Verona Public School District Curriculum Overview ......polynomial identity (x 2 + y)2 = (x2 – y...

Verona Public School District

Curriculum Overview

Precalculus/Trigonometry

Curriculum Committee Members: Marc Russo Danielle Mutovic Rich Wertz Supervisor: Glen Stevenson Curriculum Developed: 2011 Board Approval Date: 9/27/11

Verona Public Schools 121 Fairview Ave., Verona, NJ 07044

www.veronaschools.org

Verona Public Schools Mission Statement:

The mission of the Verona Public Schools, the center of an engaged and supportive community, is to empower students to achieve their potential as active learners and productive citizens through rigorous curricula and meaningful, enriching experiences.

Course Description:

This course is designed to enhance students’ preparation for Calculus in high school or college. The course will focus on improving students’ knowledge of trigonometric and other types of functions, including polynomial, rational, exponential and logarithmic functions. Other topics include: Analytic Trigonometry, Applications of Trigonometry, Sequences and Series, Conic Sections, Parametric Equations, Polar Coordinates, Limits, Probability and Statistics. Much of this course involves realworld applications and mathematical modeling. Student must provide their own TI NSpire or TI NSpire CAS graphing calculator; these will be an important tool that will routinely be used in instruction.

Prerequisite(s):

Algebra II

http://www.veronaschools.org/

Standard 8: Technology Standards

8.1: Educational Technology: All students will use digital tools to access, manage, evaluate, and synthesize information in order to solve problems individually and collaborate and to create and communicate knowledge.

8.2: Technology Education, Engineering, Design, and Computational Thinking Programming: All students will develop an understanding of the nature and impact of technology, engineering, technological design, computational thinking and the designed world as they relate to the individual, global society, and the environment.

X

A. Technology Operations and Concepts B. Creativity and Innovation C. Communication and Collaboration D. Digital Citizenship E. Research and Information Fluency F. Critical thinking, problem solving, and decision making

X

X

A. The Nature of Technology: Creativity and Innovation B. Technology and Society C. Design D. Abilities for a Technological World E. Computational Thinking: Programming

SEL Competencies and Career Ready Practices Social and Emotional Learning Core Competencies: These competencies are identified as five interrelated sets of cognitive, affective, and behavioral capabilities

Career Ready Practices: These practices outline the skills that all individuals need to have to truly be adaptable, reflective, and proactive in life and careers. These are researched practices that are essential to career readiness.

Selfawareness: The ability to accurately recognize one’s emotions and thoughts and their influence on behavior. This includes accurately assessing one’s strengths and limitations and possessing a wellgrounded sense of confidence and optimism.

CRP2. Apply appropriate academic and technical skills. CRP9. Model integrity, ethical leadership, and effective management. CRP10. Plan education and career paths aligned to personal goals.

Selfmanagement: The ability to regulate one’s emotions, thoughts, and behaviors effectively in different situations. This includes managing stress, controlling impulses, motivating oneself, and setting and working toward achieving personal and academic goals.

X

CRP3. Attend to personal health and financial wellbeing. CRP6. Demonstrate creativity and innovation. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP11. Use technology to enhance productivity.

Social awareness: The ability to take the perspective of and empathize with others from diverse backgrounds and cultures, to understand social and ethical norms for behavior, and to recognize family, school, and community resources and supports.

CRP1. Act as a responsible and contributing citizen and employee. CRP9. Model integrity, ethical leadership, and effective management.

Relationship skills: The ability to establish and maintain healthy and rewarding relationships with diverse individuals and groups. This includes communicating clearly, listening actively, cooperating, resisting inappropriate social pressure, negotiating conflict constructively, and seeking and offering help when needed.

X CRP4. Communicate clearly and effectively and with reason. CRP9. Model integrity, ethical leadership, and effective management. CRP12. Work productively in teams while using cultural global competence.

Responsible decision making: The ability to make constructive and respectful choices about personal behavior and social interactions based on consideration of ethical standards, safety concerns, social norms, the realistic evaluation of consequences of various actions, and the wellbeing of self and others.

X

CRP5. Consider the environmental, social, and economic impact of decisions. CRP7. Employ valid and reliable research strategies. CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. CRP9. Model integrity, ethical leadership, and effective management.

Standard 9: 21st Century Life and Careers

9.1: Personal Financial Literacy: This standard outlines the important fiscal knowledge, habits, and skills that must be mastered in order for students to make informed decisions about personal finance. Financial literacy is an integral component of a student's college and career readiness, enabling students to achieve fulfilling, financiallysecure, and successful careers.

9.2: Career Awareness, Exploration & Preparation: This standard outlines the importance of being knowledgeable about one's interests and talents, and being well informed about postsecondary and career options, career planning, and career requirements.

9.3: Career and Technical Education: This standard outlines what students should know and be able to do upon completion of a CTE Program of Study.

A. Income and Careers B. Money Management C. Credit and Debt Management D. Planning, Saving, and Investing E. Becoming a Critical Consumer F. Civic Financial Responsibility G. Insuring and Protecting

X

A. Career Awareness (K4) B. Career Exploration (58) C. Career Preparation (912)

X

A. Agriculture, Food & Natural Res. B. Architecture & Construction C. Arts, A/V Technology & Comm. D. Business Management & Admin. E. Education & Training F. Finance G. Government & Public Admin. H. Health Science I. Hospital & Tourism J. Human Services K. Information Technology L. Law, Public, Safety, Corrections & Security M. Manufacturing N. Marketing O. Science, Technology, Engineering & Math P. Transportation, Distribution & Log.

Course Materials

Core Instructional Materials: These are the board adopted and approved materials to support the curriculum, instruction, and assessment of this course.

Differentiated Resources: These are teacher and department found materials, and also approved support materials that facilitate differentiation of curriculum, instruction, and assessment of this course.

● Precalculus with Limits: A Graphing Approach ● Delta Math ● NJCTL ● Khan Academy Precalculus ● Eureka Math: A Story of Functions Modules ● Various online sources

Curriculum Scope & Sequence

Subject/Grade Level: MATHEMATICS/HIGH SCHOOL Course: PRE-CALCULUS CP/HONORS

*The goals and standards addressed are the

same for both levels of Pre-Calculus;

however, the depth at which they are

explored will vary based on the level of the

course.

Unit Duration Common Core Standards/ Unit

Goals

Transfer Goal(s) Enduring

Understandings

Essential Questions

1

Algebra Review

8 days Unit Goals:

Polynomial Identities

Exponents & Radicals

Factoring

Rational Expressions

Solving Equations

Standards:

A-APR4. Prove polynomial identities

and use them to describe numerical

relationships. For example, the

polynomial identity (x2 + y

2)

2 = (x

2 –

y2)

2 + (2xy)

2 can be used to generate

Pythagorean triples.

A-SSE2. Use the structure of an

expression to identify ways to rewrite

it. For example, see x4 – y4 as (x2)

2 –

(y2)

2, thus recognizing it as a

difference of squares that can be

factored as (x2 – y

2)(x

2 + y

2).

Students will be able to

independently use their

learning to justify their

approaches and their

steps when solving

problems.

- Solving algebraic

equations is a basic

exercise in their

knowledge of the

order of operations.

- It can be determined

(for the most part) if

an expression is (or

is not) completely

simplified.

- Basic rules of

equality are the key

to ensure accuracy

in mathematics.

- How do we solve an

unfamiliar equation?

- How do we know if an

expression is

completely simplified?

- Besides checking our

work, what are some

strategies to help us

gain confidence that we

are solving a problem

correctly?

2

Functions

9 days Unit Goals:

Analyzing Graphs

Parent functions

Transformations



learning to analyze the

graph of a real-life

- Transformations of

functions can be

represented

graphically or

- Can all transformations

of basic functions be

represented in a

predictable algebraic

BOE APPROVED 9/27/11


Goals


Understandings

Essential Questions

Composition

Inverses

Standards:

F-IF4. For a function that models a

relationship between two quantities,

interpret key features of graphs and

tables in terms of the quantities, and

sketch graphs showing key features

given a verbal description of the

relationship. Key features include:

intercepts; intervals where the

function is increasing, decreasing,

positive, or negative; relative

maximums and minimums;

symmetries; end behavior; and

periodicity.

F-IF7. Graph functions expressed

symbolically and show key features

of the graph, by hand in simple cases

and using technology for more

complicated cases.

a. Graph linear and quadratic

functions and show intercepts,

maxima, and minima.

b. Graph square root, cube root, and

piecewise-defined functions,

including step functions and absolute

value functions.

F-BF1. Write a function that

describes a relationship between two

quantities.

c. (+) Compose functions. For

example, if T(y) is the temperature in

function and use their

insights to help them

make informed decisions

about that function.

algebraically.

- Graphical

representations of

functions can

provide additional

insight into a

function’s behavior.

way?

- When is it more

appropriate to analyze a

function algebraically?

Graphically?


Goals


Understandings

Essential Questions

the atmosphere as a function of

height, and h(t) is the height of a

weather balloon as a function of time,

then T(h(t)) is the temperature at the

location of the weather balloon as a

function of time.

F-BF3. Identify the effect on the

graph of 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); find the value of k given

the graphs. Experiment with cases

and illustrate an explanation of the

effects on the graph using technology.

Include recognizing even and odd

functions from their graphs and

algebraic expressions for them.

F-BF4. Find inverse functions.

a. 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. For example, f(x) =2x+3

or f(x) = (x+1)/(x–1) for x ≠1.

b. (+) Verify by composition that one

function is the inverse of another.

c. (+) Read values of an inverse

function from a graph or a table,

given that the function has an inverse.

d. (+) Produce an invertible function

from a non-invertible function by

restricting the domain.


Goals


Understandings

Essential Questions

3

Fundamental

Theorem of

Algebra &

Rational

Functions

9 days Unit Goals:

Quadratics

Polynomial Division

End-Behavior

Zeros

Complex Numbers (and

vectors)

Fundamental Theorem of

Algebra

Rational Functions

Standards:

N-CN4. (+) Represent complex

numbers on the complex plane in

rectangular and polar form (including

real and imaginary numbers), and

explain why the rectangular and polar

forms of a given complex number

represent the same number.

N-CN5. (+) Represent addition,

subtraction, multiplication, and

conjugation of complex numbers

geometrically on the complex plane;

use properties of this representation

for computation. For example, (–1 +

√3 i)3 = 8 because (–1 + √3 i) has

modulus 2 and argument 120°.

N-CN6. (+) Calculate the distance

between numbers in the complex

plane as the modulus of the

difference, and the midpoint of a

segment as the average of the

numbers at its endpoints.



learning to determine

what an “accurate” graph

of a polynomial function

would look like.

- Polynomial and

rational functions

can be sketched

quickly and

accurately using

nothing but

algebraic skills.

- All zeros of a

polynomial function

can be found by

using division to

break the function

down into the

product of linear and

quadratic factors.

- What makes an accurate

sketch of a polynomial

function?

- What makes a good

window for the graph of

a polynomial function?

- What is the best way to

find the zeroes of a

polynomial function?


Goals


Understandings

Essential Questions

N-VM1. (+) Recognize vector

quantities as having both magnitude

and direction. Represent vector

quantities by directed line segments,

and use appropriate symbols for

vectors and their magnitudes (e.g., v,

|v|, ||v||, v).

N-VM4. (+) Add and subtract vectors.

a. Add vectors end-to-end,

component-wise, and by the

parallelogram rule. Understand that

the magnitude of a sum of two vectors

is typically not the sum of the

magnitudes.

b. Given two vectors in magnitude

and direction form, determine the

magnitude and direction of their sum.

c. Understand vector subtraction v – w

as v + (–w), where –w is the additive

inverse of w, with the same

magnitude as w and pointing in the

opposite direction. Represent vector

subtraction graphically by connecting

the tips in the appropriate order, and

perform vector subtraction

component-wise.

N-CN7. Solve quadratic equations

with real coefficients that have

complex solutions.

N-CN8. (+) Extend polynomial

identities to the complex numbers.

For example, rewrite x2 + 4 as (x +

2i)(x – 2i).


Goals


Understandings

Essential Questions

N-CN9. (+) Know the Fundamental

Theorem of Algebra; show that it is

true for quadratic polynomials.

A-APR2. Know and apply the

Remainder Theorem: For a

polynomial p(x) and a number a, the

remainder on division by x – a is p(a),

so p(a) = 0 if and only if (x – a) is a

factor of p(x).

A-APR3. Identify zeros of

polynomials when suitable

factorizations are available, and use

the zeros to construct a rough graph

of the function defined by the

polynomial.

A-APR6. 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), using

inspection, long division, or, for the

more complicated examples, a

computer algebra system.





complicated cases.

c. Graph polynomial functions,

identifying zeros when suitable

factorizations are available, and


Goals


Understandings

Essential Questions

showing end behavior.

d. (+) Graph rational functions,

identifying zeros and asymptotes

when suitable factorizations are

available, and showing end behavior.

4

Exponential and

Logarithmic

Functions

9 days Unit Goals:

Exponential functions

Log functions

Properties of logs

Log Equations

Models

Standards:





complicated cases.

e. Graph exponential and logarithmic

functions, showing intercepts and end

behavior, and trigonometric functions,

showing period, midline, and

amplitude.

F-IF8. Write a function defined by an

expression in different but equivalent

forms to reveal and explain different

properties of the function.

b. Use the properties of exponents to

interpret expressions for exponential

functions. For example, identify

percent rate of change in functions

such as y = (1.02)t, y = (0.97)

t, y =

(1.01)12t

, y = (1.2)t/10

, and classify

them as representing exponential



learning to investigate

important real-world

phenomena from a

graphical and an

algebraic perspective.

- Logarithmic

functions are the

inverse of

exponential

functions.

- Exponential and

logarithmic

functions model

real-world

phenomena.

- Inverse functions

allow us to solve

equations

algebraically.

- Why do we need the

logarithm function?

- What real-world

phenomena are modeled

by exponential or

logarithmic functions?


Goals


Understandings

Essential Questions

growth or decay.

F-BF5. (+) Understand the inverse

relationship between exponents and

logarithms and use this relationship to

solve problems involving logarithms

and exponents.

L-FE4. 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; evaluate

the logarithm using technology.

5

Right Triangle

& Unit Circle

Trig

12 days Unit Goals:

SohCahToa

Co-functions

Identities

Unit Circle

Radians

Reference Angles

Standards:

F-TF8. Prove the Pythagorean

identity sin2(θ) + cos

2(θ) = 1 and use

it to find sin(θ), cos(θ), or tan(θ)

given sin(θ), cos(θ), or tan(θ) and the

quadrant of the angle.

F-TF1. Understand radian measure of

an angle as the length of the arc on

the unit circle subtended by the angle.

F-TF2. Explain how the unit circle in

the coordinate plane enables the

extension of trigonometric functions



learning to understand

the implications of right

triangle trigonometry in

the unit circle.

- Trig functions are

ratios of sides of

right triangles.

- Trig functions

evaluated at a

certain angle are

constant, regardless

of the size of the

triangle.

- Trig identities allow

us to express trig

expressions in

different, but

equivalent ways.

- The Unit Circle

allows us to evaluate

trig functions at

quadrantal angles.

- Reference angles

allow us to evaluate

trig functions at

angles greater than

- What does evaluating a

trig function at a given

angle mean in real life?

- How does changing the

size of a right triangle

affect the sine, cosine

and tangent of its

angles?

- What is the value in

knowing trig identities?

- How does the unit circle

solidify (and enhance)

our understanding of

trig functions?

- What is the purpose of

measuring angles in

radians?


Goals


Understandings

Essential Questions

to all real numbers, interpreted as

radian measures of angles traversed

counterclockwise around the unit

circle.

F-TF3. (+) Use special triangles to

determine geometrically the values of

sine, cosine, tangent for π/3, π /4 and

π /6, and use the unit circle to express

the values of sine, cosine, and tangent

for π –x, π +x, and 2π –x in terms of

their values for x, where x is any real

number.

F-TF4. (+) Use the unit circle to

explain symmetry (odd and even) and

periodicity of trigonometric functions.

90 degrees.

- Radians are often a

more appropriate

way of describing

angles.

- Tangent and secant

are named after their

relationship to the

unit circle.

6

Graphing Trig

Functions

10 days Unit Goals:

Sine and Cosine Waves

Amplitude, Frequency, Period

Transformations

Tangent and Cotangent

Secant and Cosecant

Inverse Trig Functions

Standards:





complicated cases.

e. Graph exponential and logarithmic

functions, showing intercepts and end

behavior, and trigonometric functions,

showing period, midline, and



knowledge of periodic

functions to analyze real-

life periodic phenomena.

- Changes to the

algebraic equation of

a function cause

predictable changes

to the function’s

graph.

- Basic properties of

trig graphs can be

linked to a deep

understanding of the

unit circle and

fundamental trig

identities.

- What is the relationship

between a trig equation

and the trig function’s

graph?

- How can the unit circle

begin to explain the

graphs of sin, cos, tan,

cot, sec and csc?


Goals


Understandings

Essential Questions

amplitude.

F-TF5. Choose trigonometric

functions to model periodic

phenomena with specified amplitude,

frequency, and midline.

F-TF6. (+) Understand that restricting

a trigonometric function to a domain

on which it is always increasing or

always decreasing allows its inverse

to be constructed.

F-TF7. (+) Use inverse functions to

solve trigonometric equations that

arise in modeling contexts; evaluate

the solutions using technology, and

interpret them in terms of the context.

7

Trig Equations

5 days Unit Goals:

Linear Trig Equations

Quadratic Trig Equations

Trig Equations with more

than one Function

Standards:

A.REI2. Understand solving

equations as a process of reasoning

and explain the reasoning.



learning to explain the

relationship between trig

waves, trig equations

and the unit circle.

- The symmetry of the

unit circle allows

trig equations to

often have multiple

answers.

- Trig equations can

be treated like much

more basic equations

by using the concept

of substitution.

- How can we determine

if an arc trig function

will yield multiple

angles in a given

interval?

- What is the algebraic

and graphical

relationship between

trig equations and

quadratic/linear

equations?

8

Triangle Trig

10 days Unit Goals:

Area

Law of Sines

Law of Cosines

Ambiguous Case

Forces



learning of trigonometric

formulas to solve real-

life surveying problems.

- The Law of Cosines,

Law of Sines and

area formulas are

generalized versions

of Pythagorean

Theorem,


of the Law of Cosines,

Law of Sines and area

formula to theorems you

previously learned?

- What is the utility of the


Goals


Understandings

Essential Questions

Standards:

G-SRT6. Understand that by

similarity, side ratios in right triangles

are properties of the angles in the

triangle, leading to definitions of

trigonometric ratios for acute angles.

G-SRT7. Explain and use the

relationship between the sine and

cosine of complementary angles.

G-SRT8. Use trigonometric ratios and

the Pythagorean Theorem to solve

right triangles in applied problems.

G-SRT9. (+) 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.

G-SRT10. (+) Prove the Laws of

Sines and Cosines and use them to

solve problems.

G-SRT11. (+) Understand and 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).

SohCahToa and

A=1/2bh.

- Trigonometry allows

you to find distances

or angles that you

could not have

measured.

Law of Sines and the

Law of Cosines?

9

Combined

Sinusoids

7 days Unit Goals:

Sum and Difference Formulas

Multiple Angle Formulas



learning to perform

- The relationship

between a function

and an argument is

- Why can’t you

distribute a function to

corresponding pieces of


Goals


Understandings

Essential Questions

Standards:

F-TF9. (+) Prove the addition and

subtraction formulas for sine, cosine,

and tangent and use them to solve

problems.

harmonic analysis. not multiplication.

- The composition of

ordinates is merely

the sum or product

of the ordinates of a

function.

its argument?

- What is the algebraic

and graphical

interpretation of

function composition?

10

Sequences,

Series & the

Binomial

Theorem

8 days Unit Goals:

Arithmetic Sequences and

Series

Geometric Sequences and

Series

Induction

Binomial Theorem

Standards:

A-SSE4. Derive the formula for the

sum of a finite geometric series (when

the common ratio is not 1), and use

the formula to solve problems. For

example, calculate mortgage

payments.

A-APR5. (+) Know and apply the

Binomial Theorem for the expansion

of (x+ y)n in powers of x and y for a

positive integer n, where x and y are

any numbers, with coefficients

determined for example by Pascal’s

Triangle.

F-IF3. Recognize that sequences are

functions, sometimes defined

recursively, whose domain is a subset

of the integers. For example, the

Fibonacci sequence is defined



learning to evaluate

salary offers using the

concepts of sequences

and series.

- Mathematical

induction is a valid

form of proof for

sequence-type

problems.

- Sequence and series

formulas are

common-sense

shortcuts.

- Some infinite series

converge.

- What is proof?

- How could the sum of

an infinite number of

numbers possibly

converge?


Goals


Understandings

Essential Questions

recursively by f(0) = f(1) = 1, f(n+1)

= f(n) +f(n-1) for n ≥1.

F-BF2. Write arithmetic and

geometric sequences both recursively

and with an explicit formula, use

them to model situations, and

translate between the two forms.

11

Conic Sections,

Parametric

Equations &

Polar

Coordinates

12 days Unit Goals:

Conics

Parametric Equations

Polar Coordinates

Standards:

G-GPE1. Derive the equation of a

circle of given center and radius using

the Pythagorean Theorem; complete

the square to find the center and

radius of a circle given by an

equation.

G-GPE2. Derive the equation of a

parabola given a focus and directrix.

G-GPE3. (+) Derive the equations of

ellipses and hyperbolas given the foci,

using the fact that the sum or

difference of distances from the foci

is constant.



learning to model a real-

life phenomenon using

conic sections.

- Parametric equations

allow an

independent time (or

angle) variable to

dictate both x and y

position.

- Polar coordinates are

an alternative way to

specify location on

the plane.

- Equations of conic

sections can be

reorganized and

analyzed to produce

adequate graphs.

- What is the benefit of

using parametric

equations? Rectangular

equations?

- What is the benefit of

using polar coordinates?

Rectangular

coordinates?

- What is the importance

of conic sections?

12

Matrices

8 days Unit Goals:

Systems of Equations

Operations with matrices

Inverses

Determinants



learning to perform data

analysis using matrices.

- Matrices allow for a

streamlined method

for solving systems.

- Matrices have

properties similar to,

but not the same as

- What is the purpose of

learning matrices?


between operations with

matrices and operations

with real numbers?


Goals


Understandings

Essential Questions

Standards:

N-VM6. (+) Use matrices to represent

and manipulate data, e.g., to represent

payoffs or incidence relationships in a

network.

N-VM7. (+) Multiply matrices by

scalars to produce new matrices, e.g.,

as when all of the payoffs in a game

are doubled.

N-VM8. (+) Add, subtract, and

multiply matrices of appropriate

dimensions.

N-VM9. (+) Understand that, unlike

multiplication of numbers, matrix

multiplication for square matrices is

not a commutative operation, but still

satisfies the associative and

distributive properties.

N-VM10. (+) Understand that the

zero and identity matrices play a role

in matrix addition and multiplication

similar to the role of 0 and 1 in the

real numbers. The determinant of a

square matrix is nonzero if and only if

the matrix has a multiplicative

inverse.

N-VM11. (+) Multiply a vector

(regarded as a matrix with one

column) by a matrix of suitable

dimensions to produce another vector.

Work with matrices as

those of real

numbers.


Goals


Understandings

Essential Questions

transformations of vectors.

N-VM12. (+) Work with 2 × 2

matrices as transformations of the

plane, and interpret the absolute value

of the determinant in terms of area.

A-REI8. (+) Represent a system of

linear equations as a single matrix

equation in a vector variable.

A-REI9. (+) Find the inverse of a

matrix if it exists and use it to solve

systems of linear equations (using

technology for matrices of dimension

3 × 3 or greater).

13

Limits

11 days Unit Goals:

Evaluating Limits

Properties of Limits

Continuity

Standards:

F.IF.7d. Analyze functions using

different representations.



learning to determine if a

function has a limit at a

certain value.

- A function does not

have to be defined at

a point for its limit

to exist at that point.

- Limits only exist if

the two one-sided

limits exist and are

equal.

- What is a limit?

- How do we know if a

limit exists?

- What is the importance

of the concept of

continuity? The

Intermediate Value

Theorem?

14

Families of

Functions

8 days Unit Goals:

Regressions

Interpolations and

Extrapolations

Families of Functions

Standards:

S-ID6. Represent data on two

quantitative variables on a scatter

plot, and describe how the variables



learning to discuss

implications and make

suggestions based on

data analysis.

- The normal curve

only applies to

certain data sets.

- Regressions help us

make predictions

based on trends and

relationships.

- How can the normal

curve help us make

predictions?

- Why are some data

normal and others not?

- How do we find a curve

of best fit?


Goals


Understandings

Essential Questions

are related.

a. Fit a function to the data; use

functions fitted to data to solve

problems in the context of the data.

Use given functions or choose a

function suggested by the context.

Emphasize linear, quadratic, and

exponential models.

b. Informally assess the fit of a

function by plotting and analyzing

residuals.

c. Fit a linear function for a scatter

plot that suggests a linear association.

S-ID7. Interpret the slope (rate of

change) and the intercept (constant

term) of a linear model in the context

of the data.

S-ID8. Compute (using technology)

and interpret the correlation

coefficient of a linear fit.

S-ID9. Distinguish between

correlation and causation.

Verona Public School District Curriculum Overview ......polynomial identity (x 2 + y)2 = (x2 – y...

Documents

Transcript of Verona Public School District Curriculum Overview ......polynomial identity (x 2 + y)2 = (x2 – y...