Download unpacking benchmarks - Michigan City Area Schools

Essential Outcomes
Geometry
1. Know and use the correct symbols for lines, rays, angles, segments, perpendicular and parallel. (Standard 1, 8 Core
Standard 1)
Learning Goals
A) Students will understand and be able to use appropriate symbols for lines, rays, segments, and angles
(1.1, 1.2, 8.1)
B) Students will understand, be able to differentiate and use correct symbols for segments, length of segments,
angles and measure of angles
(1.1, 1.2, 8.1)
C) Students will understand and be able to use correct symbols for parallel and perpendicular lines.
(1.1, 1.2, 1.3, 1.4, 8.1)
2. Find slope, length, and midpoint of segments. (Standard 1, 2, 3, 8, Core Standard 7)
Learning Goals
A) Students will understand and be able to apply the formula for slope given two points, the equation of a line, or
given a graph
(1.4, 8.1, 8.2)
B) Students will understand and be able to apply the formula for midpoint of a segment and find an endpoint given
the midpoint and the second endpoint.
(1.1, 8.1, 8.2)
C) Students will understand and be able to identify congruent segments
(1.2, 2.6, 3.4, 8.1)
D) Students will understand and be able to apply the distance formula given two points
(1.1,1.4, 5.1, 8.1, 8.2)
1
3. Identify angles and triangles by measure, by markings, and determine angle measure by using symbols or special angle
relationships (Standard 4, 8 Core Standard 2, 9)
Learning Goals
A) Students will understand and be able to identify acute, right, obtuse, straight and congruent angles
(4.1, 8.1)
B) Students will understand and be able to identify the relationship between complementary and supplementary
angles
(4.2, 4.4, 4.6, 8.1)
C) Students will understand and be able to classify triangles by side length and angle measure
(4.1, 4.2, 4.3, 4.4, 8.1)
D) Students will understand and be able to use Isosceles Triangle Theorem
(4.8, 4.9, 8.1, 8.6)
4. Identify and use special angles formed by lines and a transversal, vertical angles, and linear pairs. (Standard 1, 3, 4, 8 Core
Standard 1, 7)
Learning Goals
A) Students will understand and be able to identify corresponding angles, same-side interior (exterior) angles,
alternate interior (exterior) angles, vertical angles, and linear pairs.
(1.3, 3.4, 8.1)
B) Students will understand and be able to apply the rules for the above angle pairs when two lines are parallel or
not
(1.4, 4.9, 8.2)
2
5. Identify polygons and find interior and exterior angle measures.
(Standard 2, 6, 8 Core Standard 4)
Learning Goals
A) Students will be able to identify and name polygons by number of sides
(2.1, 2.2, 8.1)
B) Students will understand and be able to apply the formula for interior angle sum of all polygons
(2.3, 2.2, 2.5, 8.1, 8.2, 8.9)
C) Students will understand and be able to apply the formula for exterior angles
(2.3, 2.5, 8.1, 8.2, 8.9)
D) Students will understand the relationship between the interior and exterior angles of polygons
(2.2, 2.6)
6. Write equations of lines in slope-intercept, standard, and point-slope forms; be able to graph lines. (Standard 1, 3, 4, 8
Core Standard 7)
Learning Goals
A) Students will understand and be able to change between various forms of linear equations
(1.4, 8.1, 8.9)
B) Students will understand and be able to identify the necessary information to graph a line
(1.2, 1.4, 4.9, 8.1, 8.9)
C) Students will understand and be able to distinguish whether lines are parallel, perpendicular or neither by
looking at the slope
(1.4, 8.1)
D) Students will understand and be able to use slopes of parallel and perpendicular lines to write equations of
related lines
(1.2, 1.4, 3.4, 4.9, 8.1)
3
7. Know what information is needed to prove triangles congruent and do simple proofs in different forms including 2-column,
paragraph, indirect, flow, and coordinate. (Standard 2, 3, 4, 8 Core Standard 2, 7, 9)
Learning Goals
A) Students will understand and be able to identify the five ways of proving triangles are congruent
(2.3, 4.3, 4.6, 8.3)
B) Students will understand and be able to use CPCTC after proving triangles are congruent
(2.3, 2.4, 4.4, 8.3)
C) Students will understand the logical sequencing and be able to write an original proof
(2.6, 3.4, 8.3, 8.7, 8.8)
8. Know the relationships and find the parts of special right triangles and use the Pythagorean Theorem. (Standard 5, 8 Core
Standard 2, 3)
Learning Goals
A) Students will understand and be able to identify the parts of a right triangle
(5.3, 8.1)
B) Students will understand and be able to use the relationship between sides of special right triangles (30-60-90,
45-45-90) to find other sides
(5.3, 8.1)
C) Students will understand and be able to use the Pythagorean Theorem its converse and its corollary
(5.1, 8.1)
D) Students will understand and be able to reduce radials to simplest radical form
(A 1.1.2)
E) Students will understand and be able to use the Triangle Inequality Theorem to determine possible third side
lengths (5.6, 8.1)
F) Students will understand and be able to identify whether 3 side lengths are possible for a triangle
(5.1)
4
9. Use basic trigonometric functions. (Standard 5, 8 Core Standard 3)
Learning Goals
A) Students will understand and be able to identify sine, cosine and tangent ratios and use their symbols correctly
(5.4, 5.5, 8.1, 8.2)
B) Students will understand and be able to use trigonometric functions to find missing angles and sides
(5.6, 8.1, 8.2)
10. Correctly use formulas for area, volume, perimeter, circumference, arc length, surface area, and sector area with correct
units.
(Standard 3, 7, 8 Core Standard 4, 5, 6)
Learning Goals
A) Students will understand and be able to use formulas to find areas of squares, rectangles, triangles,
parallelograms, trapezoids, rhombi, kite, regular polygons and circles
(3.3, 3.4, 4.7, 7.7, 8.1, 8.2)
B) Students will understand and be able to use formulas for perimeter of polygons, and circumference of circles
(3.3, 3.4, 4.7, 7.5, 8.1)
C) Students will understand and be able to use formulas for arc length, area of sectors and circle segments
(6.5, 6.7, 7.5, 8.1)
D) Students will understand and be able to use formulas for surface area and volume of cylinders, cones,
pyramids, prisms, and spheres
(7.3, 7.7, 8.1)
11. Identify and know the properties of the family of quadrilaterals.
(Standard 3, 8 Core Standard 4, 7, 9)
Learning Goals
A) Students will understand and be able to identify quadrilaterals by their special properties and vice versa
(3.1, 3.2, 3.3, 3.4, 8.1, 8.2)
5
12. Figures can be reflected, rotated, translated, and dilated. (Standard 2 Core Standard 2, 8)
Learning Goals
A) Students will understand and be able to identify transformations from pictures
(2.4)
B) Students will understand and be able to use rules for transformations to draw an image transformed from a preimage
( 2.4)
C) Students will understand and be able to use scalar multiplication to draw a dilation (2.4)
13. Identify, use, and prove similar figures. (Standard 3 Core Standard 2, 7)
Learning Goals
A) Students will understand and be able to identify similar figures
(3.4, 4.4)
B) Students will understand and be able to use properties of similar figures to find missing parts
(3.4, 4.4, 5.2)
C) Students will understand and be able to prove figures are similar (3.4, 4.9)
14. Find and use the equation of a circle, use formulas to determine segments and angles related to circles (Standard 6,8 Core
Standard 5, 7)
Learning Goals
A) Students will understand and be able to identify the various parts (center and radius) of a circle given the
equation and vice versa
(6.1, 6.2, 6.8)
B) Students will understand and be able to identify relationships among radii, chords, secants, tangents, and
diameters
(6.2)
C) Students will understand, be able to identify and find the measures of central angles, inscribed angles (by
chords), exterior angles (formed by secants and tangents) and interior angles (by chords)
(6.3, 6.5)
6
15. Use logic and conditional statements to make conclusions (Standard 8 Core Standard 9)
Learning Goals
A) Students will understand and be able to write conditional statements, converses, bi-conditionals, inverses and
contra-positive statements
(8.4, 8.5, 8.7)
B) Students will understand and be able to determine the truth value of statements, find counter examples.
(8.7, 8.8, 8.9)
7
MICHIGAN CITY HIGH SCHOOL
Geometry
Ongoing/All Year
1st Quarter
2nd Quarter
3rd Quarter
4th Quarter
Course Title
Assessment
Assessment
Assessment
Assessment
GEOMETRY
1, 15, 2, 6, 4, QTR1
Standard
1.1
3.4
8.4
Standard
1.2 1.3 1.4
4.9 5.1 8.1
8.5 8.7 8.8
3, 7, 13, 8, QTR2
2.6
8.2
8.9
2.3
4.2
4.9
8.1
Standard
2.4 2.6 3.4
4.3 4.4 4.6
5.1 5.2 5.3
8.3 8.6 8.7
9, 5, 11, 14, QTR3
4.1
4.8
5.6
8.8
2.1
3.1
5.5
6.5
Standard
2.2 2.3 2.5
3.2 3.3 3.4
5.6 6.1 6.2
6.8 8.1 8.2
10A, 10B, 10C, 12 QTR4
2.6
5.4
6.3
8.9
2.4
6.7
8.2
3.3
7.3
Standard
3.4 4.7
7.7 7.5
6.5
8.1
Bundles
1, 9, 2, 8
Bundles
2, 3, 6
Bundles
3, 4, 7
Bundles
5, 10
Best Practice Methods
Best Practice Methods
Best Practice Methods
Best Practice Methods
Similarities and Differences
Frequent and Immediate
Feedback
Graphic Organizers
Construct
Investigate
Re-teaching
Similarities and Differences
Frequent and Immediate
Feedback
Graphic Organizers
Construct
Investigate
Re-teaching
Similarities and Differences
Frequent and Immediate
Feedback
Graphic Organizers
Construct
Investigate
Re-teaching
Similarities and Differences
Frequent and Immediate
Feedback
Graphic Organizers
Construct
Investigate
Re-teaching
8
GEOMETRY Bundle #1 Standard Indicator: Geometry
Standard 1: Points, Lines, Angles & Planes
1.1, 1.4
Declarative Knowledge
Concepts
There are formulas for finding segment lengths,
midpoints, slopes and equations for lines.
Organizing
Ideas
Students will understand:
1. How to find the length and midpoints of
segments.
2. How to find slopes and different forms of
linear equations.
Details
Vocabulary
1.
2.
3.
4.
5.
Distance formula
Midpoint formula
Slope formula
Parallel lines have the same slope.
Perpendicular slopes are opposite
reciprocals.
6. Slope – Intercept form
7. Point – Slope form
8. Order of Operations
9. Properties of equalities
10. Steps to simplify radicals
Parallel, Perpendicular, Slope, skew, Midpoint,
Segment, Distance, Linear, Coordinates,
Reciprocals, Intercept, Equation, X& Y axes, Slope
– intercept form, Point – slope form, positive &
negative slopes, variable, symbols for parallel,
perpendicular, segment, angles, lines, rays, slope,
measurements of angles and segments
Procedural Knowledge
Processes
1.
2.
Reading Process
Order of Operations
Skills
1.
Multiply, Divide, Add, Subtract, and simplify
fractions.
Adding and subtracting integers.
Plot points and graph equations on the coordinate
plane.
Use Order of Operations to solve problems
Simply radicals
Problem Solving
2.
3.
4.
5.
6.
9
GEMOMETRY Bundle #2 Standard Indicator: Geometry
Standard 1: Points, Lines, Angles, and Planes
1.3
Declarative Knowledge
Concepts
Organizing
Ideas
Details
Vocabulary
Procedural Knowledge
There are relationships between special
pairs of angles formed by parallel lines and
transversals.
Students will understand that transversals
create special pairs of angles.
Processes
1. Order of operations
2. Reading Process
1. Alternate interior angles are
congruent.
2. Same side interior angles are
supplementary
3. Corresponding angles are congruent.
4. Vertical angles are congruent.
5. Linear pairs are supplementary.
6. Steps to solve and write equations
Alternate, Interior, Exterior, Corresponding,
Vertical Angles, Linear pair,
Supplementary, Complementary, Adjacent,
Congruent, Transversal, Parallel, Same –
side, Angles
Skills
1. Adding and subtracting
2. Identify if angles are on the
same side or alternate sides
of the transversal.
3. Identify if angles are interior
or exterior in relationship to
the parallel lines.
4. Solve Equations by Showing
Work.
10
GEOMETRY Bundle #3
Standard Indicator: Geometry
Standard 5: Right Triangles
5.1, 5.2, 5.3, 5.4, 5.6
Declarative Knowledge
Concepts
Organizing
Ideas
Details
Vocabulary
Procedural Knowledge
There are rules for finding sides and angles in right
triangles.
Students will understand:
1. How to use the Pythagorean Theorem to solve
problems.
2. How to identify and use the trigonometric functions.
3. How to use special right triangles to solve problems.
4. How to use the Geometric Mean relationships.
Processes
1. Pythagorean Theorem
2. Sine, Cosine, Tangent
3. Special right triangles ( 30-60 and 45 -45)
4. Geometric Mean formulas
5. Order of operations
Pythagorean Theorem, Geometric mean, Sine, Cosine,
Tangent, Right triangle, inverse, Isosceles triangle,
Similar triangles, Hypotenuse, Opposite leg, Adjacent leg,
arcsine, arccosine, arctangent
Skills
1. Reading Process
2. Writing Process
3. Order of Operations
1. Proper use of a scientific
calculator.
2. Identify the parts of a right
triangle.
3. Simplify radicals.
4. Cross multiplication
5. Solve Equations by Showing
Work.
6. Use Order of Operations to
Problem Solving
11
GEOMETRY Bundle #4
Standard Indicator: Geometry
Standard 6: Circles
6.2, 6.5, 6.6, 6.7, 6.8
Declarative Knowledge
Concepts
Organizing
Ideas
Details
Vocabulary
1.
There are relationships for finding area,
arc length, angles, and segment lengths
of circles.
2. There are equations for circles.
Students will:
1. Write an equation for a circle
2. Calculate circumference, arc length, and
area of circles and sectors.
3. Use measures of arcs and related angles.
4. Use the relationships among parts of a
circle.
1. Equation of a circle
2. Formulas for area and circumference.
3. Arc length and area of sectors.
4. Relationships among radii, chords, secants,
tangents and diameters.
5. Relationships among arcs, central and
inscribed angles, angles formed by
tangents and secants and chords.
6. Steps for solving quadratic equations
- Quadratic formula
- Factoring
Circle, Center, Radius, Diameter, Arc, Sector,
Central Angle, Inscribed Angle, Chord,
Tangent, Secant, Concentric, Circumference,
Midpoint, Distance, π, congruent,
circumscribed
Procedural Knowledge
Processes
Skills
1.
2.
3.
Writing Process
Reading Process
Order of Operations
1.
2.
3.
4.
Use the Distance formula
Use the Midpoint formula
Solving quadratic equations
Calculator usage
5. Basic Rounding Rules
12
GEOMETRY Bundle #5
Standard Indicator: Geometry
Standard 7: Polyhedra and Other Solids
7.1, 7.2, 7.3, 7.5, 7.6, 7.7
Declarative Knowledge
Concepts
Organizing
Ideas
Details
Vocabulary
There are rules describing relationships and
symmetries, using congruence and
similarity for polyhedra and other solids.
Students will understand:
1. How to describe regular and nonregular polyhedra.
2. How to use Euler’s Formula.
3. How to calculate volumes and
surface areas of solids.
4. How to use properties of congruent
and similar solids.
1. Euler’s Formula
2. Formulas for volumes of solids.
3. Formulas for lateral and surface areas
of solids.
4. Similarity ratios.
Regular, Non-regular, Net, Prism, Polyhedra,
Cylinder, Pyramid, Cone, Sphere, Base,
Composite, Oblique, Right, Edge, Polygon,
Similar, Apothem, Face, Slant height, Height,
Vertices, Volume, Area, Surface Area, Lateral
Area, Perimeter, Cross-Section, π,
Circumference, Square and Cubic Units,
Congruent
Procedural Knowledge
1. Reading Process
2. Writing Process
3. Order of Operations
Processes
Skills
1.
2.
3.
4.
5.
6.
7.
Multiplying Fractions.
Using a Scientific Calculator.
Reducing Fractions.
Identifying Perfect Squares and Cubes.
Basic Rounding Rules
Basic Conversion Units.
Break Apart an Irregular Shape into
Basic Solids.
8. Use order of operations to solve
problems
9. Find Cube Roots
10. Use Pythagorean Theorem to solve
problems
13
GEOMETRY Bundle # 6
Standard Indicator: Geometry
Standard 4: Triangles
4.1, 4.2, 4.4, 4.5, 4.6, 4.8
Declarative Knowledge
Concepts
Organizing
Ideas
Details
Vocabulary
1.
There are rules for proving triangles similar and
congruent.
2. Triangles have special properties.
Students will understand:
1.
How to classify triangles.
2.
How to prove triangles congruent and similar.
1. Triangles are classified by their angles and
sides.
2. Triangle Angle Sum Theorem
3. SSS, SAS, ASA, AAS, HL.
4. AA~, SAS~, SSS~.
5. Longest side is opposite largest angle.
6. Properties of Midsegments.
7. Triangle Inequality Theorem
8. Properties of Altitudes, Medians,
Perpendicular and Angle Bisectors.
9. Steps for writing a proof.
Altitude, Median, Angle Bisector, Perpendicular
Bisector, Acute, Scalene, Obtuse, Right, Segment,
Equilateral, Isosceles, Vertex, Equiangular, Exterior
Angle, Remote Interior Angle, Sum, Congruent,
Similar, Inequality, Corresponding Parts, CPCTC,
Midsegment, Included Angle, Included Side, Triangle
Angle Sum Theorem
Procedural Knowledge
Processes
1.
2.
3.
Writing Process
Reading Processs
Order of Operations
Skills
1.
2.
3.
Logical Reasoning.
Solving Equations.
Drawing Diagrams and marking
congruent parts.
Write a proof
4.
14
GEOMETRY Bundle # 7
Standard Indicator: Geometry
Standards 2 and 3: Polygons
2.1, 2.2, 2.3, 2.5, 3.1, 3.2, 3.3, 4.7
Declarative Knowledge
Procedural Knowledge
Concepts
Organizing
Ideas
Details
Vocabulary
1. There are rules for finding the area,
perimeter, and angle measures.
2. Polygons have specific properties.
Students will understand:
1. How to calculate perimeter and area.
2. How to find interior and exterior angle
measures.
3. How to classify different polygons.
1. Properties of Triangles.
2. Properties of Quadrilaterals.
3. Properties of Regular Polygons.
4. Formulas for Area and Perimeter
5. Formula for Finding Interior Angles of a
Polygon.
Kite, Trapezoid, Isosceles Trapezoid,
Parallelogram, Rhombus, Rectangle, Square,
Triangle, Pentagon, Hexagon, Octagon, Height,
Decagon, Diagonals, Base, Opposite Angles,
Apothem, Perimeter, Perpendicular, Altitude,
Radius, Side, Exterior/Interior Angles, Similar,
Congruent, Square Units, Regular, n-gon, Convex,
Concave, Composite
Processes
1. Writing Process
2. Reading Process
3. Order of Operations
Skills
1. Solving Equations.
2. Writing Equations.
3. Drawing and Marking
Diagrams.
4. Recognize Parts of a
Polygon.
5. Basic Calculator Skills.
6. Basic Rounding Rules.
7. Knowing Place Values.
8. Using Correct Units.
9. Basic Conversion Units.
10. Break Apart an Irregular
Shape into Basic Polygons.
11. Use Pythagorean Theorem to
Solve problems
15
GEOMETRY Bundle # 8
Standard Indicator: Geometry
Standard 8: Mathematical Reasoning
8.1, 8.2
Declarative Knowledge
Procedural Knowledge
Concepts
Organizing
Ideas
1.
2.
3.
1.
2.
3.
Details
Vocabulary
1.
2.
3.
4.
5.
6.
7.
8.
Problems may be solved in a variety of ways.
Solutions should be reasonable.
Steps taken to solve problems are justifiable.
Students will choose an appropriate method to
solve problems.
Students will be able to justify steps when
solving problem.
Students will determine and verify whether a
solution is valid.
Draw a diagram
Make a chart
Solve a simpler problem
Work backwards
Write an equation
Properties for equality and inequality
Look for a pattern
Choose the appropriate formula, or method
Formula, equation, diagram, solution, reasonable, graph
dimensions,
Processes
1.
2.
3.
Skills
1.
Reading Process
Writing Process
Order of Operations
Solving equations and
showing work
2. Apply appropriate strategies
3. Proper use of a scientific
calculator
4. Basic rules for rounding
5. Interpret information and
results
6. Explain reasoning
7. Make Charts
8. Write an equation
9. Classify by patterns
10. Use order of operations to
solve problems
11. Draw diagrams to assist in
solving problems
16
GEOMETRY Bundle # 9
Standard Indicator: Geometry
Standard 8: Mathematical Reasoning
6.3, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8
Declarative Knowledge
Procedural Knowledge
Concepts
Organizing
Ideas
Details
Vocabulary
1. Mathematical arguments follow logical
patterns
2. Statements are justified by reasons
1. Students will write and interpret if-then
statements
2. Students will apply theorems, postulates,
corollaries, and definitions to form logical
arguments
3. Students will write a variety of styles of proofs
1. Write proofs in various forms
a. two column
b. paragraph
c. indirect
d. coordinate
e. flow
2. Determine coordinates for coordinate
geometry proofs
3. Identify the hypothesis
Inverse, converse, contra-positive, bi-conditional,
conditional, conjecture, theorem, corollary,
postulate, counter-example, coordinate, inductive,
deductive
Processes
1. Writing Process
2. Reading Process
Skills
1. Draw conclusions
2. Draw and label a diagram
from given information
3. Follow the steps to write a
proof
4. Use rules of logic to solve
problems
17
GEOMETRY Bundle # 10
Standard Indicator: Geometry
Standard 8: Mathematical Reasoning
1.2, 2.4, 2.6, 3.4, 4.3, 4.9, 6.1, 6.4, 7.4, 8.9
Declarative Knowledge
Procedural Knowledge
Concepts
Organizing
Ideas
Details
Vocabulary
1. Constructions can be used in problem
solving
2. Transformations of figures follow
specific rules
1. Students will choose an appropriate
method for constructing figures.
2. Students will choose appropriate rules
to transform figures
1. Construct:
a. Copy segments
b. Copy angles
c. Perpendicular bisectors of
segments
d. Angle bisectors
2. Apply transformations to polygons to
determine congruence, similarity,
symmetry, and create tessellations
Transformation, reflection, translation, dilation,
rotation, tessellation, symmetry, “strike an arc”,
convenient radius, copy, construct, draw, sketch,
compass, straight-edge, glide-reflection, intersect,
isometry, similar, congruent, corresponding parts,
trace
Processes
1. Writing Process
2. Reading Process
3. Order of Operations
Skills
1.
2.
3.
4.
5.
6.
7.
8.
9.
Draw a line with a straight-edge
Use a compass appropriately
Trace
Use scissors safely
Following directions
Scalar multiplication
Matrix addition
Graph on the coordinate plane
Use a compass to and straight
edge for constructions
10. Create tessellations
18
Assessment Plan
Essential Outcome 1:
Know and use the correct symbols for lines, rays, angles, segments, perpendicular and parallel.
Summative Assessment: Selected response: symbols, measures of segments and angles
Describe assessment and
timeline
Method
Knowledge Types of
Reasoning
Formative:
Worksheet
generated
by
Geometry
teachers
X
multiple
choice and
matching
Students will understand and be able to
use appropriate symbols for lines, rays,
segments, angles, length of segments,
planes, angles and measure of angles,
symbols for parallel and perpendicular
lines.
Students will understand and be able to
use congruent segments (segment
midpoints and segment bisectors) and
angles (angle bisectors) as well as
segment and angle addition to solve for
missing measures. Understand and use
the terms collinear, coplanar, and
skew.
Performance Products
Skills
X
Short answer,
solving equations
10 question
Timeline: 7 days, assess on day
8
19
Assessment Plan
Essential Outcome 2:
Find slope, length, and midpoint of segments.
Summative Assessment: Selected Response: slope of lines, distance formula, midpoint formula
Describe assessment and
timeline
Method
Knowledge Types of
Reasoning
Formative:
Students will understand and be
able to apply the formula for
slope given two points, the
equation of a line (slopeintercept, point-slope, or standard
form), or given a graph.
Students will understand and be
able to apply the formula for
midpoint of a segment and find
an endpoint given the midpoint
and the second endpoint.
Identify congruent segments
(using midpoint), apply the
distance formula
Timeline: 6 days, assess day 7
Worksheet
by
Geometry
teachers
X
Count
spaces on a
graph
Know the
forms of a
line
X
Know the
formulas
Performance Products
Skills
X
Changing linear
equations from one
form to another
Apply the slope
formula.
X
Use the equations
for midpoint and
distance
20
Essential Outcome 3:
Identify angles and triangles by measure, by markings, and determine angle measure by using symbols or special
angle relationships
Summative Assessment: Selected response: identify angles, classify triangles, use special angle relationships, use
isosceles triangle theorem
Describe assessment and
timeline
Formative:
Students will understand and be
able to identify acute, right,
obtuse, straight, congruent
angles and the relationship
between complementary and
supplementary angles. Students
will be able to use the Triangle
Angle Sum Theorem.
Students will understand and be
able to classify triangles by side
length and angle measure, and
use Isosceles Triangle Theorem
Timeline: 10 days teaching, day
6 assess
Method
Worksheet
made by
Geometry
teachers
Knowledge
Types of
Reasoning
X
X
Matching or Solving equations
multiple
given algebraic
choice
values for
identification complementary and
of types of
supplementary
angles
angles
X
X
Multiple
Solve for side
choice
lengths and angle
identification measures using the
of types of
ITT.
triangles
Performance Products
Skills
21
Essential Outcome 4:
Identify and use special angles formed by lines and a transversal, vertical angles, and linear pairs.
Summative Assessment: Selected response: identify types of angles, find angle measures
Describe assessment and
timeline
Formative:
Students will understand and be
able to identify corresponding
angles, same-side interior
(exterior) angles, alternate
interior (exterior) angles, vertical
angles, and linear pairs.
Students will understand and be
able to apply the rules for the
above angle pairs when two lines
are parallel or not.
Timeline: 6 days, assess day 7
Method
Worksheet
made by
Geometry
teachers
Knowledge Types of
Reasoning
X
X
Know how Solve for missing
each angle angle measures
is related to knowing how the
every other angles are related
angle
Performance Products
Skills
22
Essential Outcome 5:
Identify polygons and find interior and exterior angle measures.
Summative Assessment: Selected Response: identify polygons, find interior angles sums, find interior and
exterior angles of regular polygons.
Describe assessment and
Method
Knowledge Types of
Performance Products
timeline
Reasoning
Skills
Worksheet X
X
Formative:
Students will be able to identify
made by
Matching, Short answer, solve
and name polygons by number of Geometry
short
equations.
sides
teachers
answer
Students will understand and be
X
able to apply the formulas for
Know
interior angle sum of all
formulas
polygons, exterior angle sum,
and understand the relationship
between the interior and exterior
angles of polygons
Timeline: 6 days, assess day 7
23
Essential Outcome 6:
Write equations of lines in slope-intercept, standard, and point-slope forms; be able to graph lines.
Summative Assessment: Selected response: graph a line, write the equation of a line give the graph, use slope to
determine relationship of lines,
Describe assessment and
timeline
Formative:
Students will understand and be
able to identify the necessary
information to graph a line
Students will understand and be
able to distinguish linear
relationships by looking at the
slope, write equations of related
lines
Timeline: 4 days, assess day 5
Method
Worksheet
made by
Geometry
teachers
Knowledge Types of
Reasoning
X
X
Find the
Write the equation
slope and
of new line given a
the yrelationship to a
intercept
line and a point
X
Identify
equal
slopes and
opposite
inverses
Performance Products
Skills
* Assessment should take only the first 10-15 minutes
24
Essential Outcome 7: Know what information is needed to prove triangles congruent and do simple proofs in
different forms including 2-column, paragraph, indirect, flow, and coordinate
Summative Assessment: Selected response: identify SSS, SAS, ASA, AAS & HL. Use CPCTC to prove
secondary triangles are congruent. Write proofs.
Describe assessment and
Method
Knowledge Types of
Performance Products
timeline
Reasoning
Skills
Formative: Students will
Teacher
X
X
X
understand and be able to
generated
Given 2
Given two triangles
Write an
identify the five ways of proving worksheet
triangles
with markings and
original
triangles are congruent
or activity
with
common parts
proof
Students will understand and be
markings
X
able to use CPCTC after proving
Fill in the blank or
triangles are congruent, and use
matching reasons,
logical sequencing and be able to
given the
write an original proof
statements
Timeline: 6 days assess on day 7
25
Essential Outcome 8:
Know the relationships and find the parts of special right triangles and use the Pythagorean Theorem.
Summative Assessment: Selected response: Use Pythagorean Theorem, special right triangles, and triangle
inequality theorem
Describe assessment and
Method
Knowledge Types of
Performance Products
timeline
Reasoning
Skills
Formative:
Students will understand and be able to
identify the parts of a right triangle,
use the Pythagorean Theorem, its
converse and corollary. Be able to
reduce radials to simplest radical form.
Worksheet
made by
Geometry
teachers
Worksheet
(Geometry IF
Students will understand and be able to Wkst p. 58)
use the relationship between sides of
special right triangles (30-60-90, 4545-90) to find other sides
X
Identify the
parts of a
right triangle
X
Just do it!
X
Use the Pythagorean
theorem, corollary and
converse
X
Given three sides, will
they make a triangle?
Given two sides, what
are the range of
possible third sides
Students will understand and be able to
use the Triangle Inequality Theorem to
determine possible third side lengths.
Timeline: 9 days, assess on day 10
26
Essential Outcome 9:
Use basic trigonometric functions
Summative Assessment: Selected response: Find angle measures, given side lengths, find side lengths given angle
measures
Describe assessment and Method
Knowledge Types of
Performance
Products
timeline
Reasoning
Skills
Teacher
X
X
Be able to use their
Formative:
Students will understand and
be able to identify sine, cosine
and tangent ratios and use
their symbols correctly.
generated
worksheet or
activity
Know the
ratios, solve
rations
Apply the rations to
find missing
measures
own calculator
correctly
Students will understand and
be able to use trigonometric
functions (sin, cos, tan)to find
missing angles and sides.
Timeline: 6 days assess on
day 7
27
Revisit-We may want to break this apart into smaller units or something
Essential Outcome 10: Correctly use formulas for area, volume, perimeter, circumference, arc length, surface
area, and sector area with correct units
Summative Assessment: Find perimeters and areas of polygons and circles, arc length, arc measure, sector area,
circle segment area
Describe assessment and timeline
Method
Knowledge Types of
Performance Products
Reasoning
Skills
Formative: Students will understand and be
able to use formulas to find perimeters and
areas of squares, rectangles, triangles,
parallelograms, trapezoids, rhombi, kite,
regular polygons
Timeline: 8 days, assess on day 9*
Formative: Students will understand and be
able to use formulas for area of circles,
circumference of circles, arc length, area of
sectors and circle segments
Timeline: 4 days assess on day 5
Teacher
generated
worksheet
X
Matching,
know the
formulas
Teacher
generated
worksheet
or activity
X
Know the
formulas
X
Use the correct
formula correctly, use
special right triangles
and Pythagorean
theorem
X
Correctly use the
formulas and apply to
given information,
use special right
triangles
Formative: Students will understand and be
able to use formulas for surface area and
volume of cylinders, cones, pyramids,
prisms, and spheres
Timeline: 5 days assess on day 6
28
Essential Outcome 11:
Identify and know the properties of the family of quadrilaterals.
Summative Assessment: Selected response, know the 5 ways of proving a quadrilateral is a parallelogram, know the special
properties of: triangles, rhombuses, squares, trapezoids, isosceles trapezoids, kites, and parallelograms. Be able to use the properties to
solve for missing measures
Describe assessment and Method
timeline
15 questions
Formative: Students will
understand and be able to
identify quadrilaterals by their
special properties and vice
versa
Timeline: 8 days, assess on
day 8
Formative: Students will be 5 question short
response
able to understand and use
properties of quadrilaterals to
solve for missing measures.
Timeline: 3-4 days assess on
day 4
Knowledge
Types of
Reasoning
Performance
Skills
X
Solving equations
X
Be able to solve
equations
Products
X
Matching
properties
with shape or
checklist
X
Know how
measures are
related using
properties
29
Essential Outcome 12:
That figures can be reflected, rotated, translated, and dilated
Summative Assessment: Product: booklet made illustrating the various transformations
Describe assessment and
timeline
Method
Knowledge
Formative: Students will
understand and be able to identify
transformations from pictures
Timeline: 2 days, assess on day 3
5 questions
X matching
Formative: Students will
understand and be able to use rules
for transformations to draw an
image transformed from a pre-image
Timeline: 4 days, assess on day 4
Formative: : Students will
understand and be able to use scalar
multiplication to draw a dilation
4 questions
X Know the
rules for
transformations
and apply them
to draw images
X Be able to
multiply by
rational
numbers
Timeline: 1 day
3 questions
Given A and A’ find
the sf, given the
other coordinates,
use the sf to find the
remaining, graph
Types of
Reasoning
Performance Products
Skills
X Be able to
draw a
reasonable
image
X Be able to
draw a dilation
30
Essential Outcome 13:
Identify, use and prove similar figures
Summative Assessment: Selected response,
Describe assessment and Method
timeline
15 questions
Formative: Students will
understand and be able to
identify similar figures
Timeline: 2 days, assess on
day 3
Formative: Students will
understand and be able to use
properties of similar figures to
find missing parts.
Timeline: 5 days, assess on
day 6
Formative: Students
understand and be able to
prove figures are similar
Timeline: 3 days, assess day
4
Knowledge
X
Be able to check
cross products. Be
able to simplify
fractions
5 question short X
response
Use side splitter
thm, triangle angle,
bisector thm, right
triangle similarity
thm.
Proof, given
X
statements,
Know methods of
student provides proving
reasons
similarity (AA~,
SSS~, SAS~)
Types of
Reasoning
Performance
Skills
Products
X
If similar give sf, if
not, tell why
X
Use scale factors to
find missing
measures. Solve
equations.
X
Be able to solve
equations
X
Write a proof
31
Essential Outcome 14: Find and use the equation of a circle, use formulas to determine segments and
angles related to circles
Summative Assessment: Selected response,
Describe assessment and timeline
Method
Knowledge
Formative: Students will understand and be
able to identify the various parts (center and
radius) of a circle given the equation and vice
versa
Timeline: 2, assess on day 3
Formative: Students will understand, identify
and use relationships among radii, chords,
secants, tangents, and diameters
Timeline: 3, assess day 4
5 questions,
short response
Be able to
recognize the
equations and
identify the
various parts
Know the
formulas for
finding segment
lengths
Be able to draw
a circle given
the equation or
the center and
radius
Solve equations
Formative: : Students will understand, be able
to identify and find the measures of central
angles, inscribed angles (by chords), exterior
angles (formed by secants and tangents) and
interior angles (by chords)
Timeline: 5
10 questions
Know the
formulas for
finding angles
and arcs (360 in
a circle, 180 in
a triangle)
Solve equations
10 questions
Types of
Reasoning
Performance Products
Skills
32
Essential Outcome 15: Use logic and conditional statements to make conclusions
Summative Assessment: Selected response,
Describe assessment and timeline
Method
Formative: Students will understand 5 matching
questions
and be able to write conditional
statements, converses, biconditionals, inverses and contrapositive statements, hypothesis,
conclusions, negation,
contradiction.
Timeline: 3, assess on day 4
Formative: Students will
understand and be able to
determine the truth value of
statements, find counter-examples,
use Laws of Detachment,
Syllogism
Timeline: 2, assess day 3
5 questions
Knowledge
Types of
Reasoning
Identify H
and C.
Understand
negation
Know
conditional
and contrapositive
statements
have the
same truth
value as do
inverses and
converses
Performance Products
Skills
Write
statements
Use Laws of
Syllogism,
and
Detachment
to make
conclusions
33
34