Number, Number Sense and Operations 
(Based on
State of Ohio
Curriculum Standards) 
1. Determine what properties
(closure, identity, inverse, commutative and associative) hold for
operations with complex numbers.


Math Dictionary
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2. Apply combinations as a method
to create coefficients for the Binomial Theorem, and make connections to
everyday and workplace problem situations. 

Binomial Probabilities Find the
probability of a number of successes or failures in a binomial
experiment using a tree diagram, a bar graph, and direct calculation.

Permutations and Combinations Experiment
with permutations and combinations of a number of letters represented by
letter tiles selected at random from a box. Count the permutations and
combinations using a dynamic tree diagram, a dynamic list of
permutations, and a dynamic computation by the counting principle.

Measurement 
1. Solve problems involving
derived measurements; e.g., acceleration and pressure. 

2. Use radian measures in the
solution of problems involving angular velocity and acceleration. 

3. Apply informal concepts of
successive approximation, upper and lower bounds, and limits in
measurement situations; e.g., measurement of some quantities, such as
volume of a cone, can be determined by sequences of increasingly
accurate approximations. 

Pyramids and Cones  Activity AVary the
height and base‑edge or radius length of a pyramid or cone and examine
how its three‑dimensional representation changes. Determine the area of
the base and the volume of the solid. Compare the volume of a skew
pyramid or cone to the volume of a right pyramid or cone.

Geometry and Spatial Sense 
1. Use matrices to represent
translations, reflections, rotations, dilations and their compositions. 

2. Derive and apply the basic
trigonometric identities; i.e., angle addition, angle subtraction and
double angle. 

Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use
stepbystep feedback to diagnose incorrect steps.

Sum and Difference Identities for Sine and Cosine
Choose the correct steps to evaluate a trigonometric expression using
sum and difference identities. Use step‑by‑step feedback to diagnose
incorrect steps.

3. Relate graphical and algebraic
representations of lines, simple curves and conic sections. 

Circles Compare the graph of a circle with
its equation. Vary the terms in the equation and explore how the circle
is translated and scaled in response.

Ellipse  Activity A Compare
the equation of an ellipse to its graph. Vary the terms of the equation
of the ellipse and examine how the graph changes in response. Drag the
vertices and foci, explore their Pythagorean relationship, and discover
the string property.

Hyperbola  Activity A Compare the
equation of a hyperbola to its graph. Vary the terms of the equation of
the hyperbola. Examine how the graph of the hyperbola and its asymptotes
changes in response.

4. Recognize and compare specific
shapes and properties in
multiple geometries; e.g., plane, spherical and hyperbolic. 

Platonic Solids  Virtual Manipulative This online activity allows
you to experiment with five platonic solids, counting their faces,
edges, and vertices.

Shapes This
website will allow your students to learn all about shapes and have fun
at the same time

Patterns, Functions and Algebra 
1. Analyze the behavior of
arithmetic and geometric sequences and series as the number of terms
increases. 

Arithmetic Sequences Find the
value of individual terms in arithmetic sequences using graphs of the
sequences and direct computation. Vary the common difference and examine
how the sequences change in response.

Arithmetic and Geometric
Sequences Find the value of
individual terms in an arithmetic or geometric sequence using graphs of
the sequence and direct computation. Vary the common difference and
common ratio and examine how the sequence changes in response.

Geometric Sequences Explore
geometric sequences by varying the initial term and the common ratio and
examining the graph. Compute specific terms in the sequence using the
explicit and recursive formulas.

2. Translate between the numeric
and symbolic form of a sequence or series. 

Arithmetic Sequences Find the
value of individual terms in arithmetic sequences using graphs of the
sequences and direct computation. Vary the common difference and examine
how the sequences change in response.

Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric
sequence using graphs of the sequence and direct computation. Vary the
common difference and common ratio and examine how the sequence changes
in response.

Geometric Sequences Explore
geometric sequences by varying the initial term and the common ratio and
examining the graph. Compute specific terms in the sequence using the
explicit and recursive formulas.

3. Describe and compare the
characteristics of transcendental and periodic functions; e.g.,
general shape, number of roots, domain and range, asymptotic
behavior, extrema, local and global behavior.


Cosine Function Compare the graph of the cosine
function with the graph of the angle on the unit circle. Drag a point along
the cosine curve and see the corresponding angle on the unit circle.

Exponential Functions  Activity A
Explore the graph of an exponential function. Vary the coefficient and
base of the function and investigate the changes to the graph of the
function.

Logarithmic Functions  Activity A Compare the
equation of a logarithmic function to its graph. Change the base of the
logarithmic function and examine how the graph changes in response. Use the
line y = x to compare the associated exponential function.

Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and
examine how the graph is translated or scaled. Connect these transformations
with the domain of the function, and the asymptote in the graph.

Sine Function Compare the graph of the sine
function with the graph of the angle on the unit circle. Drag a point along
the sine curve and see the corresponding angle on the unit circle.

Tangent Function Compare the graph of the
tangent function with the graph of the angle on the unit circle. Drag a
point along the tangent curve and see the corresponding angle on the
unit circle.

Translating and Scaling Sine and Cosine Functions  Activity A
Experiment with the graph of a
trigonometric function of the form y = a sin[b (x ? c)] + d. Relate the
equation and graph to amplitude, period, and frequency.

4. Represent the inverse of a
transcendental function symbolically. 

5. Set up and solve systems of
equations using matrices and graphs, with and without technology. 
Matrices: Equations and
Systems of Equations
This study guide from
Encyclopedia Britannica covers a discussion of inverse matrices,
determinants, matrix equations, and simultaneous equations. 
6. Make arguments about
mathematical properties using mathematical induction. 
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7. Make mathematical arguments
using the concepts of limit. 

8. Compare estimates of the area
under a curve over a bounded interval by partitioning the region with
rectangles; e.g., make successive estimates using progressively smaller
rectangles. 

9. Translate freely between polar
and Cartesian coordinate systems. 

Points in Polar Coordinates Identify
the polar coordinates of a point. Drag the point in the plane and
investigate how its r and theta coordinates change in response. Compare
its Cartesian coordinates.

10. Use the concept of limit to
find instantaneous rate of change for a point on a graph as the slope of
a tangent at a point. 

Data Analysis and Probability 
1. Identify and use various
sampling methods (voluntary response, convenience sample, random sample,
stratified random sample, census) in a study. 

2. Transform bivariate data so it
can be modeled by a function; e.g., use logarithms to allow nonlinear
relationship to be modeled by linear function. 

3. Describe the shape and find
all summary statistics for a set of univariate data, and describe how a
linear transformation affects shape, center and spread. 

4. Apply the concept of a random
variable to generate and interpret probability distributions, including
binomial, normal and uniform. 

Binomial Probabilities Find the
probability of a number of successes or failures in a binomial
experiment using a tree diagram, a bar graph, and direct calculation.

5. Use sampling distributions as
the basis for informal inference. 

6. Use theoretical or
experimental probability, including simulations, to determine
probabilities in realworld problem situations involving uncertainty,
such as mutually exclusive events, complementary events, and conditional
probability. 
