Port Clinton City Schools Academic Content Standard Based K-12 Mathematics Course of Study  Math II
Standard: Number, Number Sense and Operations
6
Factors; square/ cube numbers;
GCF/LCM;
Rational #s;
Ratio/proportion;
Order of operations;
Integers; / fractions
7
8
Place value and powers of
10; Scientific notation;
Order of operations w/
integers/fractions/ decimals;
Solve w/rational #s;
%; integers
9
Scientific notation (and
compute with); Subsets
of real #s;
Inverse/identity
properties;
Square root;
Properties of systems
(closure, inverse, etc.);
Equiv. forms of rational/
irrational #s;
Square roots; cube roots
10
Use roots in problems
(including nth root);
Factorial notation
11
Properties of
vectors/matrices;
Complex #s;
Fractional/negative
exponents
12
Properties of complex
#s;
Binomial Theorem
All benchmarks and indicators are Ohio Academic Content Standards Grade 9 unless otherwise noted.
Ohio Benchmarks
Standard Grade Level Indicators –
Instructional Strategies/
Grade Band 8-10
Code
Number, Number Sense and Operations
Commentary/Assessment/Best Practices
A. Use scientific notation to
N10A01a
1a. Review and extend scientific notation to
Reinforce Mathematical Processes Benchmark
express large numbers and
express and compute with large and small
B – Apply mathematical knowledge and skills
numbers less than one.
numbers.
routinely in other content areas and practical
situations.
C. Apply properties of operations
and the real number system
and justify when they hold for
a set of numbers.
N10C01
1. Identify and justify whether properties (closure,
identity, inverse, commutative and associative)
hold for a given set and operations; e.g., even
integers and multiplication.
E. Compare, order and
determine equivalent forms of
real numbers.
N10E02
2. Compare, order and determine equivalent
forms for rational and irrational numbers.
F. Explain the effects of
operations on the magnitude
of quantities.
N10F03
3. Explain the effects of operations such as
multiplication or division, and of computing
powers and roots on the magnitude of
quantities.
A Formulate a problem or mathematical
model in response to a specific need or
situation, determine information required
to solve the problem, choose method for
obtaining this information, and set limits
for acceptable solution.
B Apply mathematical
knowledge and skills
routinely in other
content areas and
practical situations..
C. Recognize and use connections between equivalent
representations and related procedures for a mathematical
concept; e.g., zero of a function and the x-intercept of the graph
of the function, apply proportional thinking when measuring,
describing functions, and comparing probabilities..
D Apply reasoning processes and skills
to construct logical verifications or
counter-examples to test conjectures
and to justify and defend algorithms
and solutions.
Math II – page 1
Port Clinton City Schools Academic Content Standard Based K-12 Mathematics Course of Study  Math II
Ohio Benchmarks
Grade Band 8-10
G. Estimate, compute and solve
problems involving real
numbers, including ratio,
proportion and percent, and
explain solutions.
I. Estimate, compute and solve
problems involving scientific
notation, square roots and
numbers with integer
exponents.
Standard
Code
N10G04
Grade Level Indicators –
Number, Number Sense and Operations
4. Demonstrate fluency in computations using
real numbers.
N10I05
5. Estimate the solutions for problem situations
involving square and cube roots.
Instructional Strategies/
Commentary/Assessment/Best Practices
Reinforce Mathematical Processes Benchmark
D – Apply reasoning to processes and skills to
construct logical verifications or counterexamples to test conjectures and to justify and
defend algorithms.
Websites relevant to Number, Number Sense and Operations Standard:
http://school.discovery.com/lessonplans/programs/scale/index.html
http://www.bced.gov.bc.ca/careers/aa/lessons/aom14.htm
http://illuminations.nctm.org/index_d.aspx?id=285
http://illuminations.nctm.org/index_d.aspx?id=252
http://www.pbs.org/newshour/extra/teachers/math/
http://nces.ed.gov/nationsreportcard/itmrls/qtab.asp?listarr=%221992-12m14+10%22
Topics: Mathematics -- Algebra; Reasoning and Proof; Numbers and Operations; Number theory
Ohio Department of Education Model Curricula Lesson Plans:
http://ims.ode.state.oh.us/ODE/IMS/Search/QuickJumpResults.asp?st=1&la=en&col=lp&qt=contentarea:ma|%20grade:09
E. Use a variety of mathematical
representations flexibly and
appropriately to organize, record and
communicate mathematical ideas.
F. Use precise mathematical
language and notations to
represent problem situations and
mathematical ideas.
G. Write clearly and coherently
about mathematical thinking
and ideas.
Number Island grade 9
H. Locate and interpret mathematical
information accurately, and communicate
ideas, processes and solutions in a
complete and easily understood manner.
Math II – page 2
Port Clinton City Schools Academic Content Standard Based K-12 Mathematics Course of Study  Math II
Standard: Measurement
6
Compare concepts –
surface area/ volume;
Estimate perimeter/
circumference;
Use correct measurement
for context
7
8
Derived measurements
(rates, etc.);
Proportional;
Develop area formulas
9
Compare common units;
levels of precision;
Derive formulas – surface
area/ volume;
Indirect meas. w/ proportion;
Int/ext of polygons
Convert measurements (same
system);
Unit analysis;
Ratio of sides to determine ratio
of areas/volumes;
Scale drawings;
Trigonometric ratios
10
Error analysis;
Central/inscribed
angles in a circle
All benchmarks and indicators are Ohio Academic Content Standards Grade 9 unless otherwise noted.
Ohio Benchmarks
Standard
Grade Level Indicators –
Grade Band 8-10
Code
Measurement
D. Use proportional reasoning
M10D01
1. Convert rates within the same measurement
and apply indirect
system; e.g., miles per hour to feet per second;
measurement techniques,
kilometers per hour to meters per second.
including right triangle
trigonometry and properties of M10D02
2. Use unit analysis to check computations
similar triangles, to solve
involving measurement.
problems involving
measurements and rates.
5. Solve problems involving unit conversion for
M10D05
situations involving distances, areas, volumes
and rates within the same measurement system.
11
Significant digits in
measurements;
Radian measure;
Surface area of cone
12
Derived measurements
(acceleration/pressure);
Radian measure;
Approximation of limits
Instructional Strategies/
Commentary/Assessment/Best Practices
Which unit best applies for a certain object
Websites relevant to the Measurement Standard:
http://school.discovery.com/lessonplans/programs/scale/
Topics: Mathematics -- Algebra; Linear equations; Measurement; Length, distance; Rates, ratio, proportion
Ohio Department of Education Model Curricula Lesson Plans:
http://ims.ode.state.oh.us/ODE/IMS/Search/QuickJumpResults.asp?st=1&la=en&col=lp&qt=contentarea:ma|%20grade:10
Using Geometric Probability- Until We Meet grade 10
A Formulate a problem or mathematical
model in response to a specific need or
situation, determine information required
to solve the problem, choose method for
obtaining this information, and set limits
for acceptable solution.
B Apply mathematical
knowledge and skills
routinely in other
content areas and
practical situations..
C. Recognize and use connections between equivalent
representations and related procedures for a mathematical
concept; e.g., zero of a function and the x-intercept of the graph
of the function, apply proportional thinking when measuring,
describing functions, and comparing probabilities..
D Apply reasoning processes and skills
to construct logical verifications or
counter-examples to test conjectures
and to justify and defend algorithms
and solutions.
Math II – page 3
Port Clinton City Schools Academic Content Standard Based K-12 Mathematics Course of Study  Math II
Standard: Geometry and Spatial Sense
6
7
Classify figures by
properties;
Standard language;
Describe results of
transformations;
Draw similar figures;
Build/sketch 3-D objects
Proportion in similar/
congruent figures;
Figures subsets of other
figures;
Use Pythagorean
Theorem;
Solve with
congruent/similar figures
8
Test conjectures about
figures;
<s w/ parallel lines;
Use similar figures;
Coord. geometry;
Nets
9
Define basic trig ratios;
Use right triangle trig to
solve problems;
Slope/distance in
coordinate systems
10
Formal definitions; test
conjectures; prove
theorems; construct right
angles, equilateral
triangles, etc.; symmetries;
use coordinate rules for
translations; solve
problems with circles
All indicators are from Ohio Academic Content Standards Grade 9 unless otherwise indicated.
Ohio Benchmarks
Standard Grade Level Indicators –
Grade Band 8-10
Code
Geometry and Spatial Sense
A. Formally define geometric figures.
G10A06a
6a. Identify the reflection and rotation symmetries of
two-dimensional figures. (Grade 10).
G10A02
2. Recognize and explain the necessity for certain
terms to remain undefined, such as point, line and
plane.
E. Draw and construct
representations of two- and threedimensional geometric objects
using a variety of tools, such as
straightedge, compass and
technology.
G10E06
6. Draw nets for a variety of prisms, pyramids,
cylinders and cones.
F. Represent and model
transformations in a coordinate
plane and describe the results.
G10F05
5. Draw the results of translations, reflections,
rotations and dilations of objects in the coordinate
plane, and determine properties that remain fixed;
e.g., lengths of sides remain the same under
translations.
E. Use a variety of mathematical
representations flexibly and
appropriately to organize, record and
communicate mathematical ideas.
F. Use precise mathematical
language and notations to
represent problem situations and
mathematical ideas.
G. Write clearly and coherently
about mathematical thinking
and ideas.
11
Polar coordinates;
Vectors for translations;
Law of Sines/Cosines
Cross-section of 3-D
figures
12
Matrices for
transformations;
Trig identities;
Use different geometries
Instructional Strategies/
Commentary/Assessment/Best
Practices
H. Locate and interpret mathematical
information accurately, and communicate
ideas, processes and solutions in a
complete and easily understood manner.
Math II – page 4
Port Clinton City Schools Academic Content Standard Based K-12 Mathematics Course of Study  Math II
Grade Level Indicators –
Geometry and Spatial Sense
Ohio Benchmarks
Grade Band 8-10
Standard
Code
I. Use right triangle trigonometric
relationships to determine lengths
and angle measures.
G10I01
1. Define the basic trigonometric ratios in right
triangles: sine, cosine and tangent.
G10I02
2. Apply proportions and right triangle trigonometric
ratios to solve problems involving missing lengths
and angle measures in similar figures.
Instructional Strategies/
Commentary/Assessment/Best
Practices
Websites for the Geometry and Spatial Sense Standard:
http://standards.nctm.org/document/eexamples/chap6/6.2/index.htm
Topics: Mathematics -- Algebra; Polynomials; Geometry; Models, construction; Representation
Ohio Department of Education Model Curricula Lesson Plans:
http://ims.ode.state.oh.us/ODE/IMS/Search/QuickJumpResults.asp?st=1&la=en&col=lp&qt=contentarea:ma|%20grade:10
Using Geometric Probability- Until We Meet grade 10
A Formulate a problem or mathematical
model in response to a specific need or
situation, determine information required
to solve the problem, choose method for
obtaining this information, and set limits
for acceptable solution.
B Apply mathematical
knowledge and skills
routinely in other
content areas and
practical situations..
C. Recognize and use connections between equivalent
representations and related procedures for a mathematical
concept; e.g., zero of a function and the x-intercept of the graph
of the function, apply proportional thinking when measuring,
describing functions, and comparing probabilities..
D Apply reasoning processes and skills
to construct logical verifications or
counter-examples to test conjectures
and to justify and defend algorithms
and solutions.
Math II – page 5
Port Clinton City Schools Academic Content Standard Based K-12 Mathematics Course of Study  Math II
Standard: Patterns, Functions, and Algebra
6
Include geometric
patterns;
Equivalent forms of
expressions;
Solve linear
equations;
Graphs for 2-variable
situations
7
Describe patterns
w/variables;
Linear or non-linear
Linear equations on coord.
system;
Equivalent forms of
expressions;
Variable changes –
linear/non-linear
8
Relate table/graph/ equation;
Generalize (nth term);
Ident. linear/non-lin.;
Compare graph of line to equation;
Solve 2X2 systems;
Solve linear;
Solve simple quadratic;
How variable changes affect
graphs
9
10
Define functions;
Functions to describe
patterns;
Zeros equiv. to roots;
Equivalent forms of
equations/expressions;
Solve/interpret 2X2 systems;
Solve quadratics;
Direct/inverse variation
f(x) notation;
Compare families of
functions (sq. root,
cubic, abs. val., basic
trig);
Solve for one variable in
terms of another;
Real world problems
All indicators are from Ohio Academic Content Standards Grade 9 unless otherwise indicated.
Ohio Benchmarks
Standard Grade Level Indicators –
Grade Band 8-10
Code
Patterns, Functions and Algebra
A. Generalize and explain patterns
and sequences in order to find
the next term and the nth term.
A10A02
2. Generalize patterns using functions or relationships
(linear, quadratic, and exponential), and freely
translate among tabular, graphical and symbolic
representations.
B. Identify and classify functions as A10B01
linear or nonllinear, and contrast
their properties using tables,
graphs or equations.
1. Define function with ordered pairs in which each
domain element is assigned exactly one range
element.
C. Translate information from one
representation (words, table,
graph or equation) to another
representation of a relation or
function.
2. Generalize patterns using functions or relationships
(linear, quadratic and exponential), and freely
translate among tabular, graphical and symbolic
representations.
E. Use a variety of mathematical
representations flexibly and
appropriately to organize, record and
communicate mathematical ideas.
A10C02
F. Use precise mathematical
language and notations to
represent problem situations and
mathematical ideas.
11
G. Write clearly and coherently
about mathematical thinking
and ideas.
Recursive functions;
Logarithms;
Relate equations to
symmetry types;
Inverse of a function;
Solve 3X3 systems;
Conic sections
12
Arithmetic/geometric
sequences & series;
Transcendental functions;
Periodic functions;
Solve systems w/matrices;
Use induction;
Polar to Cartesian;
Concept of limit
Instructional Strategies/
Commentary/Assessment/Best
Practices
Reinforce Mathematical Processes
Benchmark A – Formulate a problem
or mathematical model in response to
a specific need or situation, determine
information required to solve the
problem, choose method for obtaining
this information and set limits for
acceptable solution.
H. Locate and interpret mathematical
information accurately, and communicate
ideas, processes and solutions in a
complete and easily understood manner.
Math II – page 6
Port Clinton City Schools Academic Content Standard Based K-12 Mathematics Course of Study  Math II
Ohio Benchmarks
Grade Band 8-10
Standard
Code
Grade Level Indicators –
Patterns, Functions and Algebra
D. Use algebraic representations,
such as tables, graphs,
expressions, functions and
inequalities, to model and solve
problem situations.
A10D11
11. Add, subtract, multiply and divide monomials and
polynomials (division of polynomials by monomials
only).
A10D12
E. Analyze and compare functions
and their graphs using
attributes, such as rates of
change, intercepts and zeros.
A10E04
12. Simplify rational expressions by eliminating common
factors and applying properties of integer exponents.
4. Demonstrate the relationship among zeros of a
function, roots of equations, and solutions of
equations graphically and in words.
F. Solve and graph linear
equations and inequalities.
A10E05
A10F06
A10F08
Instructional Strategies/
Commentary/Assessment/Best
Practices
Reinforce Mathematical Processes
Benchmark G – Write clearly and
coherently about mathematical
thinking and ideas.
5. Describe and compare characteristics of the following
families of functions: linear, quadratic and exponential
functions; e.g., general shape, number of roots,
domain, range, rate of change, maximum or minimum.
6. Write and use equivalent forms of equations and
inequalities in problem situations; e.g., changing a
linear equation to the slope-intercept form.
8. Find linear equations that represent lines that pass
through a given set of ordered pairs, and find linear
equations that represent lines parallel or
perpendicular to a given line through a specific point.
10. Solve quadratic equations with real roots by factoring,
graphing, using the quadratic formula and with
technology.
G. Solve quadratic equations with
real roots by graphing, formula
and factoring.
A10G10
H. Solve systems of linear
equations involving two
variables graphically and
symbolically.
A10H09
A Formulate a problem or mathematical
model in response to a specific need or
situation, determine information required
to solve the problem, choose method for
obtaining this information, and set limits
for acceptable solution.
B Apply mathematical
knowledge and skills
routinely in other
content areas and
practical situations..
9. Solve and interpret the meaning of 2 by 2 systems of
linear equations graphically, by substitution, and by
elimination, with and without technology.
C. Recognize and use connections between equivalent
representations and related procedures for a mathematical
concept; e.g., zero of a function and the x-intercept of the graph
of the function, apply proportional thinking when measuring,
describing functions, and comparing probabilities..
D Apply reasoning processes and skills
to construct logical verifications or
counter-examples to test conjectures
and to justify and defend algorithms
and solutions.
Math II – page 7
Port Clinton City Schools Academic Content Standard Based K-12 Mathematics Course of Study  Math II
Ohio Benchmarks
Grade Band 8-10
Standard
Code
Grade Level Indicators –
Patterns, Functions and Algebra
J. Describe and interpret rates of
chanage from graphical and
numerical data.
A10J13a
13a. Compute and interpret slope, midpoint and distance
given a set of ordered pairs. (Grade 8)
A10J09a
9a. Recignize and explain that the slopes of parallel lines
are equal and the slopes of perpendicular lines are
nagetive reciprocals. (Grade 10)
Instructional Strategies/
Commentary/Assessment/Best
Practices
Websites relevant to the Patterns, Functions and Algebra Standard:
http://school.discovery.com/lessonplans/programs/scale/
Topics: Mathematics -- Algebra; Linear equations; Measurement; Length, distance; Rates, ratio, proportion
http://www.thirteen.org/edonline/lessons/graphing/index.html
Topics: Mathematics –Topics: Mathematics -- Algebra; Linear functions; Technology - Algebra; Linear functions; Nonlinear
functions; Graphing; Technology
http://standards.nctm.org/document/eexamples/chap6/6.2/index.htm
Topics: Mathematics -- Algebra; Polynomials; Geometry; Models, construction; Representation
http://math.rice.edu/~lanius/pres/map/index.htmlhttp://illuminations.nctm.org/index_d.aspx?id=298
Topics: Mathematics -- Algebra; Linear functions; Statistics; Data display
Professional Commentary: In this lesson, students model linear data collected in a variety of settings that range from car repair to sports to
medicine. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the line of best
fit and more.
http://illuminations.nctm.org/index_d.aspx?id=298
Topics: Mathematics -- Algebra; Linear functions; Graphing; Statistics; Data display
http://nces.ed.gov/nationsreportcard/itmrls/qtab.asp?listarr=%221992-12m14+10%22
Topics: Mathematics -- Algebra; Reasoning and Proof; Numbers and Operations; Number theory
E. Use a variety of mathematical
representations flexibly and
appropriately to organize, record and
communicate mathematical ideas.
F. Use precise mathematical
language and notations to
represent problem situations and
mathematical ideas.
G. Write clearly and coherently
about mathematical thinking
and ideas.
H. Locate and interpret mathematical
information accurately, and communicate
ideas, processes and solutions in a
complete and easily understood manner.
Math II – page 8
Port Clinton City Schools Academic Content Standard Based K-12 Mathematics Course of Study  Math II
Standard: Data Analysis and Probability
6
Circle graphs;
Histograms;
Compare measures
of center;
Design experiment
7
Box-and-Whisker
plots;
Stem-and-leaf plots;
Compare two
samples;
Misuses of data
8
9
Scatterplots; Comp. 2 types graphs–same
data;
Discrete vs. continuous;
Compare 2 data sets;
Approx. line best fit;
Add prob. for disjoint events;
Count # outcomes; Analyze sample size
Univariate vs. bivariate
data;
Interpret line of best fit;
Sampling methods;
Counting techniques;
Sample space concept;
Compound events
10
11
Measures of center/range;
Identify outliers;
Compare two variables;
Geometric probability;
Compute odds from
probability and reverse
All indicators are from Ohio Academic Content Standards Grade 9 unless otherwise indicated.
Ohio Benchmarks
Standard Grade Level Indicators –
Grade Band 8-10
Code
Data Analysis and Probability
J. Compute probabilities of
D10J09
9. Identify situations involving independent and
compound events,
dependent events, and explain differences
independent events, and
between, and common misconceptions about,
simple dependent events.
probabilities associated with those events.
Design experiment;
Least squares (with
technology);
Normal curve properties;
Evaluate validity of
study;
Random variable
12
Sampling methods;
Probability
distributions
(binomial/normal/
uniform);
Analyze probabilities
in real world
Instructional Strategies/
Commentary/Assessment/Best Practices
Websites relevant to the Data Analysis and Probability Standard:
http://math.rice.edu/~lanius/pres/map/index.htmlhttp://illuminations.nctm.org/index_d.aspx?id=298
Topics: Mathematics -- Algebra; Linear functions; Statistics; Data display
Professional Commentary: In this lesson, students model linear data collected in a variety of settings that range from car repair to sports to
medicine. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the line of best
fit
http://illuminations.nctm.org/index_d.aspx?id=290
Topics: Mathematics -- Probability; Reasoning and Proof
Ohio Department of Education Model Curricula Lesson Plans:
http://ims.ode.state.oh.us/ODE/IMS/Search/QuickJumpResults.asp?st=1&la=en&col=lp&qt=contentarea:ma|%20grade:10
Using Geometric Probability- Until We Meet grade 10
A Formulate a problem or mathematical
model in response to a specific need or
situation, determine information required
to solve the problem, choose method for
obtaining this information, and set limits
for acceptable solution.
B Apply mathematical
knowledge and skills
routinely in other
content areas and
practical situations..
C. Recognize and use connections between equivalent
representations and related procedures for a mathematical
concept; e.g., zero of a function and the x-intercept of the graph
of the function, apply proportional thinking when measuring,
describing functions, and comparing probabilities..
D Apply reasoning processes and skills
to construct logical verifications or
counter-examples to test conjectures
and to justify and defend algorithms
and solutions.
Math II – page 9