Download Alabama COS Standards

Geometry Pacing Guide
Suggested Book List
1st Grade
All Sorts of Numbers – counting
* Henry the Fourth – ordinal numbers
* 3 Little Firefighters – sorting
* It’s About Time!
* Bug Dance
* The Best Vacation Ever – data collecting,
problem solving skills
* Count on Clifford
2nd Grade
Amanda Bean’s Amazing Dream –
multiplication
* Clocks and More Clocks - time
* Much Bigger than Martin – size
“Slowly, Slowly, Slowly” said the Sloth
* Lemonade for Sale - money
* 100 Days of School – counting to 100
* Biggest Bed in the World – size
* Give Me Half – halves
3rd Grade
Sir Cumference and the Dragon Pi
* Grandfather’s Tang Story - changing
shape
* Chicken Soup with Rice – months
* Counting on Frank – size comparison,
math facts, counting
* Hershey’s Milk Chocolate Bar Fraction
* How Much is a Million
Mummy Math: An Adventure in Geometry
* Millions of Cats
* Three Days on a River in a Red Canoe
4th Grade
Carry On, Mr. Bowditch
Sir Cumference and the Great Knight of
Angle Land – acute, obtuse, straight
angles
Sir Cumference and the Sword in the Cone –
cubes, pyramids, prisms
Sir Cumference and the First Round Table –
measurement
* A Million Fish…More or Less
Dear Mr. Henshaw
A Higher Geometry
* The Village of Round and Square Houses
- shape
5th Grade
* How the Second Grade Got $8205.50 to
Visit the Statue of Liberty – money
Hannah, Divided
The Secret Life of Amanda K. Woods –
probability
Tuck Everlasting – calculate population
Gulliver’s Travel – geometry
Jayden’s Rescue – problem solving
The Curious Incident of the Dog in the
Night – time, probability
The Heroic of Hercules Amsterdam –
counting
6th Grade
The Da Vinci Code – Fibonacci Sequence
The Twenty-one Balloons – mathematical
reasoning
Journey to Topaz – measurement
7th Grade
The Sand-Reckoner – problem solving
The Pearl – currency calculation
Middle – High School
Imaginary Numbers
Mathematics in the Time of Pharaohs
Medieval Chinese Innovations
Math Talk: Mathematical Ideas in Poems
for Two Voices
High School
Against the Odds – number theory
Five Equations that Changed the World
The Man Who Loved Only Numbers
Math Equals: Biographies of Women
Mathematical Scandels
Archimede’s Revenge – application of math
Calculus and Pizza
* denotes AR books
Geometry Pacing Guide
1st Nine Weeks
Textbook
Correlation
Pacing Guide
AMSTI
2. Justify theorems related to pairs of angles,
including angles formed by parallel and
perpendicular lines, vertical angles, adjacent
angles, complementary angles, and
supplementary angles.
Example:
proving vertical angles congruent
1.6, 1.7, 1.4,
3.1, 3.2, 3.3.
3.4, 3.5, 7.1,
7.2, 7.4, 8.1,
8.2,
8.5,10.3,10.5
6
Weeks
“Shadows”
Big Ideas /
Essential
Question
Essential
Vocabulary
AHSGE / NAEP Correlations
Vertical angles,
adjacent angles,
complementary
angles,
supplementary
angles, theorem,
paragraph
proof,
transversal,
alternate
interior angles,
corresponding
angles, twocolumn proof
AHSGE- VII-1
NAEP- G3b, f, d, G2e,
M1e, f, c, h, L, j, N4c,
A1h, A2a
AHSGE-VII-3, VII-4
3.
Verify the relationships among different
classes of polygons by using their properties.
Example:
showing that a square has all
the properties of both a
rectangle and a rhombus
Determining the missing lengths of sides
or measures of angles in similar
polygons
Pythagorean
triple
6.
Apply the Pythagorean Theorem to
solve application problems, expressing answers
in simplified radical form or as decimal
approximations, using Pythagorean triples when
applicable.
AHSGE-VII-2
AHSGE-IV-2
12.
Apply distance, midpoint, and slope
formulas to solve problems and to confirm
properties of polygons.
Examples: finding the area of a
Page 2 of 15
Technology Based Lessons / Links
Geometry Pacing Guide
rectangle given the
coordinates of its vertices,
showing that the median of a
trapezoid is half the sum of
the bases
14. Classify polyhedrons according to their
properties, including the number of faces.
Example:
identifying a polyhedron
having 6 vertices and 12
edges
Identifying Euclidean solids
AHSGE-VII-4
16. Calculate surface areas and volumes of
solid figures, including spheres, cones, and
pyramids.
Developing formulas for surface area and
volume of spheres, cones, and
pyramids
Calculating specific missing dimensions
of solid figures from surface area or
volume
Determining the relationship between the
surface areas of similar figures and
volumes of similar figures
AHSGE-IV-1
17. Analyze sets of data from geometric
contexts to determine what, if any, relationships
exist.
Example:
Collect data and create a
scatterplot comparing the
perimeter and area of
various rectangles.
Determine whether a line of
best fit can be drawn.
Distinguishing between conclusions
drawn when using deductive and
statistical reasoning
Calculating probabilities arising in
geometric contexts
AHSGE-VII-6
Example:
finding the probability of
hitting a particular ring on a
Page 3 of 15
Geometry Pacing Guide
dart board whose rings are
formed by equally spaced
concentric circles
9. Use inductive reasoning to make conjectures
and deductive reasoning to justify conclusions.
Recognizing the limitations of justifying a
conclusion through inductive
reasoning
1.1
2.1-2.4
2
Weeks
inductive
reasoning,
conjecture,
counterexample,
point, line,
space, collinear
points, plane,
coplanar,
conditional,
hypothesis,
conclusion,
converse,
biconditional,
deductive
reasoning,
reflexive,
property,
symmetric,
negation,
inverse,
contrapositive,
equivalent
statement,
indirect
reasoning,
indirect proof,
postulate,
axiom, segment,
ray, opposite
rays, parallel
Page 4 of 15
NAEP- G5a, G1c, A2e
Geometry Pacing Guide
lines, skew lines,
coordinate,
congruent
segments
2ND Nine Weeks
1.
Determine the equation of a line parallel
or perpendicular to a second line through a
given point.
Textbook
Correlation
Pacing Guide
AMSTI
Big Ideas /
Essential
Question
Essential
Vocabulary
NAEP- G3g, b, f,
M1f, e, A1h, A2a
3.6 (1 day)
2. Justify theorems related to pairs of angles,
including angles formed by parallel and
perpendicular lines, vertical angles, adjacent
angles, complementary angles, and
supplementary angles.
Example:
proving vertical angles congruent
2.5 (1 day)
3. Verify the relationships among different
classes of polygons by using their properties.
Example:
showing that a square has all
the properties of both a
rectangle and a rhombus
Determining the missing lengths of sides
or measures of angles in similar
polygons
4.1-4.7
Big Ideas / Essential
Questions
2 ½ Weeks
Consecutive
angles, base
angles of a
trapezoid,
similar,
similarity ratio,
golden ratio,
indirect
measurement,
geometric mean,
Page 5 of 15
NAEP- G2e, G3f
Technology Based Lessons / Links
Geometry Pacing Guide
Consecutive
angles, base
angles of a
trapezoid, midsegment,
concurrent,
point of
concurrency,
circumcenter,
in center,
centroid,
altitude,
circumscribed
about inscribed,
median
similar,
similarity ratio,
golden ratio,
indirect
measurement,
geometric mean,
5.
Solve real-life and mathematical
problems using properties and theorems related
to circles, quadrilaterals, and other geometric
shapes.
Example:
finding the center of a solid
wooden wheel using the
perpendicular bisectors of
two chords
Determining the equation of a circle given its
center and radius
8.
Deduce relationships between two
triangles, including proving congruence or
similarity of the triangles from given information,
using the relationships to solve problems and to
establish other relationships.
Determining the geometric mean to find
missing lengths in right triangles
Midpoint, angle,
acute angle,
right angle,
obtuse angle,
straight angle,
congruent angle,
perpendicular
line
Legs of an
isosceles
triangle, base of
an isosceles
triangle, vertex
angle of an
9. Use inductive reasoning to make conjectures
and deductive reasoning to justify conclusions.
Recognizing the limitations of justifying a
conclusion through inductive
reasoning
5. Solve real-life and mathematical problems
using properties and theorems related to circles,
quadrilaterals, and other geometric shapes.
Example:
finding the center of a solid
wooden wheel using the
perpendicular bisectors of
two chords
5.1-5.5
2½
Weeks
Page 6 of 15
NAEP- G3f, b, G5a
Geometry Pacing Guide
isosceles, base
angle of
isosceles
triangle,
corollary
Determining the equation of a circle given its
center and radius
Legs of an
isosceles
triangle, base of
an isosceles
triangle, vertex
angle of an
isosceles, base
angle of
isosceles
triangle,
corollary
Legs of an
isosceles
triangle, base of
an isosceles
triangle, vertex
angle of an
isosceles, base
angle of
isosceles
triangle,
corollary
Parallelogram,
rhombus,
rectangle,
square, kite,
trapezoid,
Isosceles
trapezoid
8. Deduce relationships between two triangles,
including proving congruence or similarity of the
triangles from given information, using the
relationships to solve problems and to establish
other relationships.
Determining the geometric mean to find
missing lengths in right triangles
9. Use inductive reasoning to make conjectures
and deductive reasoning to justify conclusions.
Recognizing the limitations of justifying a
conclusion through inductive
reasoning
3. Verify the relationships among different
classes of polygons by using their properties.
Example:
showing that a square has all
the properties of both a
rectangle and a rhombus
6.1-6.6
2½
Weeks
Determining the missing lengths of sides
or measures of angles in similar
polygons
Page 7 of 15
NAEP-G3f, G4d
Geometry Pacing Guide
Parallelogram,
rhombus,
rectangle,
square, kite,
trapezoid,
Isosceles
trapezoid
5. Solve real-life and mathematical problems
using properties and theorems related to circles,
quadrilaterals, and other geometric shapes.
Example:
finding the center of a solid
wooden wheel using the
perpendicular bisectors of
two chords
Determining the equation of a circle given its
center and radius
12.
Apply distance, midpoint, and slope
formulas to solve problems and to confirm
properties of polygons.
Examples: finding the area of a
rectangle given the
coordinates of its vertices,
showing that the median of a
trapezoid is half the sum of
the bases
Parallelogram,
rhombus,
rectangle,
square, kite,
trapezoid,
Isosceles
trapezoid
Page 8 of 15
Geometry Pacing Guide
3Rd Nine Weeks
Textbook
Correlation
Pacing
Guide
7.
Use the ratios of the sides of special
right triangles to find lengths of missing sides.
Deriving the ratios of the sides of 30-6090 and 45-45-90 triangles
7.3
7.5-7.8
2
Weeks
AMSTI
Big Ideas /
Essential
Question
Essential
Vocabulary
Big Ideas / Essential
Questions
NAEP- G3d, M1L
Adjacent arc,
circumference,
pi, concentric
circles, arc
length,
congruent arcs,
sector of a
circle, segment
of a circle,
circle, center,
radius,
congruent
circles,
diameter,
central angle,
semicircle,
minor arc, major
arc
5. Solve real-life and mathematical problems
using properties and theorems related to circles,
quadrilaterals, and other geometric shapes.
Example:
finding the center of a solid
wooden wheel using the
perpendicular bisectors of
two chords
Determining the equation of a circle given
its center and radius
Page 9 of 15
Technology Based Lessons / Links
Geometry Pacing Guide
geometric
probability
17. Analyze sets of data from geometric
contexts to determine what, if any, relationships
exist.
Example:
Collect data and create a
scatterplot comparing the
perimeter and area of
various rectangles.
Determine whether a line of
best fit can be drawn.
Distinguishing between conclusions
drawn when using deductive and
statistical reasoning
Calculating probabilities arising in
geometric contexts
Example:
finding the probability of
hitting a particular ring on a
dart board whose rings are
formed by equally spaced
concentric circles
15.
Calculate measures of arcs and sectors
of a circle from given information.
Examples: finding the area of a sector
given its arc length and
radius, finding the arc length
of a sector given its area and
radius, finding the area or
arc length given the measure
of the central angle and the
radius
Adjacent
arc,
circumferen
ce, pi,
concentric
circles, arc
length,
congruent
arcs, sector
of a circle,
segment of a
circle, circle,
center,
radius,
congruent
circles,
diameter,
central
Page 10 of 15
Geometry Pacing Guide
angle,
semicircle,
minor arc,
major arc
18.
Construct with precision a circle graph
to represent data from given tables or classroom
experiments.
3.
Verify the relationships among different
classes of polygons by using their properties.
Example:
showing that a square has all
the properties of both a
rectangle and a rhombus
Determining the missing lengths of sides
or measures of angles in similar
polygons
8.3—8.4
1 Week
Adjacent
arc,
circumferen
ce, pi,
concentric
circles, arc
length,
congruent
arcs, sector
of a circle,
segment of a
circle, circle,
center,
radius,
congruent
circles,
diameter,
central
angle,
semicircle,
minor arc,
major arc
Congruent
polygons
Page 11 of 15
Geometry Pacing Guide
8. Deduce relationships between two triangles,
including proving congruence or similarity of the
triangles from given information, using the
relationships to solve problems and to establish
other relationships.
Determining the geometric mean to find
missing lengths in right triangles
9. Use inductive reasoning to make conjectures
and deductive reasoning to justify conclusions.
Recognizing the limitations of justifying a
conclusion through inductive
reasoning
9. Use inductive reasoning to make conjectures
and deductive reasoning to justify conclusions.
Recognizing the limitations of justifying a
conclusion through inductive
reasoning
9.1, 9.2, 9.3
1 Week
Proportion,
extended
proportion,
cross product
property, scale
drawing, scale
NAEP- M1m, k
10.1-10.2
10.4
2
Weeks
Polyhedron,
face, edge,
vertex, net,
cube, prism,
cylinder, right,
oblique, bases,
altitude, height,
lateral area,
surface area
NAEP-G1b, M1j
10.
Find the missing measures of sides and
angles in right triangles by applying the right
triangle definitions of sine, cosine, and tangent.
14. Classify polyhedrons according to their
properties, including the number of faces.
Example:
identifying a polyhedron
having 6 vertices and 12
edges
Identifying Euclidean solids
Page 12 of 15
Geometry Pacing Guide
prism, cylinder,
right, oblique,
bases, altitude,
height, lateral
area, surface
area
16. Calculate surface areas and volumes of
solid figures, including spheres, cones, and
pyramids.
Developing formulas for surface area and
volume of spheres, cones, and
pyramids
Calculating specific missing dimensions
of solid figures from surface area or
volume
Determining the relationship between the
surface areas of similar figures and
volumes of similar figures
Page 13 of 15
Geometry Pacing Guide
4TH Nine Weeks
Textbook
Correlation
Pacing
Guide
16. Calculate surface areas and volumes of
solid figures, including spheres, cones, and
pyramids.
Developing formulas for surface area and
volume of spheres, cones, and
pyramids
Calculating specific missing dimensions
of solid figures from surface area or
volume
Determining the relationship between the
surface areas of similar figures and
volumes of similar figures
10.6-10.7
1 Week
5. Solve real-life and mathematical problems
using properties and theorems related to circles,
quadrilaterals, and other geometric shapes.
Example:
finding the center of a solid
wooden wheel using the
perpendicular bisectors of
two chords
11.1-11.5
3
Weeks
12.1-12.4
12.7
3
Weeks
AMSTI
Big Ideas /
Essential
Question
Big Ideas / Essential
Questions
NAEP-M1j
Tangent, point
of tangency,
inscribed,
circumscribed,
chord, inscribed
angle,
intercepted arc,
secant,
standard form
of an equation ,
equation of a
circle
Symmetry,
reflectional
symmetry, line
symmetry,
rotational
symmetry, point
Determining the equation of a circle given
its center and radius
13.
Identify the coordinates of the vertices
of the image of a given polygon that is
translated, rotated, reflected, or dilated.
Example:
rotating a triangle a given
number of degrees around a
specific point, comparing
the vertices of the image and
preimage
Essential
Vocabulary
Page 14 of 15
NAEP-G3e, G4d
G2a, b, c, d, G4d
Technology Based Lessons / Links
Geometry Pacing Guide
symmetry,
tessellation,
tiling,
translational
symmetry,
transformation,
preimage, image,
isometry,
reflection,
translation,
composition,
rotation, glide
reflection, glide
reflectional,
symmetry,
dilation
Enrichment
12.5-12.6
1 Week
Page 15 of 15