Calculus (A.P

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Descriptive Geometry

COURSE: COMPUTER MATH (Standard)

TOPIC: Introduction To Computers, Simple Programming Concepts and Techniques

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) Properties of numbers are used to develop strategies for computation and estimation and judging the reasonableness of results. d) Technology can be used to interpret large sets of numbers. NCTM Standards: a) Use symbolic algebra to represent and explain mathematical relationships. b) Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations. c) Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts. d) Build new mathematical knowledge through problem solving. e) Solve problems that arise in mathematics and in other contexts. f) Apply and adapt a variety of appropriate strategies to solve problems. g) Monitor and reflect on the process of mathematical problem solving.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
1. A computer is an electronic device that manipulates symbolic information according to a list of precise instructions to perform a very few simple operations. 2. A computer can store information, perform arithmetic operations, and compare two numbers to make a decision. 3. The age of modern computers began in 1944 and as technology improved, computers improved, and became smaller, faster, cheaper, and easier to use. 4. A computer program is a planned sequence of instructions that tells a computer system what steps to perform in order to produce a desired result or output. 5. Problem solving skills are an essential tool for writing computer programs. 6. Programming statements are used to write simple programs by assigning values to variables, performing arithmetic operations, and printing the results. 7. Data can be input directly or interactively. 8. The application will determine the best method of inputting data. 9. Labeling results is important to help the user recognize what the program does and what the results mean. 10. Printing results in a table is an excellent way to clearly display output for programs with multiple results.	What is a computer? What can computers do? What is the history of the computer? How did advances in technology influence the development of the computer? What is a computer program? How are problem solving skills used in writing a computer program to solve a particular problem? What are the basic statements that are used in writing a computer program? How do you assign a value to a variable? How do you document a program and why is it important to do so? How do you print the results of your program? What is a label? Why is it important to label results? What is an output table? How do you print results in a table?
Knowledge and Skills What students are expected to know and be able to do
Students will know… Computer terminology. The basic operations a computer can perform. The historical development of the computer. Basic programming statements. Order of operations. Programming format. Methods for inputting data. Advantages and disadvantages of each method. Labels. Output tables.	Students will be able to… Demonstrate knowledge of computer terminology. List and describe the operations a computer can perform. Identify the technological advances and explain how they led to the development of new generations of computers Demonstrate an understanding of the basic programming statements. Accurately determine the results of mathematical expressions using the order of operations. Write a simple computer program in an appropriate format using the basic programming statements. Demonstrate knowledge of all the ways data can be input. Utilize the various methods to write simple programs. Demonstrate the ability to print output using labels. Demonstrate the ability to print output in a table.
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 work for a bank and are given the task of writing a computer program that will show the value of a bond for that is held for a given period of time. Using the formula for compound interest, A = P(1 + R/T)^(TN), where A is the new value, P is the original value, R is the interest rate, T is the number of times the bond is compounded per year, and N is the number of years, find the value of a $10,000 bond after 10 years at 5.5% interest compounded semi-annually. You will show the results of your program to a customer to help them make a decision concerning the amount they want to invest in bonds and for how long they want to invest. The program should be written so that different amounts can be easily entered giving the customer information for any option they may desire.	In addition to tests and quizzes, one or more of the following will be used: 1. Cooperative learning activities. 2. Informal and formal checks of exercises and programs written out before being entered into the computer.
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: Cooperative learning activities. Practice exercises and worksheet. Review worksheets. Programming assignments. Video Series “The Machine That Changed The World”

COURSE: COMPUTER MATH (Standard)

TOPIC: Advanced Programming Concepts and Techniques

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) Properties of numbers are used to develop strategies for computation and estimation and judging the reasonableness of results. d) Technology can be used to interpret large sets of numbers. NCTM Standards: a) Use symbolic algebra to represent and explain mathematical relationships. b) Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations. c) Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts. d) Build new mathematical knowledge through problem solving. e) Solve problems that arise in mathematics and in other contexts. f) Apply and adapt a variety of appropriate strategies to solve problems. g) Monitor and reflect on the process of mathematical problem solving.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
1. Branching is a process that allows a program to proceed along several paths depending upon certain conditions involving logical expressions. 2. Looping is a process that allows a program to repeat a statement or a sequence of statements over and over again. 3. An iterative loop can be used to do a particular set of operations a specific number of times or it can be used to create the data necessary for solving the problem without actually reading in the data. 4. Accumulators are used to add numbers without having to store them. 5. Counters are used to keep track of the number of times an event or condition occurred. 6. Computers have built-in functions which can be accessed when needed to solve particular problems. 7. Computers can use built-in functions to generate random numbers which are useful in writing programs that are simulations. 8. One dimension arrays involve a variable with a single subscript. 9. Arrays are useful when a large number of similar items must be stored.	What is branching? How is branching used in a program to solve problems that require decision making? What is looping? How is looping used in a program to allow a program to do repetitions of a statement or a sequence of statements? What is an iterative process? How can a loop be used in writing a program that requires repetition? What does it mean for a loop to generate data? How can this self-generating loop be used to solve problems? What is an accumulator? How are accumulators used in programs where numbers need to be totaled? What is a counter? How are counters used in programs where the number of times a condition occurred is important to know? What are built-in functions? How can built-in functions be used in writing programs? What are computer simulations? How can built-in functions be used to generate random numbers necessary in running simulations? What is an array? What are subscripted variables? What are the advantages in using an array?
Knowledge and Skills What students are expected to know and be able to do
Students will know… Branching. Looping. Iterative loops. Self-generating loops. Accumulators. Counters. Standard computer functions. Random number generators. Arrays. Subscripted variables.	Students will be able to… Use branching statements in a program to solve complex problems that require decision making. Use looping statements in a program to solve problems where a process needs to be done multiple times. Write a computer program where the number of times a set of statements needs to be repeated is known. Write a computer program where the data needed to solve the problem is generated by the loop itself. Use accumulators in writing computer programs where adding a series of numbers is necessary. Use counters in writing computer programs where knowing the number of times a condition occurs is necessary. Write computer programs that use specific built-in functions to solve problems. Write computer programs that use random number generators to run simulations. Write computer programs that require reading in and storing a large number of similar items by using subscripted variables.
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 are a computer programmer who has been hired by a school to develop a program for their teachers which will allow them to enter and store up to 25 test scores for a particular class. Your program should count the number of A’s, B’s, C’s, D’s, and F’s, calculate the class average, and show each student’s grade along with the amount above or below the class average their grade lies. The program should clearly display the output in table form.	In addition to tests and quizzes, one or more of the following will be used: Cooperative learning activities. Informal and formal checks of exercises and programs written out before being entered into the computer.
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: 1. Cooperative learning activities. 2. Practice exercises and worksheet. 3. Review worksheets. 4. Programming assignments. 5. Video Series “The Machine That Changed The World”