Course References are as follows:
ALG Algebra
GEO Geometry
PRE Pre-Algebra
ALG2 Algebra 2 (Advanced Algebra)
ALG3 Algebra 3
FST Functions, Statistics, and Trigonometry
PDM Pre-Calculus Discrete Math
STM Standards Math 1
STM2 Standards Math 2
9-12 means that all students in all math courses in these grades will work on
this objective
12.1 NUMERATION/NUMBER SENSE
12.1.1 By the end of twelfth grade, students will describe and compare the
relationships between subsets of real numbers.
ALG/STM2/PRE/ALG2 1.1a Draw Venn diagrams of sets of real
numbers.
ALG/STM2/GEO 1.1b Find intersection and union of two sets.
ALG2/FST/PDM 1.1c Identify rational and irrational numbers.
FST/PDM 1.1d Justify why a number does not belong to a specific
set.
12.1.2 By the end of twelfth grade, students will express the equivalent
forms of numbers using exponents, radicals, scientific notation, absolute
values, fractions, decimals, and percents.
ALG/STM2 1.2a Use the four operations (+, -, *, /) to simplify
algebraic fractions.
ALG/STM2/STM 1.2b Convert between fractions, decimals, and
percents.
PRE/ALG/STM2 1.2c Apply
the rules of whole-number exponents.
ALG2 /FST/ ALG3 1.2d Apply
the rules of rational exponents.
FST/ ALG3 1.2e Convert between exponential form and logarithmic
form.
ALG2/ ALG3 1.2f Simplify radicals.
12.2 COMPUTATION/ESTIMATION
12.2.1 By the end of twelfth grade, students will solve theoretical and lied problems using numbers in equivalent
forms, radicals, exponents, scientific notation, absolute values, fractions,
decimals, and percents, ratios and proportions, order of operations, and
properties of real numbers.
ALG/STM2/ 2.1a Solve problems using numbers in equivalent forms,
exponents, fractions, decimals, percents, ratios and proportions, order of
operations, and properties of real numbers.
GEO/STM 2.1b Solve problems using fractions, square roots, cube
roots, decimals, percents, ratios and proportions, order of operations, and
absolute values
ALG2/FST/PDM/ ALG3 2.1c Solve problems using numbers in
equivalent forms, radicals, exponents, absolute values, fractions, decimals,
percents, ratios and proportions, order of operations, and properties of real
numbers.
12.2.2 By the end of twelfth grade, students will justify solutions to
mathematical problems.
9-12 2.2 Justify the reasonableness of solutions.
12.2.3 By the end of twelfth grade, students will perform estimations and
computations of real numbers mentally, with paper and pencil, and with
technology.
9-12 2.3 Perform estimations and computations of real
numbers mentally, with paper and pencil, and with technology.
12.3 MEASUREMENT
12.3.1 By the end of twelfth grade, students will select and use measuring
units, tools, and/or technology and explain the degree of accuracy and
precision of measurements.
PRE/GEO 3.1a Measure angles to the nearest degree using a
protractor.
GEO 3.1b Find the length of segments using the appropriate unit of measurement for a
particular degree of accuracy.
12.3.2 By the end of twelfth grade, students will convert between metric and
standard units of measurement, given conversion factors.
ALG/STM2/FST/ 3.2a Use rate
multiplication to convert between metric and standard units of measurement.
GEO 3.2b Convert given linear measurements between metric and
standard units using conversion factors.
12.4 GEOMETRY/SPATIAL CONCEPTS
12.4.1 By the end of twelfth grade, students will calculate perimeter and area
of two-dimensional shapes and surface area and volume of three-dimensional
shapes.
ALG/STM2/STM 4.1a Calculate area of rectangles and volume
of rectangular prisms.
PRE 4.1b Calculate
perimeter and area of polygons and circles given relevant lengths.
GEO 4.1c Calculate perimeter and area of triangles, squares,
rectangles, parallelograms, trapezoids, circles, and irregular-shaped regions.
GEO/STM 4.1d Calculate surface area and volume of cones,
cylinders, spheres, pyramids, and prisms.
GEO/FST 4.1e Calculate arc measure and arc length.
12.4.2 By the end of twelfth grade, students will create geometric models to
describe the physical world.
GEO/STM 4.2a Draw two- and three-dimensional figures in
perspective.
GEO/STM 4.2b Create three-dimensional figures from
two-dimensional nets.
12.4.3 By the end of twelfth grade, students will evaluate characteristics
and properties of two- and three-dimensional geometric shapes.
GEO/STM 4.3a Compare and contrast characteristics of different
types of triangles.
GEO/STM 4.3b Use the hierarchy of quadrilaterals to compare and
contrast characteristics of different shapes.
GEO 4.3c Use transformations such as translations, rotations,
reflections, and glide-reflections to compare and contrast two-dimensional and
three-
dimensional shapes.
GEO 4.3d Determine if shapes are congruent using properties of
transformations.
GEO 4.3e Apply the
properties of congruence to show/prove triangles are congruent.
GEO 4.3f Determine the effects of changing dimensions on
perimeter, area, and volume.
GEO/STM 4.3g Classify three-dimensional shapes as surfaces or solids.
GEO/STM 4.3h Classify three-dimensional shapes as cylindrics,
conics, or spheres.
ALG2 4.3I Apply the
Fundamental Theorem of Variation to determine the effects of changing dimension
on volume and area.
ALG2/FST 4.3j Use matrices to Apply transformations to compare and contrast
two-dimensional shapes.
ALG/STM2 4.3k Find the ratio of similitude in size-change
figures.
GEO 4.3l Find symmetry lines in shapes.
GEO 4.3m Find symmetry planes in three-dimensional shapes.
12.4.4 By the end of twelfth grade, students will Apply coordinate geometry to locate describe
objects algebraically.
PRE/ALG 4.4a Plot points on a coordinate plane.
ALG/STM2/GEO/ALG2 4.4b Graph lines on the coordinate
plane.
ALG/STM2/GEO/ALG2 4.4c Find the slope of a line.
FST 4.4d Use the unit circle and right triangle trigonometry to
locate missing points.
GEO 4.4e Apply
transformations to shapes located on the coordinate plane.
ALG/STM2/PDM/FST 4.4f Apply two-dimensional slides and size changes
to shapes located on the coordinate plane.
GEO 4.4g Plot points in three-dimensional space.
12.4.5 By the end of twelfth grade, students will Apply right triangle trigonometry to find
length and angle measures.
GEO/ALG2/FST/PDM 4.5a Use sines, cosines, and tangents to
determine unknown lengths.
GEO/ALG2/FST/PDM 4.5b Determine sines, cosines, and tangents of
angles.
FST 4.5c Apply properties
of angles to find sines, cosines, and tangents in all four quadrants of the
coordinate plane.
FST/PDM 4.5d Use the Law of Sines and Law of Cosines to find
missing side lengths and angle measures.
GEO/ALG2/FST/PDM 4.5e Use inverse trigonometric functions
to find angle measures.
12.4.6 By the end of twelfth grade, students will Apply geometric properties to solve problems.
ALG/STM2/GEO/STM 4.6a Use the Pythagorean Theorem to find missing
side lengths in right triangles.
GEO/STM 4.6b Determine angle measures using properties of
parallel lines (vertical angles, correlating angles, alternate interior angles,
linear pairs).
ALG/STM2/ 4.6c Find missing lengths in similar figures
using proportions.
ALG/STM2/GEO/STM 4.6d Find missing angle measures and side
lengths by lying the Triangle Inequality
Postulate, Triangle Sum Theorem, and Polygon Sum Theorem.
ALG/STM2/GEO/STM 4.6e Determine relationships between angle
measures (complementary, supplementary, acute, obtuse, straight, zero).
GEO 4.6f Find distance between two points on coordinate
plane.
GEO 4.6g Write equations for circles.
12.4.7 By the end of twelfth grade, students will Apply deductive reasoning to arrive at a
conclusion.
ALG/STM2 4.7a Justify steps when solving an
algebraic equation using properties of real numbers.
GEO 4.7b Prove the congruence of triangles using a
two-column proof.
GEO 4.7c Determine if a statement is true or false using
instances and/or counterexamples.
ALG/STM2 4.7d Create formulas based on instances of pattern.
GEO/PDM 4.7e Make conclusions using the Law of Detachment, Law of
Transitivity, Law of Indirect Reasoning, and Law of Ruling Out Possibilities.
PDM 4.7f Prove statements using mathematical induction.
GEO/PDM 4.7g Write conditionals, converses, inverses, and contra
positives.
PDM 4.7h Prove trigonometric identities
12.5 DATA ANALYSIS, PROBABILITY, AND STATISTICALCONCEPTS
12.5.1 By the end of twelfth grade, students will select a sampling technique
to gather data, analyze the resulting data and make inferences.
FST 5.1a Make inferences using extrapolation and interpolation.
FST 5.1b Use samples to make
inferences about populations
ALG2/FST 5.1c Analyze the linearity of data using a correlation coefficient
FST 5.1d Determine relationships and interpret univariate data.
FST 5.1e Display data in an appropriate format (bar graph, circle graph, dotplot, stemplot, box plot, histogram, or scatterplot)
FST 5.1f Calculate measures of center and measures of spread for data
FST 5.1g Make inferences about data based on measures of center and spread
PRE/STM 5.1h Calculate mean, median, and mode.
PRE/STM 5.1i Compare and contrast mean, median, and mode.
PRE/FST 5.1j Display measures of center and spread using
box-and-whisker plots.
12.5.2 By the end of twelfth grade, students will write equations and make
predictions from sets of data.
ALG2/FST/ 5.2a Display data
in a scatter plot
ALG/STM2/ALG2/FST/ 5.2b
Fit a line to data using technology.
ALG/STM2/ALG2/FST/ 5.2c Relate
the slope of the regression line to the rate of change for the data set.
ALG/STM2/ALG2/FST/ 5.2d Determine
what the y-interceptor initial condition indicates about the data.
ALG/ALG2/FST 5.2e Make predictions using regression equations.
ALG2 5.2f Fit an
appropriate model to data (line, hyperbola, parabola, or inverse square
curve).
12.5.3 By the end of twelfth grade, students will Apply theoretical probability to represent
problems and make decisions.
PRE/ALG/STM2/FST/PDM 5.3a Use theoretical probabilities to make
predictions.
ALG/STM2/FST 5.3b Compare and contrast relative frequency with
probability.
12.5.4 By the end of twelfth grade, students will evaluate how
transformations on data affect the measures of central tendency and
variability.
FST 5.4a Describe the effects of data translation and scale changes
on mean, median, mode, range, maximum, minimum, standard deviation, variance,
and inter quartile range.
FST 5.4b Determine the effect of outliers on measures of center
and measures of spread.
12.5.5 By the end of twelfth grade, students will interpret data represented
by the normal distribution and formulate conclusions.
FST/ 5.5a Sketch a normal or
bell curve.
FST/ 5.5b Identify one
standard deviation from the mean.
FST/ 5.5c Identify
a sample space and determine sample size.
FST 5.5d Make conclusions about data using the mean and standard
deviation.
FST 5.5e Use properties of normal distributions and their parent
function.
12.5.6 By the end of twelfth grade, students will calculate probabilities of
independent events.
PRE/ALG/STM2/FST/PDM 5.6a Calculate probabilities using the
fundamental counting principle.
PRE/ALG/STM2/FST/PDM 5.6b Calculate permutations and
combinations.
FST/PDM 5.6c Calculate binomial probabilities.
12.6 ALGEBRAIC CONCEPTS
12.6.1 By the end of twelfth grade, students will graph and interpret algebraic
relations and inequalities.
ALG/STM2 6.1a a graph by identifying intercepts, slope,
increasing and decreasing intervals.
ALG2 6.1b Describe a graph by identifying intercepts, slope,
increasing and decreasing intervals, parallels and perpendiculars.
GEO 6.1c Describe a graph by identifying y-intercept, slope,
parallels and perpendiculars.
FST/PDM 6.1d Describe a graph by identifying intercepts, slopes,
increasing, decreasing, maximum, minimum, parallel, perpendicular and
asymptotes.
ALG2/FST 6.1e Use families of curves to describe the effect of
changing coefficients of an equation.
ALG2/FST 6.1f Describe the effects of translations and scale
changes on functions and their graphs.
ALG2/FST/PDM 6.1g Apply
the Graph Translation Theorem to make or identify graphs and find
transformation images.
ALG2/ ALG3 6.1h Create and
Apply inverses of relations and their properties.
12.6.2 By the end of twelfth grade, students will solve problems involving
equations and inequalities.
9-12 6.2a Solve linear equations and inequalities.
ALG/STM2/GEO 6.2b Solve equations of the form y=k2.
ALG2/FST/PDM 6.2c Solve quadratics using the
quadratic formula.
FST/PDM/ ALG3 6.2d Solve polynomials by graphing, factoring,
and/or the quadratic formula.
GEO 6.2e Solve equations of the form y=k3.
12.6.3 By the end of twelfth grade, students will solve problems involving
systems of two equations, and systems of two or more inequalities.
ALG/ 6.3a Solve systems by
graphing, substitution, or elimination.
ALG2/FST 6.3b Solve systems by graphing, substitution,
elimination, or matrices.
12.6.4 By the end of twelfth grade, students will solve problems using
patterns and functions.
9-12 6.4a Represent a problem in multiple formats(words,
tables, graphs, and symbols).
PRE/ALG/STM2 6.4b Evaluate numerical and algebraic expressions.
ALG2/FST/PDM/ ALG3 6.4c Find the nth term of an arithmetic
or geometric sequence.
ALG2/FST/PDM/ ALG3 6.4d Create recursive and
explicit formulas for arithmetic and geometric sequences.
FST/PDM/ ALG3 6.4e Evaluate arithmetic and geometric series.
ALG2 6.4f Apply direct and
inverse variation.
ALG2/FST/ ALG3 6.4g Recognize the properties of families
of functions.
FST/PDM/ ALG3 6.4h Recognize patterns of exponential growth and
decay and their significance to real-life situations.
FST/PDM/ ALG3 6.4i Solve problems involving exponential growth
and decay.
ALG2/FST/ ALG3 6.4j Solve problems using power functions and step
functions.
FST/PDM/ ALG3 6.4k Solve problems using logarithmic functions.
FST/PDM/ ALG3 6.4l Expand polynomials using patterns in Pascal's
Triangle.
PDM 6.4m Find limits and end behavior of functions.
FST 6.4n Find limits of sequences.
12.7 OBJECTIVES ABOVE AND BEYOND THE NEBRASKA
STATE STANDARDS
GEO 7a Identify and design tessellations using properties of
transformations and features of polygons.
FST/PDM 7b Find the quotient and remainder using long division of
polynomials.
FST/PDM 7c Apply the
Remainder Theorem to verify division of polynomials.
FST/PDM 7d Identify complex numbers.
ALG2/FST/PDM 7e Perform operations using complex numbers.
FST/PDM 7f Find the conjugate of a complex number.
FST/PDM/ ALG3 7g Apply the
Fundamental Theorem of Algebra to determine the number of zeroes for any
polynomial.
FST/PDM/ ALG3 7h Determine the types of zeroes (real and/or
complex) for any given polynomial.
FST/ ALG3 7i Factor polynomials using advanced
techniques(sums/differences of squares, cubes, odd powers, and grouping).
FST/ ALG3 7j Given zeroes of a function, determine factors,
solutions, roots, x- intercepts, and degree of the polynomial.
FST/PDM 7k Apply trigonometric
identities to find trigonometric values --- cos (a±ß),sin (a ±ß),cos(2ø),and sin(2ø).
FST/ ALG3 7l Find inverses of functions and matrices.
FST 7m Perform matrix multiplication.
FST/PDM/ ALG3 7n Find the composite(s) of functions.
PDM 7o Solve problems using modular arithmetic.
PDM 7p Find the quotient and remainder using synthetic division
of polynomials.
PDM 7q Identify and graph the reciprocal trigonometric functions.
PDM 7r Apply trigonometric
identities to find trigonometric values --- tan (a ± ß).
PDM 7s Solve equations involving trigonometric functions.
PDM 7t Graph polar equations.
PDM 7u Find roots and powers of complex numbers.
PDM 7v Write complex numbers in 4 forms --- a + bi, rectangular,
polar, and trigonometric.
PDM 7w Perform addition, subtraction, and multiplication of
vectors.
PDM 7x Find the derivative of a function. Using an equation
and/or graph of a function, interpret the derivative and Apply its meaning.
ALG2 7y Determine whether a relation is a function.
ALG2/FST/PDM/ ALG3 7z Identify domain and range of a function.
PRE/ 7aa Identify and
implement the 4-step problem solving process.
ALG2 7bb Add, subtract, and multiply matrices.
ALG2 7cc Translate quadratic equations from vertex to standard
form and vice versa.
ALG/ ALG3 7dd Multiply and simplify polynomials.
ALG/ ALG3 7ee Find common monomial factors of polynomials.
GEO 7gg Apply graph theory
to solve networks.
PDM 7hh Represent integers in other bases (not base10).
PDM 7ii Perform base 2 addition.
ALG3 7jj Write
equations for ellipses, parabolas, circles and hyperbolas.