Discrete Mathematics

Contents Page

Math Concepts and Applications

 

 

COURSE:  JAVA

TOPIC: Computer programming

 

STAGE 1: IDENTIFY DESIRED RESULTS

Content Standard(s)

Generalizations about what students should know and be able to do

Established Goals:

                                                                            

CT Frameworks:

     a)  Real world problems may be analyzed.

 

NCTM Frameworks:

  

   a)  Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

   b)  Organize and consolidate their mathematical thinking through communication.

   c)  Recognize and apply mathematics in contexts outside of mathematics.

   d)  Use representations to model and interpret physical, social, and mathematical phenomena.

 

Enduring Understandings

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

Essential Questions

Inquiry used to explore generalizations

Students will understand that:

1.     JAVA is a useful tool for solving real world problems.

2.     There are several aspects of computer programming.

 

1. What is JAVA and how is it applicable to real world situations?

2. What are the different types of situations that can be solved with JAVA?

Knowledge and Skills

What students are expected to know and be able to do

Students will know…

1.  How to model problems using JAVA programming.

2.  There are numerous applications of JAVA.

3.  How to model a project, solve it using JAVA computer programming.

 

Students will be able to…

1.  Interpret JAVA code.

2.  Write programs to model real world situations.

3.  Present and communicate how JAVA is used to solve problems in and outside of the context of mathematics.

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 the new intern in the town’s finance department, you have been asked to create a JAVA program that will calculate employees salaries based upon their hourly pay, their overtime pay, and the number of hours of overtime they work.  You must test this program with an employee with a standard 40 hour work week pay, an employee with a 40 hour work week plus 5 hours of overtime at $Y per hour and an employee with a 40 hour work week plus X hours of overtime at $Z per hour.  You will present your program and calculations to your boss and the finance committee upon completion.

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

  1. Cooperative learning activities.
  2. Informal and formal checks:  homework checks, problem of the day, and review worksheets.
  3. Projects modeling real world situations.

STAGE 3: DEVELOP LEARNING PLAN

Learning Activities:

1.  Cooperative learning activities.

2.  Projects.

3.  Informal and formal checks:  homework, problem of the day, and review worksheets.

4.  Peer editing of computer programs.

 

 

COURSE:  JAVA

TOPIC: Classes & Objects

 

STAGE 1: IDENTIFY DESIRED RESULTS

Content Standard(s)

Generalizations about what students should know and be able to do

Established Goals:                                                 

 

CT Frameworks:

    a)  Real world problems may be analyzed.

 

NCTM Frameworks:

  Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

a)      Organize and consolidate their mathematical thinking through communication.

b)      Recognize and apply mathematics in contexts outside of mathematics.

c)      Use representations to model and interpret physical, social, and mathematical phenomena.

 

Enduring Understandings

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

Essential Questions

Inquiry used to explore generalizations

Students will understand that:

1.     There is a difference between classes and objects.

 

2.     There are several aspects of computer programming.

 

3.     Java is a useful tool for solving real world problems.

 

1.     What is the difference between a class and an object and how are they defined?

 

2.     What are the different types of situations that can be solved with Java?

 

3.     What is Java and how is it applicable to real world situations?

Knowledge and Skills

What students are expected to know and be able to do

Students will know…

1.     How to differentiate between an object and class and define their own for their programs.

2.     How to model problems using Java

programming.

3.     There are numerous applications of Java.

 

Students will be able to…

1.     Create objects and classes.

2.     Interpret Java code.

3.     Write programs to model real world situations.

4.     Present and communicate how Java is used to solve problems in and outside of the context of mathematics.

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 the new intern in the town’s finance department, you have been asked to create a Java program that will calculate employees salaries based upon their hourly pay, their overtime pay, and the number of hours of overtime they work.  You must test this program with an employee with a standard 40 hour work week pay, an employee with a 40 hour work week plus 5 hours of overtime at $Y per hour and an employee with a 40 hour work week plus X hours of overtime at $Z per hour.  You will present your program and calculations to your boss and the finance committee upon completion.

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

1.     Cooperative learning activities.

2.     Informal and formal checks:  homework checks, problem of the day, and review worksheets.

3.     Projects modeling real world situations.

STAGE 3: DEVELOP LEARNING PLAN

Learning Activities:

1.  Cooperative learning activities.

2.  Projects.

3.  Informal and formal checks:  homework, problem of the day, and review worksheets.

4.  Peer editing of computer programs.

 

 

 

COURSE:  JAVA

TOPIC: Data Types & Conditionals

 

STAGE 1: IDENTIFY DESIRED RESULTS

Content Standard(s)

Generalizations about what students should know and be able to do

Established Goals:                                                 

 

CT Frameworks:

   a)  Real world problems may be analyzed.

 

NCTM Frameworks:

  

a)       Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

b)      Organize and consolidate their mathematical thinking through communication.

c)      Recognize and apply mathematics in contexts outside of mathematics.

d)      Use representations to model and interpret physical, social, and mathematical phenomena.

 

Enduring Understandings

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

Essential Questions

Inquiry used to explore generalizations

Students will understand that:

1.     There are different data types

 

2.     There is a correct ordering of decisions.

 

3.     Java is a useful tool for solving real world problems.

  

1.     What kind of data types do you think are needed?

 

2.     Why is the order of programming so important

 

3.      How is Java applicable to real world situations?

Knowledge and Skills

What students are expected to know and be able to do

Students will know…

1.     How to recognize the different type of data types (int, double, String, Boolean)

2.     How to use the different data types (int, double, String, Boolean).

3.     Recognize the correct ordering of decisions.

4.     There are numerous applications of Java.

 

Students will be able to…

 

1.     Define and manipulate the different data types (int, double, String, Boolean).

2.     Read program input.

3.     Implement decisions.

4.     Present and communicate how Java is used to solve problems in and outside of the context of mathematics.

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

You have just been hired by the local super market “Big Waterford”.  Your job as software engineer is to write a program that directs a cashier how to give change.  The program has two inputs:  the amount due and the amount received from the customer.  Compute the difference, and compute the dollars, quarters, dimes, nickels, and pennies that the customer should receive in return.  Test this program so you can have a working program to present to the cashier staff and the training seminar.

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

1.     Cooperative learning activities.

2.     Informal and formal checks: homework checks, problem of the day, and review worksheets.

3.     Projects modeling real world situations.

STAGE 3: DEVELOP LEARNING PLAN

Learning Activities:

1.  Cooperative learning activities.

2.  Projects.

3.  Informal and formal checks:  homework, problem of the day, and review worksheets.

4.  Peer editing of computer programs.

 

 

 

COURSE:  JAVA