Pre Algebra

Contents Page

Probability & Statistics

 

COURSE:   PRECALCULUS

TOPIC:  Functions

STAGE 1: IDENTIFY DESIRED RESULTS

Content Standard(s)

Generalizations about what students should know and be able to do

Established Goals:

 

CT Frameworks:

a)     A wide variety of functions can be used to model real world situations.

b)   Functions can be viewed as objects on which operations can be performed.

c)     Algebraic concepts can be extended from real numbers to include objects such as complex numbers, and vectors.

d)     The number system is extended from natural numbers, integers, rational numbers and real numbers to include the set of complex numbers.

e)     Operations such as addition and multiplication can be applied to objects such as vectors that are not numbers.

 

NCTM Standards:

a)     Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

b)     Understand meanings of operations and how they relate to one another.

c)     Compute fluently and make reasonable estimates.

d)     Understand patterns, relations and functions.

e)     Represent and analyze mathematical situations and structures using algebraic symbols.

f)      Use mathematical models to represent and understand quantitative relationships.

g)     Analyze change in various contexts.

Enduring Understandings

Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)

Essential Questions

Inquiry used to explore generalizations

 The student will understand that:

1.     There are several types of functions.

2.     Operations and transformations apply to all types of functions.

3.     Geometric and analytic information can explain the observed local and global behavior of a function.

4.     All functions have algebraic, numerical, and graphical representations.

5.     Real world situations can be modeled and solved by using various functions.

 

1.     What are the different types of functions?

2.     What are the operations that apply to all functions?

3.     How can algebraic and geometric representations be used to describe the behavior of the function?

4.     How are the algebraic, numerical, and graphical representations of  functions related?

5.     How can you use  functions to solve real life problems?

Knowledge and Skills

What students are expected to know and be able to do

Students will know…

  1. There are several types of functions including:  polynomial, logarithmic, exponential, trigonometric and their inverse, absolute value, and rational.
  2. The operations and transformations that apply to the different types of functions.
  3. The observed local and global behavior of functions can be explained with geometric and analytic information.
  4. The algebraic, numerical, and graphical representations of functions.
  5. That functions are used to model real world behavior.

 

Students will be able to…

  1. Identify several types of functions.
  2. Use the operations and transformations on the different types of functions.
  3. Find the domain, range, zeros, maxima,  minima, and inverse of functions.
  4. Solve second degree and higher equations by factoring.
  5. Solve linear and quadratic inequalities with one or two variables involving absolute value.
  6. Represent functions algebraically, numerically, and graphically.
  7. Model and solve real life problems using functions.

STAGE 2: DETERMINE ACCEPTABLE EVIDENCE

Performance Task(s)

Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)

Other Evidence

Application that is functional in a classroom context only to evaluate student achievement of desired results

 

As an air quality controller you must analyze the ventilation system at Waterford High School.  Your analysis will determine the minimum required ventilation rate in terms of the air space per child in a public school classroom. The air conditioning system in the room has the capacity of moving 450 cubic feet of air per minute.  In the given model, x is the air space per child in cubic feet, and y is the ventilation rate in cubic feet per minute:

 

y = 80.4  − 11 ln x         100 ≤ x ≤ 1500

 

Your report, which will submitted to town’s air quality committee, will include the ventilation rate per child, assuming that the room is filled

to a capacity of 30 students, and a graph that displays and explains the estimated air space required per child.

 

In addition to tests and quizzes, one or more of the following will be used:

  1. Cooperative learning activities.
  2. Graphing calculator activities.
  3. Informal and formal checks:  homework checks, problem of the day, and review worksheets.

 

STAGE 3: DEVELOP LEARNING PLAN

Learning Activities:

  1. Cooperative learning activities.
  2. Graphing calculator activities.
  3. Homework and review worksheets.
  4. Work stations.

 

 

 

COURSE: PRECALCULUS

TOPIC: Conics

 

STAGE 1: IDENTIFY DESIRED RESULTS

Content Standard(s)

Generalizations about what students should know and be able to do

Established Goals:

 

CT Frameworks:

a)     A variety of coordinate systems and transformations may be used to solve geometric problems in two- and three- dimensional geometry.

b)     Measurements that are not directly determined can be approximated with some degree of precision.

 

NCTM Frameworks:

a)     Understand relations and patterns and use various representations for them.

b)     Write equivalent forms of equations and systems of equations and solve them with fluency- mentally or with paper and pencil in simple cases and using technology in all cases.

c)     Use symbolic algebra to represent and explain mathematical relationships.

d)     Apply transformations and analyze mathematical situations.

 

Enduring Understandings

Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)

Essential Questions