construct a tangent line
from a point outside a given circle to the circle. [G-C4]
Pearson Geometry: 12.1
IXL: U.12
LTF: Tangent Line Equations (Good
review of equations of perpendicular
lines through a given point. Also a
good application of tangent lines to
coordinate geometry.)
Pearson: 12.1-12.4
IXL:
LTF:
(Quality Core) D.3.a
Identify and define line segments associated with circles
(e.g., radii, diameters, chords, secants, tangents)
(Quality Core) D.3.c
Find segment lengths, angle measures, and intercepted
arc measures formed by chords, secants, and tangents
intersecting inside and outside circles
(Quality Core) D.3.b
Determine the measure of central and inscribed angles
and their intercepted arcs
(Quality Core) D.3.d
Solve problems using inscribed and circumscribed
polygons
(Quality Core) G.1.d
Write equations for circles in standard form and solve
problems using equations and graphs
Pearson: 12.3
IXL:
LTF:
Pearson: 12.4
IXL:
LTF:
Pearson: 12.5
IXL:
LTF:
Unit 11 - Fourth 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Fourth 9-weeks
Unit 11: Surface Area and Volumes
16 days
This unit deals with cross-sections, surface areas, volumes, and ratios of these quantities between similar solids. The primary text resource is Pearson
Geometry, 11.1-11.7 for both Regular and Honors, but a particular emphasis should be on 11.7 for the Honors course.
ALCOS #38. Identify the shapes of two-dimensional
Pearson Geometry: 11.1-11.6
IXL: H.1 thru 5
cross-sections of three-dimensional objects, and identify
LTF: Volumes of Revolution
three-dimensional objects generated by rotations of two(Good chance for students to be
dimensional objects. [G-GMD4]
exposed to revolutions where they
can easily find the surface areas
and volumes. You might not do
this entire lesson, or you might
want to!)
ALCOS #39. Use geometric shapes, their measures, and
Pearson Geometry: 11.1-11.7
IXL: T.1
their properties to describe objects (e.g., modeling a tree
LTF:
trunk or a human torso as a cylinder).* [G-MG1]
ALCOS #35. Give an informal argument for the
Pearson Geometry: 11.6-11.7
IXL: T.1
formulas for the circumference of a circle; area of a
LTF: Volume of a Sphere by
circle; and volume of a cylinder, pyramid, and cone. Use
Cross-Sections (This lesson uses
dissection arguments, Cavalieri’s principle, and
the volume of a cylinder and the
informal limit arguments. [G-GMD1]
volume of a cone to derive the
ALCOS #36. Use volume formulas for cylinders,
pyramids, cones, and spheres to solve problems.* [GGMD3]
ALCOS #40. Apply concepts of density based on area
and volume in modeling situations (e.g., persons per
square mile, British Thermal Units (BTUs) per cubic
foot).* [G-MG2]
volume of a sphere using
Cavalieri’s principle.)
Pearson Geometry: 11.2-11.7
IXL: T.2 thru 6
LTF:
Pearson Geometry: 11.2-11.7
IXL: T.1,9
LTF:
ALCOS #37. Determine the relationship between
surface areas of similar figures and volumes of similar
figures. (Alabama)
(Quality Core) D.4.a
Identify and classify prisms, pyramids, cylinders, cones,
and spheres and use their properties to solve problems
(Quality Core) F.2.a
Find the lateral area, surface area, and volume of prisms,
cylinders, cones, and pyramids in mathematical and
real-world settings
(Quality Core) D.4.b
Describe and draw cross sections of prisms, cylinders,
pyramids, and cones
(Quality Core) F.2.b
Use cross sections of prisms, cylinders, pyramids, and
cones to solve volume problems
(Quality Core) E.1.f
Apply relationships between perimeters of similar
figures, areas of similar figures, and volumes of similar
figures, in terms of scale factor, to solve mathematical
and real-world problems
(Quality Core) E.1.h
Identify and give properties of congruent or similar
solids
(Quality Core) F.2.c
Find the surface area and volume of a sphere in
mathematical and real-world settings
Pearson Geometry: 11.7
IXL: T.7,8,9
LTF:
Pearson: 11.2-11.5
IXL:
LTF:
Pearson: 11.1
IXL:
LTF
Pearson: 11.7
IXL:
LTF:
Pearson: 11.6
IXL:
LTF:
Unit 9 - Fourth 9-weeks
Standard
“I Can” Statements *
Resources
Pacing
Recommendation /
Date(s) Taught
Fourth 9-weeks
Unit 9: Transformations
7 days
This unit is an algebraic/coordinate approach to many of the Geometry concepts. It emphasizes the more algebraic definition of congruence (rigid motion),
and distinguishes between which types of transformations lead to congruence, and which types lead to similarity.
ALCOS #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). [GCO2]
Pearson Geometry: 9.1-9.7
IXL: L.1-L.15
LTF:
ALCOS #4. Develop definitions of rotations, reflections,
and translations in terms of angles, circles, perpendicular
lines, parallel lines, and line segments. [G-CO4]
Pearson Geometry: 9.1-9.7
IXL: L.6
LTF:
ALCOS #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. [G-CO5]
Pearson Geometry: 9.1-9.7
IXL: L.1,4,7,10
LTF:
ALCOS #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. [G-CO6]
Pearson Geometry: 9.1-9.7
IXL: L.11
LTF: Reflection of Lines (Good
development of learning to
reflect 2 points from a line
instead of trying to reflect the
whole line at once.)
ALCOS #3. Given a rectangle, parallelogram, trapezoid,
or regular polygon, describe the rotations and reflections
that carry it onto itself. [G-CO3]
Pearson Geometry: 9.1-9.7
IXL: L.11
LTF:
ALCOS #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. [G-CO7]
Pearson Geometry: 9.1-9.7
IXL:
LTF:
ALCOS #8. Explain how the criteria for triangle
congruence, angle-side-angle (ASA), side-angle-side
(SAS), and side-side-side (SSS), follow from the
definition of congruence in terms of rigid motions. [GCO8]
ALCOS #14. Verify experimentally the properties of
dilations given by a center and a scale factor. [G-SRT1]
a. 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. [G-SRT1a]
b. The dilation of a line segment is longer or shorter in the
ratio given by the scale factor. [G-SRT1b]
Pearson Geometry: 9.1-9.7
IXL:
LTF:
ALCOS #15. 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 the
proportionality of all corresponding pairs of sides. [GSRT2]
Pearson Geometry: 9.1-9.7
IXL:
LTF:
ALCOS #16. Use the properties of similarity
transformations to establish the angle-angle (AA) criterion
for two triangles to be similar. [G-SRT3]
Pearson Geometry: 9.1-9.7
IXL:
LTF:
(Quality Core) E.1.a
Determine points or lines of symmetry and apply
properties of symmetry to figures
Pearson: 9.2
IXL:
LTF:
Pearson Geometry: 9.1-9.7
IXL:
LTF:
(Quality Core) E.1.e
Identify and draw images of transformations and use their
properties to solve problems
(Quality Core) G.1.e
Determine the effect of reflections, rotations, and
translations, and dilations and their compositions on the
coordinate plane
Pearson: 9.1-9.7
IXL:
LTF:
Alabama Technology Standards Ninth – Twelfth Grade
Operations and Concepts
Students will:
2. Diagnose hardware and software problems. Examples: viruses, error messages Applying strategies to correct malfunctioning hardware and
software Performing routine hardware maintenance Describing the importance of antivirus and security software
3. Demonstrate advanced technology skills, including compressing, converting, importing, exporting, and backing up files. Transferring data among
applications Demonstrating digital file transfer Examples: attaching, uploading, downloading
4. Utilize advanced features of word processing software, including outlining, tracking changes, hyperlinking, and mail merging.
5. Utilize advanced features of spreadsheet software, including creating charts and graphs, sorting and filtering data, creating formulas, and applying
functions.
6. Utilize advanced features of multimedia software, including image, video, and audio editing.
Digital Citizenship
9. Practice ethical and legal use of technology systems and digital content. Explaining consequences of illegal and unethical use of technology
systems and digital content Examples: cyberbullying, plagiarism Interpreting copyright laws and policies with regard to ownership and use of digital
content Citing sources of digital content using a style manual Examples: Modern Language Association (MLA), American Psychological Association
(APA)
Research and Information Fluency
11. Critique digital content for validity, accuracy, bias, currency, and relevance.
Communication and Collaboration
12. Use digital tools to publish curriculum-related content. Examples: Web page authoring software, coding software, wikis, blogs, podcasts
13. Demonstrate collaborative skills using curriculum-related content in digital environments.
Examples: completing assignments online; interacting with experts and peers in a structured, online learning environment
Critical Thinking, Problem Solving, and Decision Making
14. Use digital tools to defend solutions to authentic problems. Example: disaggregating data electronically
Creativity and Innovation
15. Create a product that integrates information from multiple software applications. Example: pasting spreadsheet-generated charts into a
presentation