Download 2015 Algebraic Geometry

2015 Algebraic Geometry
Grade Level/Course: Algebraic Geometry
Content Area: Mathematics
Grade Level/Course Overview:
The fundamental purpose of this course is to formalize and extend students’ geometric experiences from the earlier grades.
Students will explore more complex geometric situations and deepen their explanations of geometric relationships, moving
towards formal mathematical arguments. They will prove basic theorems and solve problems about triangles,
quadrilaterals, and other polygons; establish triangle congruence criteria based on analyses of rigid motions; apply similarity
in right triangles to understand right triangle trigonometry; use formulas to find the volume of three-dimensional objects;
and use the languages of set theory to expand their ability to compute and interpret theoretical and experimental
probabilities.
Strands/Domains
1. Geometry
a. Congruence
b. Similarity, Right Triangles, and Trigonometry
c. Geometric Measurement and Dimension
d. Modeling with Geometry
2. Statistics and Probability
a. Conditional Probability
b. Using Probability to Make Decisions
Program Understandings (pk-12)
1.
2.
3.
4.
5.
6.
7.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Units of Study
1. Introduction to Geometry and Basic Constructions
2. Introduction to Proofs
3. Triangle Congruence
4. Triangles and Coordinate Proofs
5. Similarity
6. Trigonometry
7. Quadrilaterals and Coordinate Geometry
8. 2D vs 3D
9. Circles – Part 1- (extension topic)
10. Circles – Part 2 – (extension topic)
11. Probability
12. Constructions Involving Circles – (extension topic)
Interdisciplinary Themes
1.
2.
3.
4.
5.
Patterns
Cause and Effect
Scale, Proportion, and Quantity
Systems and Systems Models
Structure and Function
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Experiment with transformations in the
plane
Standard: 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.
Standard Code: G-CO.1.
DOK Target for this standard: 1=Recall
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Rotations / reflections and translations are based on the notions of point, line, distance along a
line and distance around circular arc.
Know?
Define:
•
•
•
•
•
•
•
•
angle
circle
perpendicular
parallel
line segment
point
line
arc
Be able to do?
• name an angle, line, line segment, ray,
arc, circle with the correct notation
• identify parallel and perpendicular lines
from a diagram
• identify line / ray / line segment
• draw and label points, angles, lines, rays
and segments correctly
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Experiment with transformations in the
plane
Standard: 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).
Standard Code: G-CO.2.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Rotations / reflections and translations are based on the notions of point, line, distance along a
line and distance around circular arc.
Know?
•
•
•
•
•
•
•
•
•
•
rotations
reflections
triangle
rectangle
parallelogram
trapezoid
regular polygon
symmetry
dilation
translation
Be able to do?
• identify translations, rotations and
reflections in real world situations
• identify dilations, translations, rotations
and reflections of triangles, rectangles,
parallelograms, trapezoids or regular
polygons in the coordinate plane
• plot a transformation given a set of points
to be translated
• compare transformations that preserve
size/length to those that do not
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Experiment with transformations in the
plane
Standard: Given a rectangle, parallelogram,
trapezoid, or regular polygon, describe the
rotations and reflections that carry it onto itself.
Standard Code: G-CO.3.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
What should students…
Understand?
Rotations / reflections and translations are based on the notions of point, line, distance along a
line and distance around circular arc.
Know?
different ways to do transformations in a
plane
functions
Be able to do?
• describe rotations and reflections that
map a polygon onto itself
• identify lines/axes of symmetry
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Experiment with transformations in the
plane
Standard: Develop definitions of rotations,
reflections, and translations in terms of angles,
circles, perpendicular lines, parallel lines, and
line segments.
Standard Code: G-CO.4.
DOK Target for this standard:
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
•
•
•
•
•
What should students…
Understand?
Rotations / reflections and translations are based on the notions of point, line, distance along a
line and distance around circular arc.
Know?
rigid transformations
rotations
reflections
translation
angles
circles
perpendicular lines
parallel lines
line segment
Be able to do?
• create definitions of rotations, reflections,
and translations as rigid transformations
• visualize and identify rotations,
reflections, and translations that map a
preimage to an image
• understand properties that are preserved
in rotations, reflections and translations
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Experiment with transformations in the
plane
Standard: 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.
Standard Code: G-CO.5.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
What should students…
Understand?
Rotations / reflections and translations are based on the notions of point, line, distance
along a line and distance around circular arc.
Know?
rigid transformations
rotations
translations
reflections
Be able to do?
• draw rotations / reflections /
translations of a geometric figure using
manipulatives
• recognize and draw compositions of
transformations including mapping
onto itself
• identify rotation / reflections /
translations on a coordinate plane
• rotate / reflect / translate / given figures
in the coordinate plane
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Understand congruence in terms of rigid
motions
Standard: 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.
Standard Code: G-CO.6.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
What should students…
Understand?
Rigid motions and their properties can be used to establish the triangle congruence criteria,
which can then be used to prove other theorems.
Know?
rigid motion
congruence
transformation
tessellation
Be able to do?
• determine if two figures are congruent
• determine the effect of a given rigid
motion
• transformation figures using geometric
descriptions of rigid motion
• use transformations to create patterns
including tessellations
• identify figures that tessellate
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Understand congruence in terms of rigid
motions
Standard: 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.
Standard Code: G-CO.7.
DOK Target for this standard:
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Rigid motions and their assumed properties can be used to establish the usual triangle
congruence criteria, which can then be used to prove other theorems.
Know?
•
•
•
•
congruence
angles
rigid motion
corresponding angles
Be able to do?
• verify two triangles are congruent
• show that the triangles are congruent
given triangles that have been transformed
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Understand congruence in terms of rigid
motions
Standard: Explain how the criteria for triangle
congruence (ASA, SAS, and SSS) follow from the
definition of congruence in terms of rigid
motions.
Standard Code: G-CO.8.
DOK Target for this standard:
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
•
What should students…
Understand?
Rigid motions and their assumed properties can be used to establish the usual triangle
congruence criteria, which can then be used to prove other theorems.
Know?
ASA
SAS
SSS
congruence
distance formula
Be able to do?
• use the definitions of congruence, based
on rigid motion, to develop and explain
the triangle congruence criteria
• complete proofs involving ASA, SAS, SSS
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Prove geometric theorems
Standard: Prove theorems about lines and
Standard Code: G-CO.9.
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
endpoint.
DOK Target for this standard: 3=Strategic 1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
Thinking
LEARNING TARGETS
•
•
•
•
•
•
•
•
•
•
What should students…
Understand?
In proving geometric theorems they need to focus on the validity of the underlying reasoning
while exploring a variety of formats for expressing that reasoning.
Know?
vertical angles
alternate interior angles
corresponding angles
transversal
parallel lines
perpendicular
perpendicular bisector
equidistance
segment
Be able to do?
• prove theorems:
- vertical angles are congruent
- transversal and parallel lines
- alternate interior angles are
congruent
- corresponding angles are congruent
- points on a perpendicular bisector of
a line are equidistant from the
endpoint
• apply proven theorems to a variety of
problems
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Prove geometric theorems
Standard: Prove theorems about triangles.
Theorems include: measures of interior angles of
a triangle sum to 180°, base angles of isosceles
triangles are congruent; the segment joining
midpoints of two sides of a triangle is parallel to
the third side and half the length; the medians of
a triangle meet at a point.
Standard Code: G-CO.10.
DOK Target for this standard: 3=Strategic
Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
What should students…
Understand?
In proving geometric theorems they need to focus on the validity of the underlying reasoning
while exploring a variety of formats for expressing that reasoning.
Know?
isosceles triangle
midpoint
median
triangle
Be able to do?
• prove theorems about triangles
- in angles equal to 180
- base angles of isosceles triangles are
congruent
- segment joining midpoints of 2 sides
of a triangle is parallel to the third
side and ½ of length
- medians of a triangle meet at a
point
• apply proven theorems to a variety of
problems
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Prove geometric theorems
Standard: 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.
Standard Code: G-CO.11.
DOK Target for this standard: 3=Strategic
Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
In proving geometric theorems they need to focus on the validity of the underlying reasoning
while exploring a variety of formats for expressing that reasoning.
Know?
•
•
•
•
•
•
congruent
angles
parallelogram
bisector
rectangle
diagonals
Be able to do?
• prove and apply theorems about
parallelograms:
- opposite sides are congruent
- opposite angles are congruent
- diagonals of a parallelogram bisect
each other
- rectangles are parallelograms with
congruent diagonals
• apply proven theorems to a variety of
problems
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Make geometric constructions
Standard: Make formal geometric
constructions with a variety of tools and
methods (compass and straightedge, string,
reflective devices, paper folding, dynamic
geometric software, etc.) Copying a segment;
copying an angle; bisecting a segment; 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.
Standard Code: G-CO.12.
DOK Target for this standard:
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Geometric constructions can be created using a variety of tools.
•
•
•
•
•
Know?
segment
angle
bisector
perpendicular
parallel
Be able to do?
• construct the following:
- copy the segment
- copy an angle
- bisect a segment
- bisect an angle
- perpendicular lines including
perpendicular bisector of a segment
- parallel lines given a point not on a
line
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Conditional Statements
Standard: Write and conceptually understand
the structure of conditional statements and
their converses.
Standard Code: MA.G.CO.01
DOK Target for this standard:
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Conditional statements and their converses may have different truth values.
•
•
•
Know?
conditional statements
If-then
truth value
Be able to do?
• write a statement in conditional form
• write the converse of a conditional
statement
• determine the truth value for a conditional
statement and its converse
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Prove geometric theorems.
Standard: Derive and apply the Segment
Addition and Angle Addition Postulates.
DOK Target for this standard: 1=Recall
2=Skill/Concept
Standard Code: MA.G.CO.02
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Adding collinear segments and adjacent angles create new segments and angles.
Know?
•
•
•
•
•
•
segments
collinear
angles
adjacent
postulate
solving equations
Be able to do?
• derive the Segment Addition and Angle
Addition Postulates
• solve for lengths of segments and
measures of angles using these postulates
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Congruence
Cluster: Understand congruence in terms of rigid motions
Standard: 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.
Standard Code: MA.G.CO.03
DOK Target for this standard: 3=Strategic
Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
What should students…
Understand?
Corresponding parts of congruent triangles can be used to prove a second pair of triangles are
congruent.
Know?
ways to prove two triangles are congruent
(SSS, SAS, ASA, AAS, HL)
corresponding parts of congruent triangles
are congruent
Be able to do?
• identify which triangles need to be proven
congruent first to show two other triangle
are congruent
• prove two triangles are congruent and
use CPCTC to prove two other triangles
congruent
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Understand similarity in terms of similarity
transformations
Standard: Verify experimentally the properties
of dilations given by a center and a scale factor:
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.
The dilation of a line segment is longer or
shorter in the ratio given by the scale factor.
Standard Code: Standard: G-SRT.1.
DOK Target for this standard:
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
•
•
•
What should students…
Understand?
A dilation is an enlargement or reduction of a pre-image through a center point.
Know?
dilation
scale factor
center of dilation
enlargement
reduction
how to find scale factor between preimage and image
the relationship between a pre-image,
image, and center
Be able to do?
•
•
•
•
determine the scale factor given a figure and
its dilation
determine the dilation given a figure and a
scale factor
find the center of dilation given a figure and its
dilation
draw a dilation given a figure and a center of
dilation
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Understand similarity in terms of similarity
transformations
Standard: 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.
Standard Code: G-SRT.2.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
What should students…
Understand?
Similar figures have congruent corresponding sides and proportional sides.
Triangles can be similar by various theorems.
Know?
definition of similar
definition of proportions
definition of corresponding parts of
changes
Be able to do?
• identify whether corresponding parts are
similar by proportional sides and
congruent angles
• identify the scale factor between two
similar changes
• write a similarity statement
• identify/label the corresponding parts of
the angles and sides using prime and now
letters????
• show that triangles are similar by SSS~ and
SAS ~
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Understand similarity in terms of similarity
transformations
Standard: Use the properties of similarity
transformations to establish the AA criterion for
two triangles to be similar.
Standard Code: G-SRT.3.
DOK Target for this standard:
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
What should students…
Understand?
Two pairs of congruent angles are sufficient to prove two triangles are similar. (AA)
Know?
Triangle Angle Sum Theorem: If 3 angles of
one triangle are congruent to 3 angles of
another triangle, then the triangles are
dilations of one another, and therefore,
similar
Be able to do?
• show that the triangles are similar given
two pairs of congruent angles in two
triangles
• derive the Third Angles Theorem
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Prove theorems involving similarity
Standard: 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.
Standard Code: G-SRT.4.
DOK Target for this standard: 3=Strategic
Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
What should students…
Understand?
Similarity is used to prove theorems about triangles.
Know?
properties of proportions
recognize the 3 similar triangles when an
altitude is drawn from the right angle of a
right triangle
Be able to do?
• show that the split sides are proportional
given a line parallel to one side of a
triangle that intersects the triangle
• find any other segment length given a
right triangle with an altitude drawn from
the right angle and 2 segment lengths
• find the geometric mean between two
numbers
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Prove theorems involving similarity
Standard: Use congruence and similarity
criteria for triangles to solve problems and to
prove relationships in geometric figures.
Standard Code: G-SRT.5.
DOK Target for this standard: 1=Recall
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Non-triangular geometric figures can be shown to be congruent or similar in the same way
triangles are.
Know?
• congruent figures are similar figures with a
scale factor of 1
Be able to do?
• prove triangles are congruent or similar
using similarity and congruency theorems
(SSS, SAS, ASA, AAS, HL 𝐴𝐴~, 𝑆𝐴𝑆 ~, 𝑆𝑆𝑆~)
• prove other geometric figures are similar
and/or congruent using the criteria found
from triangles
• show all sides proportional and all angles
congruent
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Define trigonometric ratios and solve
problems involving right triangles
Standard: 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.
Standard Code: G-SRT.6.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
What should students…
Understand?
Similar right triangles are used to generate ratios between sides, leading to trigonmetric
functions.
Know?
similar triangles
right triangles
ratio
proportion
Be able to do?
• use a corresponding angle to show the
three side ratios are the same given the
lengths of the sides of two similar right
triangles
• define the trigonmetric ratios (sine, cosine
and tangent)
• discover the relationships in special right
triangles
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Define trigonometric ratios and solve
problems involving right triangles
Standard: Explain and use the relationship
between the sine and cosine of complementary
angles.
Standard Code: G-SRT.7.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
The sine and cosine of complementary angles are equivalent.
•
•
•
Know?
Sine
Cosine
complementary
Be able to do?
• express a sine ratio in terms of a cosine
and vice-versa (co-functions)
• show that the sine of an angle is equal to
the cosine of the angle’s complement
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Define trigonometric ratios and solve
problems involving right triangles
Standard: Use trigonometric ratios and the
Pythagorean Theorem to solve right triangles in
applied problems.
Standard Code: G-SRT.8.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
•
•
•
•
•
What should students…
Understand?
Six parts of right triangles are interdependent.
All missing parts of a right triangle can be found using trigonometric ratios and/or Pythagorean
Theorem.
Know?
right triangles
SOH CAH TOA
Pythagorean theorem
square roots
inverse trigonometry
opposite and adjacent legs
hypotenuse
angle of elevation and angle of depression
Be able to do?
• draw triangle from a word problem
• identify missing parts and choose
appropriate trigonometry ratio or
Pythagorean theorem to find missing
sides
• solve equation to find missing part
• use the trig ratios and Pythagorean
theorem to solve right triangles in applied
problems
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Apply trigonometry to general triangles
Standard: (+) Derive the formula A = ½ ab
sin(C) for the area of a triangle by drawing an
auxiliary line from a vertex perpendicular to the
opposite side.
Standard Code: G-SRT.9.
DOK Target for this standard:
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
The area of oblique (non-right) triangles can be found by A=1/2 ab sin C.
•
•
•
Know?
definition of oblique triangles
Sine
formula for the area of a triangle
Be able to do?
• apply formula A = ½ ab sin C to find area of
oblique triangles
• derive A = ½ ab sin C from basic area formula
(A = ½bh) using
b
C
A
h
a
c
B
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Apply trigonometry to general triangles
Standard: (+) Prove the Laws of Sines and
Cosines and use them to solve problems.
Standard Code: G-SRT.10.
DOK Target for this standard: 1=Recall
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
The Law of Sines and Law of Cosines are used to find missing pieces of oblique (non-right)
triangles.
Know?
•
•
•
Sine
Cosine
when to use Law of Sines vs. Law of
Cosines vs. SOH CAH TOA
Be able to do?
• prove the Law of Sines and Law of Cosines
using:
b
A
h
C
c
B
a
•
use Law of Sines and Law of Cosines to solve
oblique triangles
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Similarity, Right Triangles,
and Trigonometry
Cluster: Apply trigonometry to general triangles
Standard: (+) 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).
DOK Target for this standard: 1=Recall
2=Skill/Concept
Standard Code: G-SRT.11.
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
The Law of Sines and Cosines can be used in applied problems to find missing sides and angles of
any type of triangle.
Know?
•
•
•
Law of Sines
Law of Cosines
when to use the Law of Sines vs. the Law
of Cosines
Be able to do?
• use Law of Sines and Cosines to find
unknown measures of right and oblique
triangles in real-world problems
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Circles
Cluster: Understand and apply theorems about
circles
Standard: Prove that all circles are similar.
Standard Code: G-C.1.
DOK Target for this standard: 3=Strategic
Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Circles are similar and therefore, useful ratios are created.
•
•
•
•
•
•
•
•
Know?
formula(s) for circumference
radius
diameter
circle
circumference
similarity
ratio
proportions
Be able to do?
• find ratio of similarity using
circumference/diameter and identify that
the ratio is 𝜋
• use similarity ratios to find missing
information
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Circles
Cluster: Understand and apply theorems about
circles
Standard: Identify and describe relationships
among inscribed angles, radii, and chords.
Include the relationship between central,
inscribed, and circumscribed angles; inscribed
angles on a diameter are right angles; the radius
of a circle is perpendicular to the tangent where
the radius intersects the circle.
Standard Code: G-C.2.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Segments drawn in circles create relationships between arcs and angles.
•
•
•
•
•
•
•
•
Know?
chords
tangent
arc measure
inscribed angle
central angle
diameter
secant
arc length
Be able to do?
• use relationships between diameter, radii,
chords, tangents, and secants to find
angles and arcs
• find measure of inscribed, central,
circumscribed, etc., angles and their
intercepted arcs
• use relationships to find segment lengths
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Circles
Cluster: Find arc lengths and areas of sectors of
circles
Standard: 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.
Standard Code: G-C.5.
DOK Target for this standard: 1=Recall
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Circles are similar, and therefore, useful ratios are created.
•
•
•
•
Know?
circumference of a circle
area of a circle
definition of an arc/arc length
definition of a sector
Be able to do?
• find the circumference of a circle
• find the arc length of a sector
• measure several radii and arc lengths and
compare their proportionality
• recognize that proportionality ratio is the
angle measure in radians
• compare full circle to part of circle
• derive the formula for the area of a sector
• apply the area of a sector to a wide
variety of problems (find area, find
missing information)
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Expressing Geometric
Properties with Equations
Cluster: Translate between the geometric description and
Standard: 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.
DOK Target for this standard: 1=Recall
2=Skill/Concept
3=Strategic Thinking
Standard Code: G-GPE.1.
the equation for a conic section
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
•
What should students…
Understand?
The equation of a circle can be derived from Pythagorean Theorem and that they can change
from standard form to vertex form by completing the square.
Know?
Be able to do?
distance formula
• derive the equation of a circle given center
and radius using Pythagorean Theorem
Pythagorean Theorem
(distance formula)
properties of radicals
• complete the square to find the center
completing the square
and radius of a circle
factoring
• manipulate the equations of circles from
vertex to standard form
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Expressing Geometric
Properties with Equations
Cluster: Translate between the geometric
description and the equation for a conic section
Standard: Derive the equation of a parabola
given a focus and directrix.
Standard Code: G-GPE.2.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Given a focus and directrix they can derive the equation of a parabola.
•
•
•
•
Know?
distance formula
standard form
vertex form
FOIL
Be able to do?
• derive the equation of a parabola given a
focus and directrix
• find the equation of a parabola given a
focus and directrix
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple geometric
theorems algebraically
Standard: Use coordinates to prove simple
geometric theorems algebraically. For example,
prove or disprove that a figure defined by four
given points in the coordinate plane is a
rectangle; prove or disprove that the point (1,
√3) lies on the circle centered at the origin and
containing the point (0, 2).
Standard Code: G-GPE.4.
DOK Target for this standard: 3=Strategic
Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Algebra can be applied to geometric proofs.
Know?
•
•
•
•
•
•
•
•
•
slope
distance formula
midpoint formula
coordinate plane
theorems on quadrilaterals
theorems on triangles
definitions of rectangle, square, kite,
rhombus, trapezoid, parallelogram, circle,
triangle
how to classify quadrilaterals
how to classify/name triangles
Be able to do?
• prove a figure is a specific type of
quadrilateral using distance and slope
• prove a triangle is either isosceles,
equilateral or scalene
• prove a point lies on a circle
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple geometric
theorems algebraically
Standard: 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).
Standard Code: G-GPE.5.
DOK Target for this standard: 1=Recall
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
The slope criteria for parallel and perpendicular lines can be used to solve geometric problems.
•
•
•
•
•
•
•
•
Know?
slope
parallel lines
perpendicular lines
slope-intercept form
point-slope form
perpendicular bisector
altitude
midpoint
Be able to do?
• find equations of a line parallel to a line
through a given point
• find equation of a line perpendicular to a
line through a given point
• find a perpendicular bisector to a line or
side of triangle
• find an altitude of a triangle
• find a median of a triangle
• find the median of a trapezoid
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple geometric
theorems algebraically
Standard: Find the point on a directed line
segment between two given points that
partitions the segment in a given ratio.
Standard Code: G-GPE.6.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Line segments can be partitioned proportionally.
Know?
•
•
•
•
•
•
•
ratio
distance formula
midpoint formula
proportion
endpoint
line segment
triangle proportionality theorem
Be able to do?
• determine the coordinate of a point on a
given line segment in given ratio:
- number line
- coordinate plane
• find lengths of segments with proportional
relationships:
- triangles with altitudes
- triangles with line parallel to a side
- 3 parallel lines cut by a transversal
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Expressing Geometric
Properties with Equations
Cluster: Use coordinates to prove simple geometric
theorems algebraically
Standard: Use coordinates to compute
perimeters of polygons and areas of triangles
and rectangles, e.g., using the distance formula.
DOK Target for this standard: 1=Recall
2=Skill/Concept
Standard Code: G-GPE.7.
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
•
What should students…
Understand?
The area or perimeter of a figure can be found by applying geometric concepts to points on a
coordinate plane.
Know?
distance formula
area formula
perimeter
simplify radicals
identify polygons
Be able to do?
•
•
•
use the distance formula to find the lengths of
sides
find perimeter of polygons drawn in the
coordinate plane
find areas of triangles and rectangles drawn
on the coordinate plane
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Geometric Measurement and
Dimension
Cluster: Explain volume formulas and use them to
solve problems
Standard: 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.
Standard Code: G-GMD.1.
DOK Target for this standard:
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Perimeter, area and volume of two dimensional and three dimensional shapes can be derived.
•
•
Know?
volume formulas
area formulas
Be able to do?
• use Cavalieri’s principles with cross
sections of cylinders, pyramid and cones
to compare the volumes
• use a combination of concrete models and
formal reasoning to formulate conceptual
understanding of the volume formulas
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Geometric Measurement and
Dimension
Cluster: Explain volume formulas and use them to
solve problems
Standard: Use volume formulas for cylinders,
pyramids, cones, and spheres to solve problems.
DOK Target for this standard: 1=Recall
2=Skill/Concept
Standard Code: G-GMD.3.
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
What should students…
Understand?
Volume formulas are useful for solving real-world problems.
Know?
volume formulas for:
- cylinders
- pyramids
- spheres
- cones
area formulas for:
rectangles
circles
triangles
Be able to do?
• calculate the volume of cylinders,
pyramids, spheres and cones
• use the volume formulas to solve
problems in a real-world context
• solve for a missing variable in a formula
given the volume
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Geometric Measurement and
Dimension
Cluster: Visual relationships between twodimensional and three-dimensional objects
Standard: Identify the shapes of twodimensional cross-sections of three-dimensional
objects, and identify three-dimensional objects
generated by rotations of two-dimensional
objects.
Standard Code: G-GMD.4.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
There is a relationship between two and three dimensional shapes.
•
•
•
•
Know?
names of the 2-D shapes
names of the 3-D shapes
definition of cross-section
definition of rotation
Be able to do?
• draw/visualize cross-sections created when
2-D shapes intersect 3-D shapes
• determine the different cross- sections
created when cutting the 3-D shape at
various angles
• identify the 3-D objects generated by
rotations of 2-D objects
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Modeling with Geometry
Cluster: Apply geometric concepts in modeling
situations
Standard: Use geometric shapes, their
measures, and their properties to describe
objects (e.g., modeling a tree trunk or a human
torso as a cylinder).
Standard Code: G-MG.1.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
What should students…
Understand?
Real life objects can be modeled using two dimensional and three dimensional geometric
shapes.
Know?
Be able to do?
two dimensional shapes properties
• recognize two dimensional and three
dimensional shapes in real life situations
three dimensional shapes properties
• create three dimensional objects and
discuss their properties
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Modeling with Geometry
Cluster: Apply geometric concepts in modeling
situations
Standard:
Standard Code:
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
What should students…
Understand?
• Apply concepts of density based on area and volume in modeling situations (e.g., persons per square
mile, BTU’s per cubic foot).
Know?
Be able to do?
• formulas for calculating area
• determine which formula(s) should be
used in a given situation
• formulas for calculating volume
• draw 2-dimensional and 3-dimensional
• appropriate units of measurement for
figures that model a given situation
specific quantities
• solve application problems that require
• 2-D and 3-D shapes
finding area and volume
• proportions
• density
• unit analysis
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Modeling with Geometry
Cluster: Apply geometric concepts in modeling
situations
Standard Code: G-MG.3.
Standard: 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).
DOK Target for this standard:
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Real life objects can be modeled using 2-D and 3-D geometric shapes.
Know?
•
•
2-D and 3-D shapes and their properties
formulas for area, surface area and
volume of 2-D and 3-D shapes
Be able to do?
•
•
•
•
calculate area, surface area and volume of
2-D and 3-D shapes in real-world context
find the dimension of 2-D and 3-D shapes
that satisfy certain physical constraints
given a real-world example, find errors and
re-calculate area, surface area and volume
(find errors in an estimate to build)
create a 3D project that involves surface
area and volume calculations and then
build it
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Conditional Probability and
the Rules of Probability
Cluster: Understand independence and conditional
probability and use them to interpret data
Standard: Describe events as subsets of a
sample space (the set of outcomes) using
characteristics (or categories) of the outcomes,
or as unions, intersections, or complements of
other events (“or,” “and,””not”).
Standard Code: S-CP.1.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Independence and conditional probability can be used to interpret data.
Know?
Definitions
• union (“or”) of an event
• intersection (“and”) of two events
• complement (“not”) of an event
• sample space
• subset
appropriate symbols of union, intersection, and
complement
Be able to do?
•
•
identify sample space and events within a
sample space
identify subsets from within the sample space
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Conditional Probability and
the Rules of Probability
Cluster: Understand independence and conditional
probability and use them to interpret data
Standard: Understand that two events A and B
are independent of the probability of A and B
occurring together is the product of their
probabilities, and use this characterization to
determine if they are independent.
Standard Code: S-CP.2.
DOK Target for this standard: 1=Recall
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Independence and conditional probability can be used to interpret data.
Know?
Definitions
• independent events
• conditional probability
Be able to do?
• determine if two events are independent
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Conditional Probability and
the Rules of Probability
Cluster: Understand independence and conditional
probability and use them to interpret data
Standard: Understand the conditional
probability of A given B as P(A and B)/P(B), and
interpret independence of A and B as saying
that the conditional probability of A given B is
the same as the probability of A, and the
conditional probability of B given A is the same
as the probability of B.
Standard Code: S-CP.3.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Independence and conditional probability can be used to interpret data.
Know?
• multiplication principle
Be able to do?
• use the multiplication principle to calculate
conditional probabilities
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Conditional Probability and
the Rules of Probability
Cluster: Understand independence and conditional
probability and use them to interpret data
Standard: Construct and interpret two-way
frequency tables of data when two categories
are associated with each object being classified.
Use the two-way table as a sample space to
decide if events are independent and to
approximate conditional probabilities.
Standard Code: S-CP.4.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
What should students…
Understand?
•
Independence and conditional probability can be used to interpret data.
•
•
•
•
Know?
sample space
two-way table
conditional probability
independent events
Be able to do?
• construct and interpret two-way
frequency tables for two categorical
variables
• calculate probabilities from the two-way
tables
• use probabilities from the table to
evaluate independence
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Conditional Probability and
the Rules of Probability
Cluster: Understand independence and conditional
probability and use them to interpret data
Standard: Recognize and explain the concepts
of conditional probability and independence in
everyday language and everyday situations.
Standard Code: S-CP.5.
DOK Target for this standard: 1=Recall
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Independence and conditional probability can be used to interpret data.
•
•
Know?
independent events
conditional probability
Be able to do?
• recognize and explain the concepts of
conditional probability and independence
in a real-life setting
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Conditional Probability and
the Rules of Probability
Cluster: Use the rules of probability to compute
probabilities of compound events in a uniform
probability model
Standard: Find the conditional probability of A
given B as the fraction of B’s outcomes that also
belong to A, and interpret the answer in terms
of the model.
Standard Code: S-CP.6.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Independence and conditional probability can be used to interpret data.
Know?
• conditional probability formula
Be able to do?
• calculate and interpret conditional
probability of A given B
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Conditional Probability and
the Rules of Probability
Cluster: Use the rules of probability to compute
probabilities of compound events in a uniform
probability model
Standard: Apply the Addition Rule, P(A or B) =
P(A) + P(B) – P(A and B), and interpret the
answer in terms of the model.
Standard Code: S-CP.7.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Different probability formulas can use be used to calculate and interpret real world phenomena.
Know?
Definitions
• disjoint events
• mutually exclusive events
addition rule of probability
Be able to do?
• calculate and interpret probabilities using
the addition rule
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Conditional Probability and
the Rules of Probability
Cluster: Use the rules of probability to compute
probabilities of compound events in a uniform
probability model
Standard: (+) Apply the general Multiplication
Rule in a uniform probability model, P(A and B)
= P(A)P(BA) = P(B)P(AB), and interpret the
answer in terms of the model.
Standard Code: S-CP.8.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Different probability formulas can use be used to calculate and interpret real world phenomena.
•
•
•
Know?
multiplication rule of probability
conditional probability
independent events
Be able to do?
• calculate and interpret a probability using
the multiplication rule
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Conditional Probability and
the Rules of Probability
Cluster: Use the rules of probability to compute
probabilities of compound events in a uniform
probability model
Standard: (+) Use permutations and
combinations to compute probabilities of
compound events and solve problems.
Standard Code: S-CP.9.
DOK Target for this standard: 1=Recall
2=Skill/Concept
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
What should students…
Understand?
Different probability formulas can use be used to calculate and interpret real world phenomena.
Know?
Definitions
• factorials
• combination
• permutation
Formulas to calculate probabilities of a
• combination
• permutation
Be able to do?
• determine the difference between a
permutation and a combination
• calculate probabilities using the
appropriate permutation or combination
formula
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Using Probability to Make
Decisions
Cluster: Use probability to evaluate outcomes of
decisions
Standard: (+) Use probabilities to make fair
decisions (e.g., drawing by lots, using a random
number generator).
DOK Target for this standard: 1=Recall
2=Skill/Concept
Standard Code: S-MD.6.
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
What should students…
Understand?
Probabilities exhibit relationships that can be extended, described, and generalized to make
decisions.
Know?
definition of random
how to use a random number generator
Be able to do?
• understand factors that make decisions fair
and random
o toss a die
o flip a coin
o use a spinner
2015 Algebraic Geometry
UNPACKING THE STANDARDS
Course: Geometry
Standards Used: MLS
Strand/Domain: Using Probability to Make
Decisions
Cluster: Use probability to evaluate outcomes of
decisions
Standard: (+) Analyze decisions and strategies
using probability concepts (e.g., product testing,
medical testing, pulling a hockey goalie at the
end of a game).
Standard Code: S-MD.7.
DOK Target for this standard: Recall
2=Skill/Concept
3=Strategic Thinking
1=Recall
2=Skill/Concept
3=Strategic Thinking 4=Extended Thinking
LEARNING TARGETS
•
•
•
•
•
What should students…
Understand?
Probabilities exhibit relationships that can be extended, described, and generalized to make
decisions.
Know?
multiplication rule
addition rule
permutations
combinations
Be able to do?
• use multiplication rule to find the
intersection of independent events
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵)
• use addition rule to find probabilities
(with Venn diagrams for example) of AND
and OR events
• analyze decisions and strategies using
probability concepts
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
Introduction to Geometry and Basic Constructions
SUGGESTED UNIT TIMELINE:
3 weeks
ESSENTIAL QUESTION(S):
How are points, lines, rays and segments related ? How does each pre-image relate to its image? How do transformations relate to congruence?
In what ways is it possible to construct different geometric figures?
In what ways can congruence be useful?
REFERENCE/
STANDARD #
G-CO.1
G-CO.2
G-CO.3
G-CO.4
G-CO.5
G-CO.12
STANDARDS:
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
A listing of all standards included in the unit
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.
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).
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line
segments.
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.
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices,
paper folding, dynamic geometric software, etc.) Copying a segment; copying an angle; bisecting a segment; 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.
UNIT DESCRIPTION:
Students will understand the defined and undefined terms of Geometry,
analyze and apply transformations to geometric figures and understand
properties that are preserved by these transformations.
Students will construct geometric figures using a variety of tools and
resources.
UNIT VOCABULARY
SUPPORTING
STANDARD
(S)





Point, line, plane, ray, collinear, coplanar, intersection, opposite rays, segments,
angle, vertex, circle, perpendicular, parallel, distance, circumference, rectangle,
parallelogram, trapezoid, regular polygon, transformation, rotation, reflections,
translation, dilation, vector, symmetry, congruence, construct, bisect
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE
MAJOR
STANDARD
(M)

A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
2015 Algebraic Geometry
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
G-CO.1
TEACHER INSTRUCTION
Use constructions to develop
formal definitions of
midpoint, angle bisector,
segment bisector,
perpendicular bisector and
congruence
STUDENT LEARNING
Skills Checks – p. 1-2
McDougal Littell
Textbook – p. 46
Written Exercises
Derive Midpoint and Angle
Bisector Theorems McDougal Littell Textbook
(pages 43/44)
G-CO.2
Glencoe Geometry Textbook
Rotation Demonstration
Activity
Practice Worksheets
9.1-9.6, Glencoe Book
Rotation Demonstration
(Geogebra)
Reflection Demonstration
Activity
Reflection Demonstration
(y=x) (Geogebra)
Reflection Demonstration
(hor/ver) (Geogebra)
Translation Demonstration
Translation Demonstration
(vector) (Geogebra)
G-CO.3
Horizontal stretch of a
parabola illustrations
Discover and demonstrate
rotational symmetry to map
a figure onto itself.
Rotational symmetry
activity for students
HOW WILL WE RESPOND
WHEN STUDENTS HAVE NOT
LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN STUDENTS
HAVE ALREADY LEARNED?
EXTENSIONS
2015 Algebraic Geometry
Discover how a reflection or
series of reflections can map
a figure onto itself.
Rotational symmetry
demonstration for
students
Rotation/Reflection Lesson
Glencoe Book 9.1
(reflections) and 9.3
(rotations)
G-CO.4
New York Curriculum
Lesson 15 (p. 111)
Rotation/Reflection
relationship
New York Curriculum
Lesson 16 (p. 117) Discovery
of Definition of Translation
G-CO.5
G-CO.12
New York Curriculum
Lesson 18 (p. 131)
Discovering parallel lines
using reflection
Compositions of
Transformations
Use technology (Geogebra,
SMART Notebook, Core
Math Tools, etc.) to
contstruct
Construction Tutorials
Reflection discovery
activity for students
Video introducing
transformations
Compositions of
Transformations WS
Use compass and
straight edge to
construct
Construction
Instruction Packet
Construction Tutorials
ADDITIONAL UNIT RESOURCES
Video: Review of Points, Lines, and Planes – go to LearnZillion.com and search for LZ4568
Video: Importance of Precise Geometric Terms – go to LearnZillion.com and search for LZ4571
2015 Algebraic Geometry
Transformations Review Packet
Website with additional resources (under construction)
DISCOVERY EDUCATION RESOURCES
STANDARD: G.CO.1
Video
Math
Explanation
Model
Lesson
STANDARD: G.CO.2
Video
Math
Overview
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.
Circles: Formulas and Definitions
Defining Circles
Defining Circumference, Radius and Diameter
Circular Structures: Design and Architecture
Geometry: Introduction to Angles: Definitions
Geometry: Angle Relationships: Definitions
Geometry: Points, Lines, and Planes: Definitions/Examples
Geometry: Points, Lines, and Planes: A Line Perpendicular to a Plane
Geometry: Congruence, Symmetry, and Transformations
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).
Example 2: Rotation and Translation -- The London Eye and Boating
Example 3: Reflection -- Beach Flag
Example 3: Geometric Functions -- Art
Computer Coordinates: Playing with Pixels
Geometry: Using Matrices to Perform Transformations
Geometry: Translations and Glide Reflections
Geometry: Reflections
2015 Algebraic Geometry
Math
Explanation
Geometry: Translations and Glide Reflections: Coordinate Notation
Model
Lesson
Geometry: Congruence, Symmetry, and Transformations
Congruence and Proof
2015 Algebraic Geometry
STANDARD: G.CO.3
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Video
Symmetry and Transformations
Reflections Beach Bag
Math
Explanation
Geometry: Reflections: Angles of Rotation
Geometry: Reflections: Lines and Points of Symmetry
Math
Overview
Geometry: Reflections
Model
Lesson
Geometry: Congruence, Symmetry, and Transformations
Activity
Symmetry and Transformations
STANDARD: G.CO.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and
line segments.
Video
Geometric Transformations
Math
Explanation
Geometry: Translations and Glide Reflections: Invariant Points
Geometry: Congruent Triangles and Congruence Transformations: Transformations
Math
Overview
Congruent Triangles and Congruence Transformations
Geometry: Reflections
Model
Lesson
Geometry: Congruence, Symmetry, and Transformations
2015 Algebraic Geometry
STANDARD: 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
Video
Example 1: Translations
Example 2: Rotations
Math
Explanation
Geometry: Translations and Glide Reflections: Graphing Translations of Segments
Geometry: Translations and Glide Reflections: Sketching Glide Reflections
Geometry: Reflections: Coordinate Plane Double Reflections
Geometry: Reflections: Double Reflections, Part Two
Model
Lesson
Geometry: Congruence, Symmetry, and Transformations
Activity
Algebra Rules and Combinations
STANDARD: 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. 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.
Video
Example 2: Constructing an Angle Bisector
Example 3: Constructing a Perpendicular Bisector
Example 2: Drawing a Perpendicular Line -- Planning a Wall
Example 3: Bisecting an Angle -- American Indian Museum
Math
Overview
Geometry: Constructions: Parallel and Perpendicular Lines
Math
Explanation
Geometry: Segment Length and Precision: Constructing a Bisector
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
SUGGESTED UNIT TIMELINE:
Introduction to Proofs
2 weeks
ESSENTIAL QUESTION(S):
What is the congruence relationship between the angle pairs formed from intersecting lines?
REFERENCE/
STANDARD #
G-CO.9
STANDARDS:
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
A listing of all standards included in the unit
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 endpoint.
UNIT DESCRIPTION:
Students will be able to identify and prove angle relationships that occur with
parallel lines that are cut by a transversal, intersecting lines and
perpendicular lines.
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)

UNIT VOCABULARY
Parallel lines, intersecting lines, perpendicular lines, vertical angles,
transversal, alternate interior angles, corresponding angles, perpendicular
bisector
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE (link)
A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
G-CO.9
TEACHER INSTRUCTION
Glencoe book 171-184
STUDENT LEARNING
HOW WILL WE RESPOND WHEN
STUDENTS HAVE NOT LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
EXTENSIONS
2015 Algebraic Geometry
Introduction to angle
theorems
Angle theorems with
illustrations
Parallel lines and
transversals worksheet
Re-teach site with practice
problems
New York Common Core
Curriculum Lesson 9
(unknown angle proofs)
p. 66
Khan Academy video proving
vertical angles congruent
Foldable for parallel lines
cut by a transversal
Dummies.com perpendicular
bisector proof
Practice with parallel
lines
Parallel lines resource
Perpendicular bisector
practice
Glencoe book pg 327
Parallel lines and angle
relationship
Parallel lines task
Algebraic Proofs
Segment addition and
Angle addition proofs
Parallel line proofs
Perpendicular bisector
practice
ADDITIONAL UNIT RESOURCES
Geometry Teacher – Unit 2 -http://www.geometry-teachers.com/
2015 Algebraic Geometry
DISCOVERY EDUCATION RESOURCES
STANDARD: 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; and points on a perpendicular bisector of a line
segment are exactly those equidistant from the segment's endpoints.
Video
Section B: Angles and Their Theorems
Section C: Parallel Lines and Angles
Math
Overview
Geometry: Introduction to Proofs
Geometry: Proving Two Lines Are Parallel
Math
Explanation
Geometry: Proving Two Lines Are Parallel: Proving Lines Are Parallel
Geometry: Inscribed Angles: Proofs
Model Lesson
Activity
Congruence and Proof
Congruence Theorems
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
SUGGESTED UNIT TIMELINE:
Triangle Congruence
ESSENTIAL QUESTION(S):
3 weeks
What processes are valid to prove two triangles are congruent?
What can you conclude about two triangles that are congruent?
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
REFERENCE/ STANDARDS:
STANDARD A listing of all standards included in the unit
#
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
G-CO.6
G-CO.7
figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
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.
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G-CO.8
UNIT DESCRIPTION:
Students will be able to determine if and prove that two triangles are
congruent.
UNIT VOCABULARY
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)



Rigid motion, corresponding parts,
ASA, SAS,SSS,ASA,SAS, SSS, HL, CPCTC
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE (link)
A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
G-CO.6
G-CO.7
TEACHER INSTRUCTION
Page 232-307
Glencoe Geometry Textbook
Section 4.3 – Identify
congruent figures and name
by corresponding parts
STUDENT LEARNING
Worksheet – Triangle
Angle Sum
Triangle Congruence
Skills Checks – Page 2
Video Showing Triangle Angle Worksheet –
Sum Theorem – cutting angles Corresponding parts
to form a line
Multiple Choice
Questions
Show Triangles are
Activity to Discover
Congruent – Also links to SSS, Triangle Congruences –
HOW WILL WE RESPOND WHEN
STUDENTS HAVE NOT LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
EXTENSIONS
Best Strategies by Benson – p. 27 #46
2015 Algebraic Geometry
SAS, AAS, ASA, HL
SSS, SAS, ASA, AAS, and
HL, and why AAA and SSA
don’t work
Activity to Discover SSS
and SAS – Easy to apply to
ASA
Triangle Congruence
Skills Checks – Page 1
G-CO.8
Why AAA Doesn't Work
Why SSA Doesn't Work
Glencoe Geometry
Textbook – Section 4-4 p
268 #23, 30, 31, 33
Activity to Discover
Triangle Congruences –
SSS, SAS, ASA, AAS, and
HL, and why AAA and SSA
don’t work
Best Strategies by BensonProofs on p. 5 #4-5, p. 6
#6, p. 8 #10
Why AAA and SSA Don't
Work
Video – Why SSA
sometimes works
Worksheet – Using SSS et
al to determine
congruency
Worksheet – Using SSS et
al in proofs
ADDITIONAL UNIT RESOURCES
Jeopardy – Triangle Angle Sum, Congruence, CPCTC
Worksheet – Using CPCTC in proofs
Worksheet – Using CPCTC in proofs
Project – Proof Puzzles
Best Strategies by Benson – p. 9 #12
2015 Algebraic Geometry
DISCOVERY EDUCATION RESOURCES
STANDARD: 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.
Math
Overview
Geometry: Congruent Triangles and Congruence Transformations
Geometry: Space Figures and Drawings
Math
Explanation
Geometry: Translations and Glide Reflections: Isometries
Geometry: Congruent Triangles and Congruence Transformations: Identifying Congruent Triangles
Model Lesson
STANDARD: G.CO.7
Math
Explanation
Model Lesson
STANDARD: G.CO.8
Congruence and Proof
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.
Geometry: Congruent Triangles and Congruence Transformations: Naming Congruent Sides and Angles
Geometry: Congruent Triangles and Congruence Transformations: Naming Congruent Angles and Sides
Geometry: Congruent Triangles and Congruence Transformations: Finding Congruent Triangles in Patterns
Congruence and Proof
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.
Math
Explanation
Geometry: Congruent Triangles and Congruence Transformations: Transformations
Math
Overview
Geometry Proving Angles are Congruent
Geometry Proving Angles are Congruent
2015 Algebraic Geometry
Model Lesson
Congruence and Proof
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
Triangles and Coordinate Proofs
ESSENTIAL QUESTION(S):
SUGGESTED UNIT TIMELINE:
2 weeks
How do you use prior knowledge to prove a new idea?
How do algebraic concepts relate to the segments and angles within a triangle?
How can the coordinate plane be used to prove properties of triangles?
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
REFERENCE/ STANDARDS:
STANDARD A listing of all standards included in the unit
#
G-CO.10
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°, base angles of isosceles triangles
G-GPE.4
G-GPE.5
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.
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points
in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the
point (0, 2).
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).
UNIT DESCRIPTION:
The student will define midsegment, median, centroid, perpendicular and
angle bisectors, and altitude of triangles.
The student will apply and prove properties of these parts of triangles.
Students will use the coordinate plane to complete proofs.
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)



UNIT VOCABULARY
Altitude, Angle bisector, Centroid, Equilateral, Isosceles, Median, Midsegment,
Parallel, Perpendicular, Perpendicular bisector, Scalene
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE (link)
A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
HOW WILL WE
RESPOND
WHEN
STUDENTS
HAVE NOT
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
2015 Algebraic Geometry
LEARNED?
STANDARD #
G-CO.10
TEACHER INSTRUCTION
Prove/discover that base
angles of isosceles triangles
are congruent.
-Proving base angles of
isosceles triangles congruent
STUDENT LEARNING
INTERVENTIONS
EXTENSIONS
-Calibrating Consoles (Problem-Based Tasks:
Math II, Pg 181)
-Isosceles Triangle Proof (Best
Strategies by Benson, #12)
-Angle Bisector Application (Best Strategies
by Benson, #17)
-Jigsaw Vocabulary Activity
-Isosceles Triangle Discovery
and Application
In Glencoe text on page 283291 section 4-6
G-CO.10
Define and apply
midsegment, median,
centroid, perpendicular and
angle bisectors, and altitudes
of triangles.
-Finding Centroid and
Orthocenter
-Centroid Application (Best Strategies by
Benson, #153)
-Medians and Altitude Notes
& Problems
-Finding lengths of medians in a right
triangle (Best Strategies by Benson, #155)
-Median of a Triangle Notes
-Orthocenters and Altitudes (Best Strategies
by Benson, #156)
-Concurrent Medians
Construction
In Glencoe text on page 322291 sections 5-1 and 5-2
G-GPE.5
-Finding Medians (Best Strategies by Benson,
#149)
Review slope-intercept form,
point-slope form,
perpendicular bisector,
altitude, and midpoint. In
Glencoe text on page 196204 sections 3-4
-Finding Bisectors, Medians and Altitudes
(Geometry Stations, Pg 50-54)
-9 Point Circle Project
-Review distance with triangles (Best
Strategies by Benson, #69)
-Review distance in coordinate plane (Best
Strategies by Benson, #70)
2015 Algebraic Geometry
Introduce slopes of parallel
and perpendicular lines. In
Glencoe text on page 186195 sections 3-3
Find equation of a line
parallel/perpendicular to a
line through a given point.
Find a perpendicular bisector
to a line or side of a triangle.
Find the equation for the
altitude/median of a triangle
given vertices.
-Equation of Perpendicular Bisector (Best
Strategies by Benson, #132)
-Centroid Problem (Best Strategies by Benson,
#133)
-Review slope (Best Strategies by Benson,
#134)
-Altitude Equation with Median (Best
Strategies by Benson, #135)
-Equations of Medians and Altitudes
-Equations of Medians and Altitudes
-Equations of Medians and Altitudes
-Equations of Altitudes and Perpendicular
Bisectors
-Bisectors, Medians and Altitudes
-Distance and Perpendicular lines (Geometry
Stations, Pg 205-218)
-Distance and Parallel Lines (Geometry
Stations, Pg 192-204)
Altitudes and Medians (See Teacher Resource
Files)
G-CO.10
Applications using
midsegment, median,
centroid, perpendicular and
angle bisectors, and altitude.
-Sailing Centroid (Problem-Based Tasks:
Math II, Pg 189)
-Median Application Problems
-Median Application Problems
G-CO.10
Coordinate proofs involving
midsegment, median,
centroid, perpendicular and
-Coordinate Proofs
-Constellation Coordinate Proof
2015 Algebraic Geometry
angle bisectors, and altitude.
-Coordinate Proofs
G-GPE.4
Coordinate proofs to
determine if a triangle is
isosceles, equilateral, scalene
or right using distance.
-Coordinate Proofs
-Right Triangle Proofs (#2 and #6)
-Classify Triangle by Sides
-Coordinate Proofs
-Prove a triangle is isosceles
ADDITIONAL UNIT RESOURCES
DISCOVERY EDUCATION RESOURCES
STANDARD: 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,
and the medians of a triangle meet at a point.
Video
Section B: Proving Triangles Congruent
The Angles and Their Degrees
Example 2: Geometric Proof -- Hawaii
Section A: Proving the Similarity of Triangles
Math
Overview
Geometry: Proving Triangles Are Congruent: SSS and SAS Postulates
Geometry: Proving Triangles Are Congruent: ASA Postulate and the AAS Theorem
Math
Explanation
Geometry: Introduction to Proofs: Developing Proofs
Geometry: Introduction to Proofs: Developing Proofs
Geometry: Introduction to Proofs: Flow Proofs
Model
Lesson
Congruence and Proof
2015 Algebraic Geometry
Activity
STANDARD: G.GPE.4
Video
Proving Theorems about Triangles
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).
Geometric Interpretation of the Theorem of Pythagoras
Introduction: Washington D.C. and the Coordinate Plane
Example 1: The Cartesian Coordinate System -- DC Map
Example 2: Slopes and Relationships of Lines -- DC Monuments
Example 3: Distances and Midpoints -- DC Tourists
The Distance Formula & the Midpoint Formula
Math
Overview
Geometry: Midpoints and Distance
Math
Explanation
Algebra I: The Distance Formula: Understanding the Relationship Between the Distance Formula and the Pythagorean Theorem
Geometry: Midpoints and Distance: Finding Length of a Segment Part 2
Model
Lesson
Coordinate Geometry and How It's Used
Activity
You've Got a Point
STANDARD: G.GPE.5
Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of
a line parallel or perpendicular to a given line that passes through a given point).
2015 Algebraic Geometry
Video
Section C: Properties of Linear Graphs
Properties of Parallel Lines
Math
Overview
Geometry: The Slope of Parallel and Perpendicular Lines
Math
Explanation
Geometry: Writing Equations of Lines: Parallel & Perpendicular Lines
Geometry: The Slope of Parallel and Perpendicular Lines: Writing Equations for a Perpendicular Line
Geometry: The Slope of Parallel and Perpendicular Lines: Checking For Perpendicular Lines - 1
Model
Lesson
Coordinate Geometry and How It's Used
Activity
Parallel and Perpendicular Lines
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
Similarity
ESSENTIAL QUESTION(S):
SUGGESTED UNIT TIMELINE:
3 weeks
How do you prove triangles or polygons similar?
What are the differences between similar and congruent figures?
How might the features of one figure be useful when solving problems about similar figure?
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
REFERENCE/ STANDARDS:
STANDARD A listing of all standards included in the unit
#
Verify experimentally the properties of dilations given by a center and a scale factor:
G-SRT.1
a.
G-SRT.2
G-SRT.3
G-SRT.5
G-SRT.4
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center
unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
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.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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.
UNIT DESCRIPTION:
Students will identify and apply similarity properties.
UNIT VOCABULARY





Dilation, similarity, scale factor, corresponding parts, proportion, ratio,
geometric mean, altitude
Prove polygons are similar/congruent
Write similarity statements
Identify scale factors
Prove triangles are similar/congruent by SSS, SAS, ASA, AAS, HL, SSS~,
SAS~, AA~
• Use properties of similar triangles to solve application and algebraic
problems
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
•
•
•
•
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)
2015 Algebraic Geometry
UNIT SCORING GUIDE (link)
A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
G-SRT.1
TEACHER INSTRUCTION
Website for Illustration
Real-world examples of
centers in dilations
Website page 9 of PDF
G-SRT.2
STUDENT LEARNING
Task Problems - CCSS
Problem Based Tasks for
Mathematics II – Prettying
Up the Pentagon pg. 209
& The Bigger Picture pg.
213
Task Problems - CCSS
Problem Based Tasks for
Mathematics II – Video
Game Transformations
pg. 218
Book - Geometry Station
Activities Book pg. 112
G-SRT.3
G-SRT.5
Worksheet pages 27-29
G-SRT.4
Worksheet pages 34-36
Worksheet over Similarity
Answers to worksheet
CCSS Problem Based Tasks
for Mathematics II – True
Tusses pg. 223
Task Problems - CCSS
Problem Based Tasks for
Mathematics II – Too Tall?
Pg. 238
Task Problems - CCSS
Problem Based Tasks for
Mathematics II – Down,
Down, Down pg. 226
Suddenly Sinking pg. 230
Geometry Station
HOW WILL WE RESPOND WHEN
STUDENTS HAVE NOT LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
EXTENSIONS
2015 Algebraic Geometry
Activities Book pg. 128
Identifying Similar
Triangles Activity – Grou
p Work PowerPoint
Website Here
Task Problems - CCSS
Problem Based Tasks for
Mathematics II –
Towering Heights pg. 234
ADDITIONAL UNIT RESOURCES
www.learnzillion.com and search Similarity
http://ccssmath.org/?s=geometry Common Core website
DISCOVERY EDUCATION RESOURCES
STANDARD: G.SRT.1
Verify experimentally the properties of dilations given by a center and a scale factor.
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.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Video
Example 3: Dilations
Similar Figures: Scaled Down
Geometry: Dilations
Math
Overview
Geometry: Dilations
Geometry: Understanding Similar Polygons
Math
Explanation
Geometry: Dilations: Origin Centered Dilations
Geometry: Dilations: Scale Factors
2015 Algebraic Geometry
STANDARD: G.SRT.2
Video
Math
Explanation
STANDARD: G.SRT.3
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.
Using Proportions to Create Similar Figures
Congruent and Similarity Transformations
Similar Figures: Scaled Down
Geometry: Properties of Similar Trangles
Geometry: Determining and Using Similiar Triangles: Finding Similiar Triangles in a Figure
Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar.
Video
Part Two: Special Triangles
Part Two: Special Triangles (continued from Program Four)
Math
Overview
Geometry: Properties of Similar Triangles
Geometry: Determining and Using Similar Triangles
Math
Explanation
Geometry: Determining and Using Similar Triangles: Finding Similar Triangles in a Figure
Model Lesson
STANDARD: G.SRT.5
Math
Explanation
Model Lesson
Building Bridges with Similar Triangles
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures
Geometry: Dilations: Dilation Proofs
Geometry: Building Bridges with Trigonometry
Building Bridges with Similar Triangles
2015 Algebraic Geometry
STANDARD: 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; and the Pythagorean Theorem proved using triangle similarity.
Math
Overview
Math
Explanation
Geometry: Congruent Right Triangles
Geometry: Determining and Using Similar Triangles: Proving with Similar Triangles
Geometry: Determining and Using Similar Triangles: Proofs
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
SUGGESTED UNIT TIMELINE:
2 ½ weeks
Right Triangles and Trigonometry
ESSENTIAL QUESTION(S):
How does the measure of one acute angle relate to the ratio of two side measures in any right triangle?
How do trigonometric ratios relate to similar right triangles?
How are missing side lengths and angle measures found in a right or oblique triangle?
What strategies can be used to find missing parts of triangles and how can they be used to apply to real world problems?
Can trigonometry be used to find the area of a triangle?
REFERENCE/
STANDARD #
G-SRT.6
G-SRT.7
G-SRT.8
G-SRT.10
G-SRT.11
G-SRT.9
STANDARDS:
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
A listing of all standards included in the unit
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.
Explain and use the relationship between the sine and cosine of complementary angles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Prove the Laws of Sines and Cosines and use them to solve problems.
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).
Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite
side.
UNIT DESCRIPTION:
Students will find missing sides and angles of a triangle using trigonometry.
•
•
•
•
•
SOH CAH TOA
Law of Sines, Law of Cosines
Pythagorean Theorem
Special right triangle relationships
Application problems
Students will find the area of an oblique triangle.
UNIT VOCABULARY





Pythagorean Theorem, Pythagorean Triple, Trigonometry, Trigonometry Ratio,
Sine, Cosine, Tangent, Inverse Sine, Inverse Cosine, Inverse Tangent,
Complementary, Co-Functions, Angle of Elevation, Angle of Depression, Oblique
Triangle, Law of Sine, Law of Cosine
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE (link)
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)

A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
2015 Algebraic Geometry
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
G-SRT.6
TEACHER INSTRUCTION
STUDENT LEARNING
Instructional strategies, links
to websites, resources, etc.
Anything that will help
teacher provide instruction
related to the standard(s)
Tasks, activities, links to
practice, etc.
Understand that similar
triangles share angle
measures and side ratios
45-45-90 Triangle
30-60-90 Triangle
SOH-CAH-TOA
Find sine value using side
ratios
Find cosine value using side
ratios
Find tangent value using side
ratios
G-SRT.7
G-SRT.8
G-SRT.10
Worksheet – Special
Triangles (Answer Key)
Worksheet – Special
Right Triangles (Answer
Key)
Exit Slip – Special Right
Triangles (Answer Key)
Special Right Triangles
Problems
Geometry Station
Activity for Common
Core
pgs. 139-150
Sine and Cosine of
Complementary Angles
Inverse Function Notes
Complimentary Angles
Activity
Inverse Function WS
Angle of Elevation and
Depression
Prove Law of Sines and Law
of Cosines
Angle of Elevation and
Depression WS
Glencoe Secondary Math
Aligned to the CC
Pgs. 12-16
#1-6, 8-20, 22-27, 3142, 47-50
Glencoe Secondary Math
Aligned to the CC
Pg. 15 #45 and #46
Law of Sines Problems
Law of Cosines Problems
HOW WILL WE RESPOND WHEN
STUDENTS HAVE NOT LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
EXTENSIONS
2015 Algebraic Geometry
G-SRT.11
Glencoe Secondary Math
Aligned to the CC
Pgs. 8-12
G-SRT.9
Derive A=1/2ab sin C from
basic area formula using
A=1/2bh
ADDITIONAL UNIT RESOURCES
Glencoe Secondary Math
Aligned to the CC
Pgs. 12-16
#7, 21, 28, 29, 30, 4344, 51-53
Apply formula to find
area of oblique triangles
DISCOVERY EDUCATION RESOURCES
STANDARD: G.SRT.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*
Video
Example 2: Pythagorean Theorem Proof -- History
Example 3: Using the Pythagorean Theorem -- Carpentry
Example 1: Pythagorean Theorem -- Video Game Design
Example 2: Sine, Cosine, Tangent -- Firefighting
Example 3: A Small Angle -- Flying
Introducing the Pythagorean Theorem
The Pythagorean Theorem: What It Is & How to Use It
Using the Pythagorean Theorem
Math
Overview
Geometry: The Pythagorean Theorem and Its Converse
Skill Builder
The Pythagorean Theorem
Model
Lesson
Building Bridges with Similar Triangles
Activity
Numbers for Finding your Triangle
2015 Algebraic Geometry
STANDARD: 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.
Video
Introduction: Structures and Triangles
Example 1: Special Right Triangles -- Bridges
Introduction: Jumping off of Right Triangles
Section B: Six Trig Functions
Math
Overview
Geometry: Trigonometry
Model
Lesson
Building Bridges with Similar Triangles
Activity
Finding Ratios in Right Triangles
STANDARD: G.SRT.7
Math
Explanation
Explain and use the relationship between the sine and cosine of complementary angles.
Trigonometry: Right Triangle Trigonometry: Using the Complementary Angle Theorem and Given Trigonometric Values to
Evaluate the Trigonometric Expression
Trigonometry: Right Triangle Trigonometry: Using the Fundamental Identities and Complementary Angle Theorem to Evaluate
Trigonometric Expressions
Trigonometry: Right Triangle Trigonometry: Using the Complementary Angle Theorem to Evaluate Trigonometric Expressions
Trigonometry: Right Triangle Trigonometry: Finding Angles that Satisfy Trigonometric Equations
Precalculus: Trigonometric Ratios in Right Triangles
Model
Lesson
Building Bridges with Similar Triangles
Activity
Obstacle Course
2015 Algebraic Geometry
STANDARD: G.SRT.9
Derive the formula A=1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the
opposite side.
Math
Overview
Geometry: Working with the Law of Cosines
Algebra II: Law of Sines
Algebra II: Law of Cosines
Math
Explanation
Geometry: Working with the Law of Cosines: Reasons in Proofs
STANDARD: G.SRT.10
Math
Overview
Math
Explanation
STANDARD: G.SRT.11
Prove the Law of Sines and the Law of Cosines to solve problems.
Geometry: Working with the Law of Cosines
Algebra II: Law of Sines
Algebra II: Law of Cosines
Geometry: Working with the Law of Cosines: Reasons in Proofs
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).
Math
Overview
Geometry: Using the Law of Sines in Non-Right Triangles
Math
Explanation
Geometry: Using the Law of Sines in Non-Right Triangles: The Law of Sines
Geometry: Using the Law of Sines in Non-Right Triangles: Solving Triangles-Law of Sines
Geometry: Working with the Law of Cosines: Using the Law of Cosines to Find Missing Side
Geometry: Working with the Law of Cosines: Solving Triangles Given Two Sides and Included Angle
Model Lesson
Geometry: Building Bridges with Trigonometry
2015 Algebraic Geometry
Activity
Bridge Surveying
Solving Triangles in Bridge Designs
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
Quadrilaterals and Coordinate Geometry
ESSENTIAL QUESTION(S):
SUGGESTED UNIT TIMELINE:
2 weeks
How can you use your prior knowledge to derive and apply properties of special quadrilaterals?
How can the coordinate plane used to measure, model, and calculate area and perimeter of polygons?
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
REFERENCE/ STANDARDS:
STANDARD A listing of all standards included in the unit
#
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a
G-CO.11
G-GPE.4
G-GPE.5
G-GPE.6
G-GPE.7
parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points
in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point
(0, 2).
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).
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. (Honors
Geometry only)
UNIT DESCRIPTION:
The student will be able to derive and use the properties of special
quadrilaterals using geometric and algebraic concepts on a coordinate plane.
The student will be able to calculate the area and perimeter of polygons in the
coordinate plane.
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)





UNIT VOCABULARY
Quadrilateral, parallelogram, rectangle, rhombus, square, kite, trapezoid,
isosceles trapezoid, distance, midpoint, slope, parallel, perpendicular, ratio,
diagonal, coordinate plane, triangle, perimeter, area, polygon
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE (link)
A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
TEACHER INSTRUCTION
STUDENT LEARNING
HOW WILL WE RESPOND WHEN
STUDENTS HAVE NOT LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
EXTENSIONS
2015 Algebraic Geometry
G-CO.11
Instructional strategies, links
to websites, resources, etc.
Anything that will help
teacher provide instruction
related to the standard(s)
Review Lesson- Slope lesson,
practice, and teacher resource
Review Lesson- mispoint
lesson, practice, and teacher
resource
Review lesson- Distance
formula lesson, practice, and
teacher resource
Tasks, activities, links to
practice, etc.
NCSM Great Tasks p.145148- discovery activity to
figure out all of the
properties of the special
quadrilaterals
Task- Have students draw
a venn diagram showing
the relationship between
all special quadrilaterals
Have the students discover the Example problems-Best
properties of quadrilaterals
Strategies by Benson #’s
using a discovery activity like 29, 30, 31, 32, 33
the NCSM Great tasks or the
discovery examples below
Lesson- Discover properties
about special quadrilaterals
using variable coordinates on
the coordinate plane.
G-GPE.4
G-GPE.5
G-GPE.6
G-GPE.7
Lesson- Coordinate geometry
lesson, practice, and teacher
resource
Lesson- Median of a trapezoid
applet
Lesson- Area and perimeter of
rectangle and triangle on
coordinate plane
ADDITIONAL UNIT RESOURCES
Geometry Station
Activities p.219-229Practice- Coordinate
proofs for triangles and
special quads.
Practice-Area and
perimeter of rect and
triangle on coordinate
plane
2015 Algebraic Geometry
DISCOVERY EDUCATION RESOURCES
STANDARD: 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.
Video
Euclid's Proposition 41
Math
Overview
Geometry: Proving That a Quadrilateral Is a Parallelogram
Math
Explanation
Geometry: Proving that a Quadrilateral is a Parallelogram: Proofs for Parallelograms
Geometry: Proving that a Quadrilateral is a Parallelogram: Parallelograms and Flow Proofs
Geometry: Properties of Parallelograms: Parallelogram Proofs
Geometry: Trapezoids and Kites: Proofs with Trapezoids and Kites
Model
Lesson
Congruence and Proof
Activity
Parallelogram Proof Cards
Proving Theorems about Parallelograms
STANDARD: 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).
Video
Geometric Interpretation of the Theorem of Pythagoras
Introduction: Washington D.C. and the Coordinate Plane
Example 1: The Cartesian Coordinate System -- DC Map
Example 2: Slopes and Relationships of Lines -- DC Monuments
Example 3: Distances and Midpoints -- DC Tourists
The Distance Formula & the Midpoint Formula
2015 Algebraic Geometry
Math
Overview
Geometry: Midpoints and Distance
Math
Explanation
Algebra I: The Distance Formula: Understanding the Relationship Between the Distance Formula and the Pythagorean Theorem
Geometry: Midpoints and Distance: Finding Length of a Segment Part 2
Model
Lesson
Coordinate Geometry and How It's Used
STANDARD: G.GPE.5
Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of
a line parallel or perpendicular to a given line that passes through a given point).
Video
Section C: Properties of Linear Graphs
Properties of Parallel Lines
Example 2: Slopes and Relationships of Lines __ DC Monuments
Math
Overview
Geometry: The Slope of Parallel and Perpendicular Lines
Algebra I: Parallel and Perpendicular Lines
Math
Explanation
Geometry: The Slope of Parallel and Perpendicular Lines: Checking For Perpendicular Lines - 1
Trigonometry: Parallel and Perpendicular Lines: Proving Perpendicularity
Trigonometry: Parallel and Perpendicular Lines: Finding Slopes of Parallel and Perpendicular Lines
Model
Lesson
Coordinate Geometry and How It's Used
Activity
Parallel and Perpendicular Lines
STANDARD: G.GPE.6
Math
Overview
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Geometry: Understanding Parallel Lines and Their Proportional Parts
2015 Algebraic Geometry
Math
Explanation
Geometry: Understanding Parallel Lines and Their Proportions: Real World Applications
Geometry: Determining and Using Similar Triangles: Determining Unknown Values!
Model
Lesson
Coordinate Geometry and How It's Used
Activity
You've Got a Point
STANDARD: G.GPE.7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Math
Explanation
Geometry: Midpoints and Distance: Perimeter and Distance Formula
Geometry: Midpoints and Distance: Finding Perimeter in the Coordinate Plane
Geometry: Coordinates in Space: Distance Between Points - 2
Model
Lesson
Coordinate Geometry and How It's Used
Activity
The Midpoint and Other Divisions
The Distance Formula and the Midpoint Formula
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
Two-Dimension vs. Three-Dimension
ESSENTIAL QUESTION(S):
SUGGESTED UNIT TIMELINE:
3 ½ weeks
How can two-dimensional figures be used to understand three-dimensional objects?
Where did area and volume formulas come from?
How can geometric figures be used in real-life area and volume situations?
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
REFERENCE/ STANDARDS:
STANDARD A listing of all standards included in the unit
#
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
G-GMD.1
G-GMD.3
G-GMD.4
G-MG.1
G-MG.2
G-MG.3
dissection arguments, Cavalieri’s principle, and informal limit arguments.
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects.
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTU’s per cubic foot).
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).
UNIT DESCRIPTION:
This unit investigates area and volume paying particular attention to modeling
situations.
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)






UNIT VOCABULARY
Two dimensions, three dimensions prisms, pyramids, cylinders, cones,
spheres, similar solids
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE (link)
A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
TEACHER INSTRUCTION
Instructional strategies, links
to websites, resources, etc.
STUDENT LEARNING
Tasks, activities, links to
practice, etc.
HOW WILL WE RESPOND WHEN
STUDENTS HAVE NOT LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
EXTENSIONS
2015 Algebraic Geometry
G-GMD.1
Anything that will help
teacher provide instruction
related to the standard(s)
Relate diameter and
circumference
Glencoe 1.6
Informally prove the area of a
circle
Glencoe 11.3
G-GMD.3
 Area of Circles
Calculate volume of prisms
and cylinders using the
Cavalieri principle
Glencoe 12.4
Cavalieri's Principle
Worksheet
Relate the volume of
prisms/cylinders to
pyramids/cones
Glencoe 12.4-12.5
Solve real-world problems
involving cones
Glencoe 12.3 and 12.5
Area of Prisms, Pyramids,
Cylinders, and Cones
Solve real-world problems
involving pyramids
Glencoe 12.3 and 12.5
Solve real-world problems
involving cylinders
Glencoe 12.2 and 12.4
G-GMD.4
Circle Poster
 Circumference
Solve real-world problems
involving spheres
Glencoe 12.6
Visualize cross-sections of
prisms
Surface Area and Volume
- All
Surface Area and Volume
– Prisms and Cylinders
Surface Area and Volume
– Spheres
Online Activity - Volume
of Cones, Cylinders, and
Spheres
2015 Algebraic Geometry
Glencoe 12.2 and 12.4
Visualize cross-sections of
pyramids
Glencoe 12.3 and 12.5
Visualize cross-sections of
cylinders
Glencoe 12.2 and 12.4
Visualize cross-sections of
cones
Glencoe 12.3 and 12.5
G-MG.1
Predict 3D results of rotating
simple figures
Volume of prisms, cylinders,
pyramids, spheres, cones
NOTES.notebook
G-MG.2
2D vs. 3D - Volume.ks-ig
Prism and Cylinders LA SA
G-MG.3
Pyramids and Cones LA SA
A Day at the Beach
..\..\Geometry\Chapter
12\Extra Practice Word
Problems Prisms, Cylinders
and Spheres.docx
ADDITIONAL UNIT RESOURCES
Performance Task – A Day at the Beach
2015 Algebraic Geometry
DISCOVERY EDUCATION RESOURCES
STANDARD: G.GMD.1
Video
Math
Overview
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.
Section C: Circleville (Circumference of Circles)
Section F: Volume
Area and Volume
The Volume of Rectangular Solids
The Volume of Cylindrical Solids
Geometry: Area of Regular Polygons and Circles
Geometry: Volumes of Prisms and Cylinders
Geometry: Volumes of Pyramids and Cones
Math
Explanation
Geometry: Volumes of Prisms and Cylinders: Cavalieri's Principle
Geometry: Volumes of Prisms and Cylinders: Experimenting with Prisms and Cylinders
Model
Lesson
Geometry: Three-Dimensional Shapes
STANDARD: G.GMD.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Introduction: Geometric Quantities and Fantastic Animation
Example 1: Surface Area -- Boxes and Cans
Video
Example 2: Volume -- Pools and Cans
Example 3: Surface Area and Volume -- Cheese
Geometry: Volumes of Prisms and Cylinders: Hollow Solids
Math
Geometry: Volumes of Prisms and Cylinders: Prism Volume
Explanation
Geometry: Volumes of Prisms and Cylinders: Triangular Prism Volume
2015 Algebraic Geometry
Geometry: Volumes of Prisms and Cylinders: Cylinder Volume
Geometry: Volumes of Pyramids and Cones: Volume of a Cone and Cavalier's Principle
Model
Lesson
Geometry: Three-Dimensional Shapes
Activity
Turn up the Volume
STANDARD: 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.)
Video
Bridges
Triangles: Bridges of Support
Geometric Constructions
Model
Lesson
Geometry: Building Bridges With Trigonometry
Activity
Bridge Surveying
Looking at Bridges
STANDARD: G.MG.2
Video
STANDARD: G.GMD.4
Video
Apply concepts of density based on area and volume in modeling situations (e.g. persons per square mile, BTU’s per cubic foot.)
Definition of Density in Physics
Measurement: Fluid Volume
Use Ratio to Calculate Population per Square Mile (BGL)
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects
generated by rotations of two-dimensional objects.
Example 1: Scale Drawings--Maps
Example 2: Blueprints--Museum
Example 3: Planar Cross-Sections--Earth and MRI
2015 Algebraic Geometry
Math
Overview
Geometry: Space Figures and Drawings
Math
Explanation
Geometry: Space Figures and Drawings: Cube Cross Sections
Geometry: Space Figures and Drawings: Foundation and Orthographic Drawings
Geometry: Surface Areas of Prisms and Cylinders: Solids of Revolution
Geometry: Volumes of Prisms and Cylinders: Solids of Revolution
Geometry: Surface Areas of Pyramids and Cones: Solids of Revolution
Geometry: Volumes of Pyramids and Cones: Rotating Shapes and Volume
STANDARD: 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).
Video
Terri Norstrand: Skatepark Designer
Topographic Maps
Model
Lesson
Geometry: Building Bridges with Trigonometry
World Goes Round in Circles
The Real Number System: Heavenly Observations
Activity
Building a Scale Model
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
Circles – Part 1
SUGGESTED UNIT TIMELINE:
2 ½ weeks
ESSENTIAL QUESTION(S):
1. Why are all circles similar?
2. How can the arc length and area of sector formulas be derived using similarity?
3. What are radians and how were they derived?
4. How can the equations of circles be derived using the Pythagorean Theorem?
5. How can coordinate geometry be used to solve real-life problems?
REFERENCE/
STANDARD
#
G-C.1
G-C.5
G-GPE.1
G-GPE.4
STANDARDS:
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
A listing of all standards included in the unit
Prove that all circles are similar.
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.
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.
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points
in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point
(0, 2).
UNIT DESCRIPTION:
Students will discover that all circles are similar by using the length of the arc
and other measurements. The proportionality of the length of an arc
intercepted by an angle to the radius will be discovered. Students will also
derive the formula for the area of a sector. Students will learn the origin of
radians and its role as the constant of proportionality.
UNIT VOCABULARY


Tangents, secants, arc, chords, ratio, diameter, radius, Pythagorean Theorem,
Conic, Completing the Square, Distance Formula, Properties of Radicals,
Factoring.
In addition, students use their prior algebraic understanding of the quadratic
equation and Pythagorean Theorem to find the equation of a circle. Students
will understand how to utilize the coordinate plane to determine whether a
given point is on a circle.
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)


2015 Algebraic Geometry
UNIT SCORING GUIDE (link)
A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
G-C.1
G-C.5
G-C.5
G-C.1
TEACHER INSTRUCTION
Lesson for proving circles
similar using similar triangles
Website that illustrates area of
sectors and introduces
radians & area of a sector
Website that helps explain
radians in plain terms
Explanation and practice of
proving that all circles are
similar using the concept of
transformations and dilations
G-C.5
Glencoe Geometry Baseball
book section 11-3
G-C.5
Sectors and segments of
circles website
Activity with sectors and
pizza
Balloon activity showing
circles are similar
Website for proving circles
similar using translations
Applet demonstrating arc
length
Lesson- Equations of Circles.
Teaches the basics of circles.
(see teacher exchange files)
G-C.5
G-C.1
G-C.1
G-C.5
G.GPE.1
Lesson- Completing the
STUDENT LEARNING
Worksheet practice for
similar circles
Activity investigating
radians
Problem Based Tasks for
Math II (orange book)
Similar Circles
Pg. 265 Following in
Archimedes’ Footsteps
Problem Based Tasks for
Matt II (orange book)
Defining Radians pg. 290
Around the Merry-GoRound
Practice for sectors and
segments
Activity investigating arc
length and area of a sector
Practice – Equations of
Circles Day 1 Worksheet
(see teacher exchange
files)
Practice – Completing the
HOW WILL WE RESPOND WHEN
STUDENTS HAVE NOT LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
EXTENSIONS
2015 Algebraic Geometry
G.GPE.4
square with circles (see
teacher exchange files)
Square with Circles
Worksheet (see teacher
exchange files)
Lesson plan - Deriving the
equation of a circle using the
Pythagorean Theorem
Practice – see lesson plan
Lesson – Determining
whether a point is on a circle
(see teacher exchange files)
Practice – Determining
whether a point is on a
circle worksheet (see
teacher exchange files)
Lesson plan – Proving
whether a point is on a circle.
ADDITIONAL UNIT RESOURCES
www.learnzillion.com
Practice – see lesson plan
Online practice that covers the entire Unit.
Multiple Choice practice over Circles (PDF available)
DISCOVERY EDUCATION RESOURCES
STANDARD: G.C.1
Prove that all circles are similar.
Video
Recap: Similarity
Circular Structures: Design and Architecture
Example 3: Circle- Pools
Activity
Deriving the Equation for a Circle
Sector Area
Model
Lesson
Circles: Understanding Structure
2015 Algebraic Geometry
STANDARD: 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.
Video
Defining & Problem Solving with Sectors
Math
Overview
Geometry: Special Segments in Circles
Geometry: Geometric Probability
Math
Geometry: Geometric Probability: Probability in Sector of a Circle
Explanation
Model
Lesson
STANDARD: G.GPE.1
Math
Overview
Math
Explanation
Model
Lesson
Circles: Understanding Structure
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.
Geometry: Equations of Circles
Geometry: Exploring Circles
Geometry: Equations of Circles: Center and Radius
Geometry: Equations of Circles: Equation of Circle Given Center and Radius
Geometry: Equations of Circles: Equation of Circle Given Points
Geometry: Exploring Circles: Determining the Radius, Diameter, and Circumference
Trigonometry: Circles: Understanding Graphs of Circles and Writing the Equation from the Center and Radius
Coordinate Geometry and How It's Used
Circles: Understanding Structure
World Goes Round in Circles
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
SUGGESTED UNIT TIMELINE:
Circles – Part 2
ESSENTIAL QUESTION(S):
2 weeks
What are the relationships between parts of a circle? Can those relationships be used to find unknown parts of a circle?
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
REFERENCE/ STANDARDS:
STANDARD A listing of all standards included in the unit
#
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and
G-C.2
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.
UNIT DESCRIPTION:
The goal of this unit is to establish the numerical relationship between arcs
and angles of a circle and to provide ways of calculating segments related to
circles.
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)

UNIT VOCABULARY
Arc, central angle, chord, circumscribed angle, inscribed angle, major arc,
minor arc, point of tangency, radii, secant, semicircle, tangent
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE (link)
A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
TEACHER INSTRUCTION
G-C.2
G-C.2
G-C.2
G-C.2
Website that illustrates
inscribed angles in a
semicircle are right angles.
Presentation that shows
central and inscribed angles
Website that explains that a
tangent is perpendicular to
STUDENT LEARNING
Geometry Station
Activities for Common
Core State Standards
Pages 151-165
Problem Based Tasks for
Math II (orange book)
HOW WILL WE RESPOND WHEN
STUDENTS HAVE NOT LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
EXTENSIONS
2015 Algebraic Geometry
G-C.2
G-C.2
G-C.2
G-C.2
G-C.2
G-C.2
G-C.2
G-C.2
the radius to the circle of the
radius of the circle at the
point where the tangent
intersects the circle
Glencoe Geometry Baseball
Book resources section 10-2
through 10-7
Insider Teacher Exchange
Files for Unit
Website for chords and circles
Website for tangents and
circles
Website for special segments
in circles
Website for Constructing
Tangents
Website for special segments
in circles (Sketchpad)
Website for special segments
are two intersecting lines and
a circle
Chord Central Angles
Conjecture
Masking the Problem
pg. 268
Practice for chords and
circles
Practice for tangents and
circles
Practice for special
segments in circles
Problem Based Tasks for
Math II (orange book)
Properties of Tangents of a
Circle
The Circus is in Town! Is
it Safe? pg. 271
ADDITIONAL UNIT RESOURCES
Explanation of standards in friendly language with example problems
Benson Workshop Problems on District
Teacher Files
Clock Problem (pg. 9-10)
Circle-Angle #45 (pg. 27)
Circles #80-87 (pgs. 46-51)
Radius #90 (pg. 52)
Circumference #91 (pg. 53)
Concentric Circles and Circumference
#93 (pg. 54)
Tangent line and circles on coordinate
plane #137 (pg. 79)
2015 Algebraic Geometry
DISCOVERY EDUCATION RESOURCES
STANDARD: 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 perpendicular to
the tangent where the radius intersects the circle.
Video
Sines and Chord Lengths
Ancient Astronomy: The Connection Between Sines and Chords and Circles
Math
Overview
Geometry: Inscribed Angles
Geometry: Arcs and Chords
Math
Explanation
Geometry: Inscribed Angles: Angle Measures and Variables
Geometry: Inscribed Angles: Proofs
Geometry: Arcs and Chords: Center of Circles
Geometry: Arcs and Chords: Proofs
Geometry: Arcs and Chords: Theorems
Model Lesson
Circles: Understanding Structure
Activity
Arc Length and Radius
2015 Algebraic Geometry
COURSE: Geometry
UNIT TITLE:
Probability
ESSENTIAL QUESTION(S):
SUGGESTED UNIT TIMELINE:
3 weeks
What is a sample space and how do you represent it?
When do you use permutations and combinations with probability?
What does it mean to be independent, dependent, and mutually exclusive?
REFERENCE/
STANDARD #
S-CP.1
S-CP.2
S-CP.3
S-CP.4
S-CP.5
S-CP.6
S-CP.7
S-CP.8
S-CP.9
S-MD.6
S-MD.7
STANDARDS:
WHAT DO WE WANT STUDENTS TO KNOW, UNDERSTAND, AND BE ABLE TO DO?
A listing of all standards included in the unit
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions,
intersections, or complements of other events (“or,” “and,””not”).
Understand that two events A and B are independent of the probability of A and B occurring together is the product of their
probabilities, and use this characterization to determine if they are independent.
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the
conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the
probability of B.
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the
two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of
the model.
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in
terms of the model.
Use permutations and combinations to compute probabilities of compound events and solve problems.
Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a
game).
UNIT DESCRIPTION:
In this unit students will use conditional probability, represent sample
space, use permutations and combinations, and find probabilities of
compound events.
UNIT VOCABULARY










Sample space, complement, union, intersection, tree diagram, permutation,
combination, independent events, dependent events, conditional probability,
mutually exclusive, classical probability, empirical probability, frequency table
HOW DO WE KNOW STUDENTS HAVE LEARNED?
UNIT ASSESSMENT BLUEPRINT
UNIT SCORING GUIDE
MAJOR
SUPPORTING
STANDARD STANDARD
(M)
(S)

A compilation of the proficiency levels and exemplars for the unit that defines mastery of the standards.
2015 Algebraic Geometry
FACILITATING ACTIVITIES
Strategies and methods for teaching and learning
STANDARD #
S-CP.1
TEACHER INSTRUCTION
Introduce sample space,
outcome, classical/empirical
with deck of cards, coins,
dice, skittles, spinners
Lesson over sample space
STUDENT LEARNING
Empirical probability:
Activities with concrete
manipulatives
Spinner Activity
Probability and Data
Analysis Activities
Problem Based Tasks for
Math II (orange book)
Describing Events
pg. 325
S-CP.2
Explanation of standard
Lesson about Independence
Problem Based Tasks for
Math II (orange book)
Understanding
Independent Events
pg. 330
Worksheet
Titanic Problem
S-CP.3, 5, 6
Conditional Probability
Lesson
Problem Based Tasks for
Math II (orange book)
Introducing Conditional
Probability pg. 334
S-CP.4, 5, 6
Addition Rule lesson
Problem Based Tasks for
Math II (orange book)
Using Two-Way
Frequency Tables
pg. 337
Two-way table lesson
Two-way table
worksheet
HOW WILL WE RESPOND WHEN
STUDENTS HAVE NOT LEARNED?
INTERVENTIONS
HOW WILL WE RESPOND WHEN
STUDENTS HAVE ALREADY LEARNED?
EXTENSIONS
2015 Algebraic Geometry
S-CP. 6
Using probability to make
fair decisions
Resource for teachers
Problem Based Tasks for
Math II (orange book)
Making Decisions
pg. 358
Conditional probability
demonstrated
Worksheets for fair
decisions
Interactive Activities for
students
S-CP.7
Lesson Decision Trees
Help with Addition Rule
S-CP.7
S-CP.8
Additional lesson on decision
trees
Lesson on Addition Rule
Video explaining
Multiplication Rule
Problem Based Tasks for
Math II (orange book)
Analyzing Decisions
pg. 362
Problem Based Tasks for
Math II (orange book)
The Addition Rule
pg. 341
Problem Based Tasks for
Math II (orange book)
The Multiplication Rule
pg. 345
Explanation of
Multiplication Rule
S-CP.9
Lesson over Permutations and Problem Based Tasks for
Combinations
Math II (orange book)
Combinations and
Permutations pg. 350
Permutations and
Combinations Student
Resource
ADDITIONAL UNIT RESOURCES
Glencoe Geometry textbook sections: 0-3, 13-1, 13-2, 13-4, 13-5, 13-6
Math is Fun website – explains concepts pretty basic
2015 Algebraic Geometry
DISCOVERY EDUCATION RESOURCES
STANDARD: S.CP.1
Describe events as subsets of a sample space (the set of outcomes), using characteristics (or categories) of the outcomes, or as
unions, intersections, or complements of other events ("or," "and," "not").
Video
The Statistics of Sampling
Sampling Techniques
Math
Explanation
Algebra II: Compound Events: Compliments of Events
Algebra II: Compound Events: Applications of Event Complements
Model
Lesson
What's the Chance?
STANDARD: S.CP.2
Understand that two events A and B are independent of the probability of A and B occurring together is the product of their
probabilities, and use this characterization to determine if they are independent.
Video
Example 1: Independent Events-- Ultimate Frisbee
Understanding the Odds
Joint Probability: Understanding the Odds
Math
Overview
Algebra I: Independent Events
Model
Lesson
What's the Chance?
Activity
Frequency Suduko
2015 Algebraic Geometry
STANDARD: S.CP.3
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that
the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the
same as the probability of B.
Video
Example 3: Compound Events -- Life Expectancy and Insurance
Model Lesson
What's the Chance?
STANDARD: S.CP.4
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified.
Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
Video
Frequency Distribution
Example 2: Frequency Distribution and Line Graphs-- High Temperature
Math
Explanation
Algebra I: Measures of Central Tendency: Finding Mean, Median,...
Activity
Frequency Suduko
STANDARD: S.CP.5
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
Video
Example 3: Conditional Probabilities -- Baseball Batting Order
Example 1: Independent Events-- Ultimate Frisbee
Model Lesson
What's the Chance?
Activity
Mad Chemist
2015 Algebraic Geometry
STANDARD: S.CP.6
Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in
terms of the model.
Video
Section B: The Uniform Distribution
Model Lesson
What's the Chance?
STANDARD: S.CP.7
Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
Math
Overview
Algebra II: Compound Events
Math
Explanation
Algebra II: Compound Events: Finding Missing Probabilities
Algebra II: Compound Events: Probability of A and B
Algebra II: Dependent and Independent Probabilities: Probability of Independent Events
Model Lesson
What's the Chance?
STANDARD: S.CP.8
Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the
answer in terms of the model.
Math
Explanation
Algebra II: Dependent and Independent Probabilities: Dependent Probabilities
Model Lesson
What's the Chance?
2015 Algebraic Geometry
STANDARD: S.CP.9
Use permutations and combinations to compute probabilities of compound events and solve problems.
Video
Permutations and Combinations: Part 1
Permutations and Combinations: Part 2
Probabilities of Compound Events
Math
Overview
Algebra II: Counting and Combinations
Math
Explanation
Algebra II: Basic Probability: Combinations vs. Permutations
Algebra II: Counting and Combinations: Combinations vs. Permutations
Model
Lesson
What's the Chance?
STANDARD: S.MD.6
Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator)
Video
What Are the Odds?: Heart Attack
Discovering Math: Advanced: Probability
Math
Explanation
Algebra II: Basic Probability: Probability With Random Numbers
Algebra II: Dependent and Independent Probabilities: Independent..
STANDARD: 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)
Video
What Are the Odds?: Car Accidents
Math Starters: Shopping Mall Starters
Analyzing Everyday Risks, Benefits, and Alternatives in Decisions
What Are the Odds?: House Fires
Math
Overview
Algebra II: Basic Probability
Algebra II: Dependent and Independent Probabilities
2015 Algebraic Geometry