Download Algebra 1A - Carl Junction Schools

Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Course Overview
Mathematics is a knowledge/communication enabling students to adapt within a technologically-based environment. Students will
develop the mathematical confidence to grow as individuals, to achieve lifelong skills of reasoning and problem solving, and to be
productive in our globally diverse society.
Course Rationale
ALGEBRA 1A: This course is designed for students who need extended time to learn Algebra I. This is the first year of a two year
process. Topics will include basic math skills and Pre-Algebra review, solving linear equations and inequalities, manipulate
polynomials and exponents and analyzing data. This class is closed to open enrollment. Students will be placed in this sequence
based upon assessment data and counselor/administrative approval. One year, one credit for incoming Freshman only.
Learning Targets
1. (Power Standard) Understand operations and use them to simplify expressions containing variables and real numbers.
2. (Power Standard) Understand operations and use them to simplify expressions containing exponents.
3. (Power Standard) Analyze and interpret data and measures of central tendencies.
4. (Power Standard) Solve linear and absolute value equations and inequalities.
5. (Power Standard) Understand, simplify and be able to factor polynomials.
1a. Apply operations to real numbers, using mental computation or paper-and-pencil calculations for simple cases and technology for
more complicated cases.
1b. Judge the reasonableness of numerical computations and their results.
2a. Describe and use algebraic manipulations, including factoring and rules of integer exponents and apply properties of exponents
(including order of operations) to simplify expressions.
3a. Represent data with plots on the real number line. (box, histograms, dot plots).
3b. Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.
4a. Use symbolic algebra to represent and solve problems that involve linear and quadratic relationships including equations and
inequalities.
4b. Use and solve equivalent forms of equations (linear, absolute value and quadratic).
4c. Explain each step in solving a simple equation.
4d. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letter.
5a. Interpret expressions that represent a quantity in terms of its content.
5b. Understand that polynomials form a system analogous to the integers; add, subtract and multiply polynomials.
Do: Add and subtract matrices of appropriate dimensions
Do: Add vectors end-to-end
Do: Add vectors using the Parallelogram Rule
Do: Add vectors using their components
Do: Apply arithmetic operations of addition, subtraction, and multiplication to polynomials
Do: Calculate relative frequencies including joint, marginal, and conditional
Do: Calculate relative frequencies including joint, marginal, and conditional relative frequencies
Do: Calculate the average rate of change of a function (presented symbolically or as a table) over a specified interval
Do: Calculate the average rate of change of a function (presented symbolically or as a table) over a specified interval
Do: Calculate the distance between numbers in the complex plane as the modulus of the difference
Do: Calculate the expected value of a random variable
Do: Calculate the expected value of a random variable
Do: Calculate the midpoint of a segment as the average of the numbers at its endpoints
Do: Calculate unit conversions
Do: Choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the
original expression
Do: Choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the
original expression
Do: Choose and produce an equivalent form of an exponential expression to reveal and explain properties of the quantity represented by
the original expression
Do: Choose and produce an equivalent form of an exponential expression to reveal and explain properties of the quantity represented by
the original expression
Do: Compute the direction of cv knowing that when |c|v ? 0, the direction of cv is either along v (for c > 0) or against v (for c < 0)
Course Summary
Powered by BuildYourOwnCurriculum
Page
1
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Do: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v
Do: Construct a tangent line
Do: Construct an equilateral triangle, square, and regular hexagon inscribed in a circle
Do: Construct arcs on circle C from the midpoint Q, having length of CQ
Do: Construct circumscribed circles of a triangle
Do: Construct exponential functions, including geometric sequences, given a graph, a description of a relationship, or two input-output
pairs (include reading these from a table)
Do: Construct inscribed circles of a triangle
Do: Construct linear functions, including arithmetic sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table)
Do: Construct the perpendicular bisector of the line segment between the center, C to the outside point, P
Do: Create a sign chart for a polynomial f(x) using the polynomial's x-intercepts and testing the domain intervals for which f(x) greater
than and less than zero
Do: Create at least two equations in two or more variables to represent relationships between quantities
Do: Create equations (linear and exponential) and inequalities in one variable and use them to solve problems
Do: Create equations and inequalities in one variable and use them to solve problems
Do: Create equations and inequalities in one variable to model real-world situations
Do: Derive a formula [i.e. equivalent to the formula S + a (1-rn)/(1-r) ] for the sum of a finite geometric series (when the common ratio is
not 1)
Do: Derive a formula [i.e. equivalent to the formula S + a (1-rn)/(1-r)] for the sum of a finite geometric series (when the common ratio is
not 1)
Do: Design an argument to prove theorems about triangles
Do: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated
Do: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated
Do: Discover three-dimensional objects generated by rotations of two-dimensional objects
Do: Draw a transformed figure and specify the sequence of transformations that were used to carry the given figure onto the other
Do: Explain why real-world or mathematical phenomena exhibit characteristics of periodicity
Do: Explain why real-world or mathematical phenomena exhibit characteristics of periodicity
Do: Factor a quadratic expression to produce an equivalent form of the original expression
Do: Factor a quadratic expression to produce an equivalent form of the original expression
Do: Find the equation of a line parallel to a given line that passes through a given point
Do: Find the equation of a line perpendicular to a given line that passes through a given point
Do: Find the expected value of a random variable for a probability distribution
Do: Find the expected value of a random variable for a probability distribution
Do: Find the expected value of a random variable for a probability distribution
Do: Find the expected value of a random variable for a probability distribution
Do: Generate arithmetic and geometric sequences from recursive and explicit formulas
Do: Generate arithmetic and geometric sequences from recursive and explicit formulas
Do: Give examples showing how extraneous solutions may arise when solving rational and radical equations
Do: Given a line segment (including those with positive and negative slopes) and a ratio, find the point on the segment that partitions the
segment into the given ratio
Do: Given an arithmetic or geometric sequence as an explicit formula, translate into the recursive form
Do: Given an arithmetic or geometric sequence as an explicit formula, translate into the recursive form
Do: Given an arithmetic or geometric sequence in recursive form, translate into the explicit formula
Do: Given an arithmetic or geometric sequence in recursive form, translate into the explicit formula
Do: Graph a given function by replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative)
Do: Graph a line, or boundary line, and shade the appropriate region for a two variable linear inequality
Do: Graph a system of linear inequalities and shade the appropriate overlapping region for a system of linear inequalities
Do: Graph exponential functions, by hand in simple cases or using technology for more complicated cases, and show intercepts and end
behavior
Do: Graph exponential functions, by hand in simple cases or using technology for more complicated cases, and show intercepts and end
behavior
Do: Graph exponential, logarithmic, and trigonometric functions, by hand in simple cases or using technology for more complicated
cases. For exponential and logarithmic functions, show: intercepts and end behavior; for trigonometric functions, show: perio
Do: Graph exponential, logarithmic, and trigonometric functions, by hand in simple cases or using technology for more complicated
cases. For exponential and logarithmic functions, show: intercepts and end behavior; for trigonometric functions, show: perio
Do: Graph linear functions by hand in simple cases or using technology for more complicated cases and show/label intercepts of the
graph
Do: Graph linear functions by hand in simple cases or using technology for more complicated cases and show/label intercepts of the
Course Summary
Powered by BuildYourOwnCurriculum
Page
2
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
graph
Do: Graph polynomial functions, by hand in simple cases or using technology for more complicated cases, and show/label maxima and
minima of the graph, identify zeros when suitable factorizations are available, and show end behavior
Do: Graph polynomial functions, by hand in simple cases or using technology for more complicated cases, and show/label maxima and
minima of the graph, identify zeros when suitable factorizations are available, and show end behavior
Do: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions, by hand in
simple cases or using technology for more complicated cases, and show/label key features of the graph
Do: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions, by hand in
simple cases or using technology for more complicated cases, and show/label key features of the graph
Do: Graph the corresponding probability distribution using the same graphical displays as for data distributions
Do: Graph the corresponding probability distribution using the same graphical displays used for data distributions
Do: Informally verify that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction,
multiplication, and division by a nonzero rational expression
Do: List five vectors. For each vector, v, determine |v| and ||v|| and sketch a directed line segment that represents the vector
Do: Multiply a vector by a matrix to produce another vector
Do: Multiply matrices by scalars to produce new matrices
Do: Multiply matrices of appropriate dimensions
Do: Perform geometric constructions using a variety of tools and methods, including: 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
Do: Prove alternate interior angles are congruent when two parallel lines are cut by a transversal and converse
Do: Prove corresponding angles are congruent when two parallel lines are cut by a transversal and converse
Do: Prove points are on a perpendicular bisector of a line segment are exactly equidistant from the segment's endpoint
Do: Prove properties of angles for a quadrilateral inscribed in a circle
Do: Prove that exponential functions grow by equal factors over equal intervals
Do: Prove that linear functions grow by equal differences over equal intervals
Do: Prove the Pythagorean identity sin2(Θ) + cos2(Θ) = 1
Do: Prove theorems about triangles
Do: Prove theorems involving similarity about triangles
Do: Prove vertical angles are congruent
Do: Represent data with plots on the real number line, using various display types by creating dot plots, histograms, and box plots
Do: Represent data with plots on the real number line, using various display types by creating dot plots, histograms, and box plots
Do: Represent vectors as directed line segments
Do: Sketch graphs showing the key features of a function, modeling a relationship between two quantities, given a verbal description of
the relationship
Do: Sketch graphs showing the key features of a function, modeling a relationship between two quantities, given a verbal description of
the relationship
Do: Solve a system of linear equations using inverse matrices
Do: Solve a system of linear equations with three or more variables using technology
Do: Solve all available types of equations and inequalities, including root equations and inequalities, in one variable
Do: Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse
Do: Solve equations and inequalities with coefficients represented by letters
Do: Solve exponential equations using logarithms
Do: Solve inequalities in one variable
Do: Solve linear and exponential equations in one variable
Do: Solve logarithmic equations using exponents
Do: Solve multi-step equations in one variable
Do: Solve multi-step inequalities in one variable
Do: Solve problems involving quantities that can be represented by vectors
Do: Solve problems involving velocity
Do: Solve quadratic equations in one variable
Do: Solve radical equations in one variable
Do: Solve rational equations in one variable
Do: Use a calculator, spreadsheet, and table to estimate areas under the normal curve
Do: Use a calculator, spreadsheet, and table to estimate areas under the normal curve
Do: Use a computer algebra system to rewrite complicated rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b
(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x)
Do: Use a normal distribution to estimate population percentages
Do: Use a normal distribution to estimate population percentages
Course Summary
Powered by BuildYourOwnCurriculum
Page
3
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Do: Use a simulation model to generate data for random sampling, assuming certain population parameters/ characteristics
Do: Use a simulation model to generate data for random sampling, assuming certain population parameters/characteristics
Do: Use appropriate statistics for center and spread to compare two or more data sets
Do: Use appropriate statistics for center and spread to compare two or more data sets
Do: Use appropriate symbols for vectors and their magnitudes
Do: Use congruency and similarity theorems for triangles to prove relationships in geometric figures
Do: Use congruency and similarity theorems for triangles to solve problems
Do: Use conjugates to find moduli of complex numbers
Do: Use conjugates to find quotients of complex numbers
Do: Use data from a randomized experiment to compare two treatments
Do: Use data from a randomized experiment to compare two treatments
Do: Use data from a sample survey to estimate a population mean or proportion
Do: Use data from a sample survey to estimate a population mean or proportion
Do: Use definitions of conic sections and Pythagorean Theorem to derive equations
Do: Use dissection arguments, Cavalieri's principle, and informal limit arguments
Do: Use geometric descriptions of rigid motions to predict the effect of a given motion on a given figure
Do: Use geometric descriptions of rigid motions to transform figures
Do: Use given and constructed arithmetic and geometric sequences, expressed both recursively and with explicit formulas, to model reallife situations
Do: Use given and constructed arithmetic and geometric sequences, expressed both recursively and with explicit formulas, to model reallife situations
Do: Use inspection to rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q
(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x)
Do: Use inverse functions to solve trigonometric equations
Do: Use inverse functions to solve trigonometric equations
Do: Use long division to rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x),
q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x)
Do: Use matrices to manipulate data
Do: Use matrices to represent data
Do: Use measures and properties of geometric shapes to describe real-world objects
Do: Use measures and properties of geometric shapes to describe real-world objects
Do: Use permutations and combinations to compute probabilities of compound events and solve problems
Do: Use permutations and combinations to compute probabilities of compound events and solve problems
Do: Use polynomial identities to describe numerical relationships
Do: Use properties of graphical representations in computations
Do: Use properties of special quadrilaterals in a proof
Do: Use strategies to help visualize relationships between two- dimensional and three dimensional objects
Do: Use the addition and subtraction formulas for sine, cosine, and tangent to solve problems
Do: Use the definition of congruence in terms of rigid motions to show that if the corresponding pairs of sides and corresponding pairs of
angles of two triangles are congruent, then the two triangles are congruent
Do: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if corresponding pairs of sides and
corresponding pairs of angles are congruent
Do: Use the formula S + a (1-rn)/(1-r) to solve problems
Do: Use the formula S + a (1-rn)/(1-r) to solve problems
Do: Use the Laws of Sines and Cosines this to find missing angles or side length measurements
Do: Use the mean and standard deviation of a data set to fit it to a normal distribution
Do: Use the mean and standard deviation of a data set to fit it to a normal distribution
Do: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p) 2 = q that has the
same solutions
Do: Use the principle that corresponding parts of congruent triangles are congruent to solve problems
Do: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the
graph, and interpret these in terms of a context
Do: Use the Pythagorean identity, sin2(Θ) + cos2(Θ) = 1, to find sin (Θ), cos (Θ), or tan (Θ), given sin (Θ), cos (Θ), or tan (Θ), and the
quadrant of the angle
Do: Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers
Do: Use the relationship between the sine and cosine of complementary angles
Do: Use the x-intercepts of a polynomial function and the sign chart to construct a rough graph of the function
Do: Using technology, compute the correlation coefficient of a linear fit
Do: Using technology, compute the correlation coefficient of a linear fit
Course Summary
Powered by BuildYourOwnCurriculum
Page
4
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Do: Using the properties of exponents, rewrite a radical expression as an expression with a rational exponent
Do: Using the properties of exponents, rewrite an expression with a rational exponent as a radical expression
Do: Verify experimentally that a dilated image is similar to its pre-image by showing congruent corresponding angles and proportional
sides
Do: Verify experimentally that a dilation takes a line not passing through the center of the dilation to a parallel line by showing the lines
are parallel
Do: Verify experimentally that dilation leaves a line passing through the center of the dilation unchanged, by showing that it is the same
line
Do: Verify experimentally that the dilation of a line segment is longer or shorter in the ratio given by the scale factor
Do: Write a function that describes a relationship between two quantities by determining an explicit expression, a recursive process, or
steps for calculation from a context
Do: Write a function that describes a relationship between two quantities by determining an explicit expression, a recursive process, or
steps for calculation from a context
Do: Write a quadratic function defined by an expression in different but equivalent forms to reveal and explain different properties of the
function and determine which form of the quadratic is the most appropriate for showing zeros and symmetry of a graph in terms of a realworld context
Do: Write a system of linear equations as a single matric equation
Do: Write a system of linear equations in vector variable form
Do: Write an exponential function defined by an expression in different but equivalent forms to reveal and explain different properties of
the function, and determine which form of the function is the most appropriate for interpretation in a real-world context
Do: Write complex numbers in the form a + bi with a and b being real numbers
Do: Write functions in equivalent forms using the process of factoring
Know: Add, subtract, multiply, and divide rational expressions
Know: Apply the Binomial theorem to expand (x+y)n, when n is a positive integer and x and y are any number, rather than expanding by
multiplying
Know: Build on work with two way tables from Algebra 1 Unit 3 S-ID.5 to develop understanding of conditional probability and
independence
Know: Build on work with two-way tables from Algebra 1 Unit 3 S-ID.5 to develop understanding of conditional probability and
independence
Know: Categorize events as independent or not using the characterization that two events A and B are independent when the probability
of A and B occurring together is the product of their probabilities
Know: Categorize events as independent or not using the characterization that two events A and B are independent when the probability
of A and B occurring together is the product of their probabilities
Know: Classify the exponential function as exponential growth or decay by examining the base
Know: Classify types of quadrilaterals
Know: Combine two functions using the operations of addition, subtraction, multiplication, and division
Know: Combine two functions using the operations of addition, subtraction, multiplication, and division
Know: Complete the square of a quadratic equation
Know: Compute Theoretical and Experimental Probabilities
Know: Compute Theoretical and Experimental Probabilities
Know: Define a circle
Know: Define a geometric series as a series with a constant ratio between successive terms
Know: Define a geometric series as a series with a constant ratio between successive terms
Know: Define a parabola including the relationship of the focus and the equation of the directrix to the parabolic shape
Know: Define a point of concurrency
Know: Define a quantity of interest to mean any numerical or algebraic quantity (e.g. , 2(a/b)=d in which 2 is the quantity of interest
showing that d must be even; (πr2h/3)=Vcone and πr2h=Vcylinder showing that Vcylinder=3*Vcone )
Know: Define a radian measure of an angle as the length of the arc on the unit circle subtended by the angle
Know: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space
Know: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space
Know: Define a reasonable domain, which depends on the context and/or mathematical situation, for a function focusing on linear and
exponential functions
Know: Define and recognize amplitude, frequency, and midline parameters in a symbolic trigonometric function
Know: Define and recognize parts of an expression, such as terms, factors, and coefficients
Know: Define and recognize parts of an expression, such as terms, factors, and coefficients
Know: Define and recognize the amplitude, frequency, and midline parameters in a symbolic trigonometric function
Know: Define and recognize the key features in tables and graphs of linear and exponential functions: intercepts; intervals where the
function is increasing, decreasing, positive, or negative, and end behavior
Know: Define and recognize the key features in tables and graphs of linear and exponential functions: intercepts; intervals where the
Course Summary
Powered by BuildYourOwnCurriculum
Page
5
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
function is increasing, decreasing, positive, or negative, and end behavior
Know: Define and recognize the key features in tables and graphs of linear, exponential, and quadratic functions: intercepts; intervals
where the function is increasing, decreasing, positive, or negative, relative maximums and minimums, symmetries, end be
Know: Define and recognize the key features in tables and graphs of linear, exponential, and quadratic functions: intercepts; intervals
where the function is increasing, decreasing, positive, or negative, relative maximums and minimums, symmetries, end be
Know: Define causation
Know: Define causation
Know: Define circle and the distance around a circular arc
Know: Define closure
Know: Define complex numbers
Know: Define density
Know: Define density
Know: Define descriptive modeling
Know: Define explicit function and recursive process
Know: Define explicit function and recursive process
Know: Define i as √-1 or i2 = -1
Know: Define image, pre-image, scale factor, center, and similar figures as they relate to transformations
Know: Define inscribed and circumscribed circles of a triangle
Know: Define inverse function
Know: Define margin of error
Know: Define margin of error
Know: Define perpendicular lines, parallel lines, line segments, and angles
Know: Define positive, negative, and no correlation and explain why correlation does not imply causation
Know: Define positive, negative, and no correlation and explain why correlation does not imply causation
Know: Define radical notation as a convention used to represent rational exponents
Know: Define rotations, reflections, and translations
Know: Define tangent, radius, perpendicular bisector, and midpoint
Know: Define terminal and initial side of an angle on the unit circle
Know: Define the Binomial Theorem and compute combinations
Know: Define the characteristics of experimental design (control, randomization, and replication)
Know: Define the characteristics of experimental design (control, randomization, and replication)
Know: Define the context of data sets as meaning the specific nature of the attributes under investigation
Know: Define the context of data sets as meaning the specific nature of the attributes under investigation
Know: Define the correlation coefficient
Know: Define the correlation coefficient
Know: Define the remainder theorem for polynomial division and divide polynomials
Know: Define trigonometric ratios as related to the unit circle
Know: Define unions, intersections, and complements of events
Know: Define unions, intersections, and complements of events
Know: Describe a typographical grid system
Know: Describe a typographical grid system
Know: Describe the characteristics of a normal distribution
Know: Describe the characteristics of a normal distribution
Know: Describe the different types of transformations including translations, reflections, rotations, and dilations
Know: Describe the inverse relationship between exponential and logarithmic functions, including equations and graphs
Know: Describe the relationships between the quantities in the problem (for example, how the quantities are changing or growing with
respect to each other); express these relationships using mathematical operations to create an appropriate equation or ine
Know: Describe the terms point, line, and distance along a line in a plane
Know: Describe transformations as functions that take points in the coordinate plane as inputs and give other points as outputs
Know: Determine if a relation is a function
Know: Determine the constant of proportionality (scale factor)
Know: Determine the domain of a radical function
Know: Determine the domain of a rational function
Know: Determine the limitations of different measurement tools
Know: Determine the value of the function with proper notation
Know: Differentiate between different types of functions using a variety of descriptors (graphical, verbal, numerical, algebraic)
Know: Differentiate between exponential and linear functions using a variety of descriptors (graphical, verbal, numerical, and algebraic)
Know: Evaluate a logarithm using technology
Know: Evaluate the domain of the combined function
Course Summary
Powered by BuildYourOwnCurriculum
Page
6
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Know: Evaluate the domain of the combined function
Know: Explain how radian measures of angles of the unit circle in the coordinate plane enable the extension of trigonometric functions to
all real numbers
Know: Explain that 1° = π/180 radians
Know: Explain that an identity shows a relationship between two quantities or expressions, that is true for all values of the variables, over
a specified set
Know: Explain that an identity shows a relationship between two quantities, or expressions, that is true for all values of the variables, over
a specified set
Know: Explain that statistical inferences about population characteristics are based on random samples from that population
Know: Explain that statistical inferences about population characteristics are based on random samples from that population
Know: Explain that statistics is a process for making inferences about population parameters, or characteristics
Know: Explain that statistics is a process for making inferences about population parameters, or characteristics
Know: Explain that the scale factor represents how many times longer or shorter a dilated line segment is than its pre-image
Know: Explain the connection between the completed square form of a quadratic expression and the maximum or minimum value of the
function it defines
Know: Explain the connection between the completed square form of a quadratic expression and the maximum or minimum value of the
function it defines
Know: Explain the connection between the factored form of a quadratic expression and the zeros of the function it defines
Know: Explain the connection between the factored form of a quadratic expression and the zeros of the function it defines
Know: Explain the connection of margin of error to variation within a data set or population
Know: Explain the connection of margin of error to variation within a data set or population
Know: Explain the construction of geometric figures using a variety of tools and methods
Know: Explain the properties of the quantity represented by the quadratic expression
Know: Explain the properties of the quantity represented by the quadratic expression
Know: Explain the relationship between a counterclockwise radian measure of an angle along the unit circle, terminal coordinate on the
unit circle of that angle, and the associated real number
Know: Explain theorems for parallelograms and relate to figure
Know: Explain why each point on a curve is a solution to its equation
Know: Explain why the rectangular and polar forms o a given complex number represent the same number
Know: Factor polynomials using any available method
Know: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A
Know: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A
Know: Find the first term in a geometric sequence given at least two other terms
Know: Find the first term in a geometric sequence given at least two other terms.
Know: Find the sums and products of rational and irrational numbers
Know: Fit a given function class (e.g., linear, exponential) to a data set
Know: Fit a given function class (e.g., linear, exponential) to a data set
Know: Fluently compute growth rates for linear, exponential, and quadratic functions
Know: Formally use dynamic geometry software or straightedge and compass to take angles to angles and segments to segments
Know: Give examples of polynomial identities
Know: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure
Know: Given a single transformation on a symbolic or graphic function, identify the effect on the graph
Know: Identify a dilation stating its scale factor and center
Know: Identify an appropriate domain based on the unit, quantity, and type of function it describes
Know: Identify an appropriate domain based on the unit, quantity, and type of function it describes
Know: Identify and describe the domain of a function, given the graph or a verbal/written description of a function
Know: Identify and describe the domain of the function given the graph or a verbal/written description of a function
Know: Identify and use properties of vertical angles, parallel lines with transversals, all angle relationships, corresponding angles,
alternate interior angles, perpendicular bisector, equidistant from endpoint
Know: Identify appropriate units of measurement to report quantities
Know: Identify arithmetic and geometric patterns in given sequences
Know: Identify arithmetic and geometric patterns in given sequences
Know: Identify characteristics of a linear inequality and a system of linear inequalities, such as: boundary line and shading, and determine
the appropriate points to test and derive a solution set from
Know: Identify corresponding angles and sides of two triangles
Know: Identify corresponding pairs of angles and sides of congruent triangles after rigid motions
Know: Identify data or discrepancies that provide the basis for rejecting a statistical model
Know: Identify data or discrepancies that provide the basis for rejecting a statistical model
Know: Identify different forms of a quadratic expression
Course Summary
Powered by BuildYourOwnCurriculum
Page
7
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Know: Identify how key features of a quadratic function relate to its characteristics in a real-world context
Know: Identify how key features of an exponential function relate to its characteristics in a real-world context
Know: Identify inscribed angles, radii, chords, central angles, circumscribed angles, diameter, tangent
Know: Identify mathematical relationships and express them using function notation
Know: Identify situations that are permutations and those that are combinations
Know: Identify situations that are permutations and those that are combinations
Know: Identify that the sum, difference, or product of two polynomials will always be a polynomial, which means that polynomials are
closed under the operations of addition, subtraction, and multiplication
Know: Identify the center of the circle
Know: Identify the domain and range of a function
Know: Identify the hypothesis and conclusion of a theorem
Know: Identify the magnitude and direction of vectors
Know: Identify the quantities in a mathematical problem or real-world situation that should be represented by distinct variables and
describe what quantities the variables represent
Know: Identify the type of function, given a table or graph
Know: Identify the type of function, given its table or graph
Know: Identify types of functions based on verbal, numerical, algebraic, and graphical descriptions and state key properties
Know: Identify various structures of expressions
Know: Identify ways to rewrite expressions, such as difference of squares, factoring out a common monomial, and regrouping
Know: Identify whether a function is linear or exponential, given its table or graph
Know: Identify whether the function is linear or exponential, given its table or graph
Know: Identify zeros, extreme values, and symmetry of the graph of a quadratic function
Know: Informally define the concept of end behavior
Know: Informally use rigid motions to take angles to angles and segments to segments (from 8th grade)
Know: 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
Know: 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
Know: Know that solving an equation means that the equation remains balanced during each step
Know: Know that the commutative, associative, and distributive properties extend to the set of complex numbers over the operations of
addition and multiplication
Know: Know the conditional probability of A given B as P(A and B)/P(B)
Know: Know the conditional probability of A given B as P(A and B)/P(B)
Know: Name the sides of right triangles as related to an acute angle
Know: Recall congruence and similarity criteria for triangles
Know: Recall definitions of angles, circles, perpendicular and parallel lines, and line segments
Know: Recall how to find the area and circumference of a circle
Know: Recall midpoint and bisector definitions
Know: Recall postulates, theorems, and definitions to prove theorems about triangles
Know: Recall previous understandings of coordinate geometry
Know: Recall previous understandings of coordinate geometry including distance, midpoint and slope formulas, equation of a line,
definitions of parallel and perpendicular lines
Know: Recall previous understandings of probability
Know: Recall previous understandings of probability
Know: Recall previous understandings of probability
Know: Recall previous understandings of probability
Know: Recall properties of equality
Know: Recall right triangle trigonometry to solve mathematical problems
Know: Recall the definition of ratio
Know: Recall the properties of equality
Know: Recall the properties of similarity transformations
Know: Recognize and describe the key features logarithmic functions
Know: Recognize and know the definition of logarithm base b
Know: Recognize and use function notation to represent linear and exponential equations
Know: Recognize and use function notation to represent linear and exponential equations
Know: Recognize and use function notation to represent linear, polynomial, rational, absolute value, exponential, and radical equations
Know: Recognize and use function notation to represent linear, polynomial, rational, absolute value, exponential, and radical equations
Know: Recognize and use properties of equality to maintain equivalent systems of equations
Know: Recognize data that various models produce
Course Summary
Powered by BuildYourOwnCurriculum
Page
8
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Know: Recognize data that various models produce
Know: Recognize even and odd functions from their graphs and equations
Know: Recognize linear or exponential function including: vertical and horizontal shifts, vertical and horizontal dilations
Know: Recognize rates of change and intercepts as parameters in linear or exponential functions
Know: Recognize situations in which a quantity grows or decays by a constant percent rate per unit (equal factors), relative to another to
solve mathematical and real-world problems
Know: Recognize situations in which one quantity changes at a constant rate per unit (equal differences), relative to another to solve
mathematical and real-world problems
Know: Recognize slope as an average rate of change
Know: Recognize slope as an average rate of change
Know: Recognize that arithmetic sequences can be expressed as linear functions
Know: Recognize that exponential functions grow by equal factors over equal intervals
Know: Recognize that f(x) = g(x) means that there may be particular inputs of f and g for which the outputs of f and g are equal
Know: Recognize that f(x) = g(x) means that there may be particular inputs of f and g for which the outputs of f and g are equal
Know: Recognize that geometric sequences can be expressed as exponential functions
Know: Recognize that if (x1, y1) and (x2, y2) share the same location in the coordinate plane that x1 = x2 and y1 = y2
Know: Recognize that if (x1, y1) and (x2, y2) share the same location in the coordinate plane that x1 = x2 and y1 = y2
Know: Recognize that if two right triangles have a pair of acute, congruent angles, that the triangles are similar
Know: Recognize that inscribed angles on a diameter are right angles
Know: Recognize that linear functions grow by equal differences over equal intervals
Know: Recognize that radius of a circle is perpendicular to the radius at the point of tangency
Know: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers
Know: Recognize that slopes of parallel lines are equal
Know: Recognize that slopes of perpendicular lines are opposite reciprocals
Know: Recognize that the graphical representation of an equation in two variables is a curve, which may be a straight line
Know: Recognize that the product of a nonzero rational number and an irrational number is irrational
Know: Recognize that the sum of a rational number and an irrational number is irrational
Know: Recognize the concepts of conditional probability and independence in everyday language and everyday situation
Know: Recognize the concepts of conditional probability and independence in everyday language and everyday situations
Know: Recognize the differences among surveys, experiments, and observational studies in making statistical inferences and justifying
conclusions explain how randomization relates to each of these methods of data collection
Know: Recognize the differences among surveys, experiments, and observational studies in making statistical inferences and justifying
conclusions explain how randomization relates to each of these methods of data collection
Know: Recognize the differences between joint, marginal, and conditional relative frequencies
Know: Recognize the differences between joint, marginal, and conditional relative frequencies
Know: Recognize the laws and properties of logarithms, including change of base
Know: Recognize the purpose of surveys, experiments, and observational studies in making statistical inferences and justifying
conclusions and explain how randomization relates to each of these methods of data collection
Know: Recognize the purpose of surveys, experiments, and observational studies in making statistical inferences and justifying
conclusions and explain how randomization relates to each of these methods of data collection
Know: Recognize units given or needed to solve problem
Know: Recognize when a modeling context involves constraints
Know: Recognize when figures are similar
Know: Recognize when the quadratic formula gives complex solutions
Know: Recognize which methods could be used to solve right triangles in applied problems
Know: Recognize which methods could be used to solve right triangles in applied problems
Know: Represent data on a scatter plot (2 quantitative variables)
Know: Represent data on a scatter plot (2 quantitative variables)
Know: Represent the residuals from a function and the data set it models, numerically and graphically
Know: Represent the residuals from a function and the data set it models, numerically and graphically
Know: Solve for an unknown angle or side of a right triangle using sine, cosine, and tangent
Know: Solve for an unknown angle or side of a right triangle using sine, cosine, and tangent
Know: Solve quadratic equations with real coefficients that have complex solutions
Know: Solve systems of linear equations by any method
Know: State, in written or verbal form, the Fundamental Theorem of Algebra
Know: Summarize categorical data for two categories in two-way frequency tables
Know: Summarize categorical data for two categories in two-way frequency tables
Know: Transform a simple system consisting of a linear equation and a quadratic equation in two variables so that a solution can be
found algebraically and graphically
Course Summary
Powered by BuildYourOwnCurriculum
Page
9
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Know: Understand that matrix multiplication for square matrices is associative and distributive
Know: Understand that matrix multiplication for square matrices is not commutative
Know: Understand that restricting y = cos x to a domain on which it is always increasing or always decreasing allows its inverse to be
constructed
Know: Understand that restricting y = sin x to a domain on which it is always increasing or always decreasing allows its inverse to be
constructed
Know: Understand that restricting y = tan x to a domain on which it is always increasing or always decreasing allows its inverse to be
constructed
Know: Understand that the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse
Know: Understand that the identity matrix plays a role in matrix addition and multiplication similar to the role of one in the real numbers
Know: Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes
Know: Understand that the zero matrix plays a role in matrix addition and multiplication similar to the role of zero in the real numbers
Know: Understand vector subtraction as a form of vector addition
Know: Use Pythagorean Theorem
Know: Use the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B)
Know: Use the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B)
Know: Use the coordinates of the vertices of a polygon to find the necessary dimensions for finding the perimeter
Know: Use the coordinates of the vertices of a polygon to find the necessary dimensions for finding the perimeter
Know: Use the coordinates of the vertices of a rectangle to find the necessary dimensions (base, height) for finding the area
Know: Use the coordinates of the vertices of a rectangle to find the necessary dimensions (base, height) for finding the area
Know: Use the coordinates of the vertices of a triangle to find the necessary dimensions (base, height) for finding the area
Know: Use the coordinates of the vertices of a triangle to find the necessary dimensions (base, height) for finding the area
Know: Use the multiplication rule with correct notation
Know: Use the multiplication rule with correct notation
Know: Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities
Know: Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities
Know: Use various, specified data-generating processes/models
Know: Use various, specified data-generating processes/models
Know: Using an established level of significance, determine if the difference between two parameters is significant
Know: Using an established level of significance, determine if the difference between two parameters is significant
Know: Using technology, identify effects of single transformations on graphs of functions
Know: Utilize the appropriate formula for volume, depending on the figure
Know: Utilize the appropriate formula for volume, depending on the figure
Think: Analyze components of the theorem
Think: Analyze decisions and strategies using probability concepts
Think: Analyze decisions and strategies using probability concepts
Think: Analyze the difference between simple and complicated linear, quadratic, square root, cube root, piecewise-defined, exponential,
logarithmic, and trigonometric functions, including step and absolute value functions
Think: Analyze the difference between simple and complicated linear, quadratic, square root, cube root, piecewise-defined, exponential,
logarithmic, and trigonometric functions, including step functions and absolute value functions
Think: Apply concepts of density based on area and volume to model real-life situations
Think: Apply concepts of density based on area and volume to model real-life situations
Think: 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)
Think: 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)
Think: Apply properties and theorems about parallel and perpendicular lines to support constructions
Think: Apply right triangle trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems
Think: Apply right triangle trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems
Think: Apply the definitions, properties, and theorems about line segments, rays, and angles to support geometric constructions
Think: Apply the general Multiplication Rule in a uniform probability model P(A and B) = P(A)P(B|A) = P(B)P(A|B)
Think: 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)
Think: Apply the general Multiplication Rule in a uniform probability model P(A and B) = P(A)P(B|A) = P(B)P(A|B)
Think: Approximate/find the solution(s) using an appropriate method. For example, using technology to graph the functions, make tables
of values or find successive approximations
Think: Approximate/find the solution(s) using an appropriate method. For example, using technology to graph the functions, make tables
of values or find successive approximations
Think: Choose an appropriate method for solving the equation
Course Summary
Powered by BuildYourOwnCurriculum
Page
10
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Think: Choose and justify a level of accuracy and/or precision appropriate to limitations on measurement when reporting quantities
Think: Choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by
the original expression
Think: Choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by
the original expression
Think: Choose appropriate methods to simulate a randomized experiment
Think: Choose appropriate methods to simulate a randomized experiment
Think: Choose appropriate units to represent a problem when using formulas or graphing
Think: Choose the appropriate measure for center (mean, median) and spread (interquartile range, standard deviation) based on the
shape of a data distribution
Think: Choose the appropriate measure for center (mean, median) and spread (interquartile range, standard deviation) based on the
shape of a data distribution
Think: Choose trigonometric functions to model periodic phenomena for which amplitude, frequency, and midline are already specified
Think: Choose trigonometric functions to model periodic phenomena for which amplitude, frequency, and midline are already specified
Think: Classify expressions by structure and develop strategies to assist in classification
Think: Compare and contrast absolute value, step- and piecewise-defined functions with linear, quadratic, and exponential functions
Think: Compare and contrast absolute value, step- and piecewise-defined functions with linear, quadratic, and exponential functions
Think: Compare and contrast problems that can be solved by different types of equations (e.g., linear, exponential)
Think: Compare and contrast the domain and range of absolute value, step- and piecewise-defined functions with linear, quadratic, and
exponential functions
Think: Compare and contrast the domain and range of absolute value, step- and piecewise-defined functions with linear, quadratic, and
exponential functions
Think: Compare and contrast the domain and range of exponential, logarithmic, and trigonometric functions with linear, quadratic,
absolute value, step- and piecewise-defined functions
Think: Compare and contrast the domain and range of exponential, logarithmic, and trigonometric functions with linear, quadratic,
absolute value, step- and piecewise-defined functions
Think: Compare common ratios for similar right triangles and develop a relationship between the ratio and the acute angle leading to the
trigonometry ratios
Think: Compare tables and graphs of exponential and other polynomial functions to observe that a quantity, increasing exponentially,
exceeds all others to solve mathematical and real-world problems
Think: Compare tables and graphs of linear and exponential functions to observe that a quantity, increasing exponentially, exceeds all
others to solve mathematical and real-world problems
Think: Compare the ratio of the circumference of a circle to the diameter of the circle
Think: Compare transformations that preserve distance and angle to those that do not (e g , translation vs. horizontal stretch)
Think: Complete the square on a quadratic expression to produce an equivalent form of an expression
Think: Complete the square on a quadratic expression to produce an equivalent form of an expression
Think: Construct a mathematically viable argument justifying a given, or self-generated, solution method
Think: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation
Think: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation
Think: Derive equation of a circle using the Pythagorean Theorem, given coordinates of the center and length of the radius
Think: Derive simple proofs involving circles
Think: Derive the equation of a line through 2 points using similar right triangles
Think: Derive the equation of a parabola given the focus and directrix
Think: Derive the equations of ellipses given the foci, using the fact that the sum of distances from the foci is constant
Think: Derive the equations of hyperbolas given the foci, using the fact that the difference of distances from the foci is constant
Think: 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
Think: Derive the quadratic formula by completing the square on a quadratic equation in x
Think: 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
Think: 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
Think: Describe rotations and reflections that carry a rectangle, parallelogram, trapezoid, or regular polygon onto itself.
Think: Describe the differences and similarities between a parent function and the transformed function
Think: Describe the possible effects the presence of outliers in a set of data can have on shape, center, and spread in the context of the
data sets
Think: Describe the possible effects the presence of outliers in a set of data can have on shape, center, and spread in the context of the
data sets
Think: Describe the transformation vector by its components
Course Summary
Powered by BuildYourOwnCurriculum
Page
11
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Think: Determine appropriate quantities for the purpose of descriptive modeling
Think: Determine appropriate strategies to solve problems involving quadratic equations, as appropriate to the initial form of the equation
Think: Determine appropriate units for the labels and scale of a graph depicting the relationship between equations created in two or
more variables
Think: Determine from given measurements in right and non-right triangles whether it is appropriate to use the Law of Sines or Cosines
Think: Determine if an equation has a solution
Think: Determine if two figures are congruent using the definition of congruence in terms of rigid motions
Think: Determine the center and radius by completing the square
Think: Determine the difference between simple and complicated linear, quadratic, square root, cube root, and piecewise-defined
functions
Think: Determine the difference between simple and complicated linear, quadratic, square root, cube root, and piecewise-defined
functions
Think: Determine the difference between simple and complicated polynomial functions
Think: Determine the difference between simple and complicated polynomial functions
Think: Determine the differences between simple and complicated linear and exponential functions and know when the use of technology
is appropriate
Think: Determine the differences between simple and complicated linear and exponential functions and know when the use of technology
is appropriate
Think: Determine the effect that rational coefficients have on the inequality symbol and use this to find the solution set
Think: Determine the explicit formula given arithmetic and geometric sequences
Think: Determine the explicit formula given arithmetic and geometric sequences
Think: Determine the magnitude and direction of the sum of two vectors given the magnitude and direction of each
Think: Determine the recursive rule given arithmetic and geometric sequences
Think: Determine the recursive rule given arithmetic and geometric sequences
Think: Determine the values of sine, cosine, and tangent using special right triangles
Think: Determine the values of sine, cosine, and tangent, using the unit circle, for any real number
Think: Determine when a graph, a description of a relationship, or two input-output pairs (include reading these from a table) represents a
linear or exponential function in order to solve problems
Think: Determine when a problem should be represented by equations, inequalities, systems of equations and/ or inequalities
Think: Determine which function best models scatter plot data represented on the coordinate plane, and describe how the two
quantitative variables are related
Think: Determine which function best models scatter plot data represented on the coordinate plane, and describe how the two
quantitative variables are related
Think: Develop a margin of error, assuming certain population parameters/characteristics, through the use of simulation models for
random sampling
Think: Develop a margin of error, assuming certain population parameters/characteristics, through the use of simulation models for
random sampling
Think: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically
Think: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically
Think: Discuss, develop, and justify the ratio of the circumference of a circle to the diameter of the circle for several circles
Think: Distinguish between correlation and causation
Think: Distinguish between correlation and causation
Think: Distinguish between situations that can be modeled with linear functions and exponential functions to solve mathematical and realworld problems
Think: Draw conclusions based on graphical and numerical summaries
Think: Draw conclusions based on graphical and numerical summaries
Think: Establish a reasonable level of significance
Think: Establish a reasonable level of significance
Think: Establish the AA criterion for similarity of triangles by extending the properties of similarity transformations to the general case of
any two similar triangles
Think: Estimate the rate of change from a linear or exponential graph
Think: Estimate the rate of change from a linear or exponential graph
Think: Evaluate and compare strategies on the basis of expected values
Think: Evaluate and compare strategies on the basis of expected values
Think: Evaluate experimental study design, how data was gathered, and what analysis (numerical or graphical) was used
Think: Evaluate functions at a given input in the domain, focusing on linear and exponential functions
Think: Evaluate functions for given values of x
Think: Evaluate the experimental study design, how the data was gathered, what analysis (numerical or graphical) was used
Think: Examine the relationship between central, inscribed, and circumscribed angles by applying theorems about their measures
Course Summary
Powered by BuildYourOwnCurriculum
Page
12
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Think: Experiment with cases and illustrate an explanation of the effects on the graph, using technology
Think: Explain how radical notation, rational exponents, and properties of integer exponents relate to one another
Think: Explain how the criteria for triangle congruence (ASA, SAS, SSS) follows from the definition of congruence in terms of rigid
motions
Think: Explain how the sine and cosine of complementary angles are related to each other
Think: Explain the concepts of conditional probability and independence in everyday language and everyday situations
Think: Explain the concepts of conditional probability and independence in everyday language and everyday situations
Think: Explain the connection between Pascal's Triangle and the determination of the coefficients in the expansion of (x+y)n, when n is a
positive integer and x and y are any number
Think: Explain the correspondence between the algebraic and graphical solutions to a simple system consisting of a linear equation and
a quadratic equation in two variables
Think: Explain the meaning of the intersection of the shaded regions in a system of linear inequalities
Think: Explain the properties of operations of rational exponents as an extension of the properties of integer exponents
Think: Explain the properties of the quantity or quantities represented by the transformed exponential expression
Think: Explain the properties of the quantity or quantities represented by the transformed exponential expression
Think: Explain why a domain is appropriate for a given situation
Think: Explain why a domain is appropriate for a given situation
Think: Explain why rational numbers are closed under addition or multiplication
Think: Explain why the x-coordinates of the points where the graph of the equations y = f(x) and y = g(x) intersect are the solutions of the
equations f(x) = g(x)
Think: Explain why the x-coordinates of the points where the graph of the equations y=f(x) and y=g(x) intersect are the solutions of the
equations f(x) = g(x)
Think: Explain why, when solving equations, it is assumed that the original equation is equal
Think: Express complex solutions as a ± bi for real numbers solutions as a and b
Think: Extend polynomial identities to the complex numbers
Think: Extend to more complex probability models. Include situations such as those involving quality control, or diagnostic tests that yield
both false positive and false negative results
Think: Extend to more complex probability models. Include situations such as those involving quality control, or diagnostic tests that yield
both false positive and false negative results
Think: Extend to more complex probability models. Include situations such as those involving quality control, or diagnostic tests that yield
both false positive and false negative results
Think: Extend to more complex probability models. Include situations such as those involving quality control, or diagnostic tests that yield
both false positive and false negative results
Think: Find solutions to trigonometric equations using inverse functions and technology
Think: Find solutions to trigonometric equations using inverse functions and technology
Think: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of the terminal point
Think: Find the conjugate of a complex number
Think: Find the expected payoff for a game of chance
Think: Find the expected payoff for a game of chance
Think: Find the inverse of a matrix
Think: Find the value of k, given the graphs of a parent function, f(x), and the transformed function: f(x) + k, k f(x), f(kx), or f(x + k)
Think: Fit a linear function for a scatter plot that suggests a linear association
Think: Fit a linear function for a scatter plot that suggests a linear association
Think: Focus on situations well modeled by trigonometric ratios for acute angles
Think: Focus on situations well modeled by trigonometric ratios for acute angles
Think: For exponential models, express as a logarithm, the solution to abct = d, where a, c, and d are numbers and the base b is 2, 10, or
e
Think: Formulate a model of figures in contextual problems to compute area and/or perimeter
Think: Formulate a model of figures in contextual problems to compute area and/or perimeter
Think: Give an informal argument for the formulas for the circumference and area of a circle
Think: Give an informal argument for the formulas for the volume of a cylinder, pyramid, and cone
Think: Give an informal argument using Cavalieri's principle for the formula for the volume of a sphere and other solid figures
Think: Given a polynomial p(x) and a number a, divide p(x) by (x - a) to find p(a) then apply the remainder theorem and conclude that p(x)
is divisible by x - a, if and only if p(a) = 0
Think: Given a real world object, classify the object as a known geometric shape - use this to solve problems in context
Think: Given a real world object, classify the object as a known geometric shape - use this to solve problems in context
Think: Given a real-world situation or mathematical problem, build standard functions to represent relevant relationships/ quantities
Think: Given a real-world situation or mathematical problem, build standard functions to represent relevant relationships/quantities
Think: Given a real-world situation or mathematical problem, determine which arithmetic operation should be performed to build the
Course Summary
Powered by BuildYourOwnCurriculum
Page
13
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
appropriate combined function
Think: Given a real-world situation or mathematical problem, determine which arithmetic operation should be performed to build the
appropriate combined function
Think: Given a real-world situation or mathematical problem, relate the combined function to the context of the problem
Think: Given a real-world situation or mathematical problem, relate the combined function to the context of the problem
Think: Given the expression of a quadratic function, interpret zeros, extreme values, and symmetry of the graph in terms of a real-world
context
Think: Given the expression of an exponential function, interpret the expression in terms of a real-world context, using the properties of
exponents
Think: Given two figures, decide if they are similar by using the definition of similarity in terms of similarity transformations
Think: Graph one or more created equations on coordinate axes with appropriate labels and scales
Think: Identify important quantities in a problem or real-world context
Think: Informally assess the fit of a function by analyzing residuals from the residual plot
Think: Informally assess the fit of a function by analyzing residuals from the residual plot
Think: Interpret complicated expressions, in terms of the context, by viewing one or more of their parts as a single entity
Think: Interpret complicated expressions, in terms of the context, by viewing one or more of their parts as a single entity
Think: Interpret differences in shape, center, and spread in the context of data sets
Think: Interpret differences in shape, center, and spread in the context of the data sets
Think: Interpret different yet equivalent forms of a function defined by an expression in terms of a context
Think: Interpret expected value as the mean of the probability distribution
Think: Interpret expected value as the mean of the probability distribution
Think: Interpret key features of graphs and tables of functions in the terms of the contextual quantities each function represents
Think: Interpret key features of graphs and tables of functions in the terms of the contextual quantities the function represents
Think: Interpret parts of an expression, such as terms, factors, and coefficients in terms of the context
Think: Interpret parts of an expression, such as terms, factors, and coefficients in terms of the context
Think: Interpret relative frequencies in the context of the data
Think: Interpret relative frequencies in the context of the data
Think: Interpret solutions as viable or nonviable options in a modeling context
Think: Interpret statements that use functions in terms of real world situations, focusing on linear and exponential functions
Think: Interpret the absolute value of the determinant in terms of area
Think: Interpret the answer in terms of the model
Think: Interpret the answer in terms of the model
Think: Interpret the answer in terms of the model
Think: Interpret the answer in terms of the model
Think: Interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval
Think: Interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval
Think: Interpret the correlation coefficient of a linear fit as a measure of how well the data fit the relationship
Think: Interpret the correlation coefficient of a linear fit as a measure of how well the data fit the relationship
Think: Interpret the data generated by a simulation model for random sampling in terms of the context of simulation models
Think: Interpret the data generated by a simulation model for random sampling in terms of the context the simulation models
Think: Interpret the parameters in a linear or exponential function in terms of a context
Think: Interpret the parameters of a trigonometric function (amplitude, frequency, and midline) in the context of real-world situations
Think: Interpret the parameters of a trigonometric function (amplitude, frequency, and midline) in the context of real-world situations
Think: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data
Think: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data
Think: Interpret the answer in terms of the model
Think: Interpret the answer in terms of the model
Think: Interpret these solutions to trigonometric equations in context
Think: Interpret these solutions to trigonometric equations in context
Think: Interpret two-way frequency tables of data when two categories are associated with each object being classified
Think: Interpret two-way frequency tables of data when two categories are associated with each object being classified
Think: Interpret units or scales used in formulas or represented in graphs
Think: Justify congruency of two triangles using transformations
Think: Justify solution(s) to equations by explaining each step in solving a simple equation using the properties of equality, beginning with
the assumption that the original equation is equal
Think: Justify that replacing one equation in a two-equation system with the sum of that equation and a multiple of the other will yield the
same solutions as the original system
Think: Justify the method used to solve systems of linear equations exactly and approximately focusing on pairs of linear equations in two
variables
Course Summary
Powered by BuildYourOwnCurriculum
1
2
Page
14
1
of
2
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Think: Justify the radii of any two circles (r1 and r2) and the arc lengths (s1 and s2) determined by congruent central angles are
proportional
Think: Justify the translation between the recursive form and explicit formula for arithmetic and geometric sequences
Think: Justify the translation between the recursive form and explicit formula for arithmetic and geometric sequences
Think: Justify which quantities in a mathematical problem or real-world situation are dependent and independent of one another and
which operations represent those relationships
Think: Notes from Appendix A: Build on student experiences graphing and solving systems of linear equations from middle school to
focus on justification of the methods used. Include cases where the two equations describe the same line (yielding infinitely
Think: Perform scalar multiplication of a vector component-wise
Think: Prove polynomial identities
Think: Prove the addition and subtraction formulas for sine, cosine, and tangent
Think: Prove the Law of Cosines
Think: Prove the Law of Sines
Think: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems
Think: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g. π r2 can be rewritten as (π r)r which makes the form of this expression resemble Bh. The quantity of interest could also be (a +b)n = a
Think: Recognize possible associations and trends in the data
Think: Recognize possible associations and trends in the data
Think: Recognize that there are data sets for which such a procedure is not appropriate
Think: Recognize that there are data sets for which such a procedure is not appropriate
Think: Recognize when the Law of Sines or Law of Cosines can be applied to a problem and solve problems in context using them
Think: Relate the domain of a function to its graph and to the quantitative relationship it describes, where applicable
Think: Relate the domain of a function to its graph and to the quantitative relationship it describes, where applicable
Think: Relate the relationship between zeros of quadratic functions and their factored forms to the relationship between polynomial
functions of degrees greater than two
Think: Relate the relationship between zeros of quadratic functions and their factored forms to the relationship between polynomial
functions of degrees greater than two
Think: Relate the shapes of two-dimensional cross-sections to their three-dimensional objects
Think: Represent addition and subtraction of complex numbers geometrically
Think: Represent complex numbers on the complex plane in polar form
Think: Represent complex numbers on the complex plane in rectangular form
Think: Represent conjugation of complex numbers geometrically
Think: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities
Think: Represent multiplication of complex numbers geometrically
Think: Represent scalar multiplication of a vector graphically
Think: Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction
component-wise
Think: Select the appropriate type of function, taking into consideration the key features, domain, and range, to model a real-world
situation
Think: Select the appropriate type of function, taking into consideration the key features, domain, and range, to model a real-world
situation
Think: Solve systems of equations
Think: Support with graphical and numerical summaries how appropriate the report of data was
Think: Support with graphical and numerical summaries how appropriate the report of data was
Think: Synthesize the theory that applies to circles that a radius is perpendicular to a tangent at the point of tangency
Think: Synthesize the theory that applies to circles that tangents drawn from a common external point are congruent
Think: Use probabilities to make fair decisions
Think: Use a variety of function representations (algebraic, graphical, numerical in tables, or by verbal descriptions) to compare and
contrast properties of two functions
Think: Use all available types of functions to create such equations, including root functions, but constrain to simple cases
Think: Use coordinates to prove simple geometric theorems algebraically
Think: Use functions fitted to data to solve problems in the context of the data
Think: Use functions fitted to data to solve problems in the context of the data
Think: Use given units and the context of a problem as a way to determine if the solution to a multi-step problem is reasonable
Think: Use probabilities to make fair decisions
Think: Use the properties of exponents to interpret expressions for exponential functions in a real-world context
Think: Use the properties of exponents to transform simple expressions for exponential functions
Think: Use the properties of exponents to transform simple expressions for exponential functions
Think: Use the structure of an expression to identify ways to rewrite it
Course Summary
Powered by BuildYourOwnCurriculum
Page
15
of
16
01/29/2014 8:36 AM
Carl Junction R-I School District
Mathematics
Grade 9, Duration 1 Year, 1 Credit
Elective Course
Algebra 1A
Think: Use the unit circle to explain periodicity of trigonometric functions
Think: Use the unit circle to explain symmetry of trigonometric functions
Think: Use units as a way to understand problems and to guide the solution of multi-step problems
Think: Use volume formulas for cylinders, pyramids, cones, and spheres to solve contextual problems
Think: Use volume formulas for cylinders, pyramids, cones, and spheres to solve contextual problems
Think: Using given scatter plot data represented on the coordinate plane, informally describe how the two quantitative variables are
related
Think: Using given scatter plot data represented on the coordinate plane, informally describe how the two quantitative variables are
related
Think: Verify that the constant of a proportion is the same as the radian measure, Θ, of the given central angle. Conclude s = r Θ
Think: Verify that the Fundamental Theorem of Algebra is true for second degree quadratic polynomials
Think: Work with 2x2 matrices as transformations of the plane
Think: Work with matrices as transformations of vectors
Think: Write functions to represent transformations
Course Summary
Powered by BuildYourOwnCurriculum
Page
16
of
16
01/29/2014 8:36 AM