Assessment Tool

Lecture 4: Arithmetic Expressions

Content Tested: Int and Double Types

Lecture Content:

Arithmetic expressions
Integer and floating-point (double) types
Unary and binary operators
Precedence
Associativity
Conversions and casts
Symbolic constants

Goals:

Develop ability to apply principles and generalizations already learned to new problems and situations
Develop problem-solving skills
Develop appropriate study skills, strategies, and habits
Improve mathematical skills
Prepare for transfer or graduate study
Learn techniques and methods used to gain new knowledge in this subject
Develop ability to perform skillfully

Assessment Technique: Problem Recognition Tasks

Purpose:

This activity allows instructors to see if students understand how to develop algorithms to solve problems and how to choose variables of appropriate types.

Activity:

In today's lecture, we discussed variables of type "int" and "double". In your group (or as an individual) generate the algorithms to solve the following problems as well as describe the variable names and types you would use if implementing the algorithm in the C language. Note that you need not write the entire C program. An example solution to the first problem is given.

1. A program to calculate the area of a circle given the radius as input.
Input (what the user might type in): radius
Output (what would be displayed to the user): area

Solution:

Algorithm: area = PI * radius * radius

Variables and Types: The type of variable area would be double and the type of variable radius would be double. PI would be a symbolic constant equal to 3.14.

2. A program to convert inches (given as a whole number) to miles, feet, and inches.
Input: inches (as a whole number)
Output: miles, feet, and inches

Solution:

Algorithm: (Hint: 1 mile is equal to 5280 feet and 1 foot is equal to 12 inches)

Variables and Types:

3. A program that calculates the amount of US money in dollars given the number of pennies, nickels, dimes, and quarters.
Input: number of pennies, nickels, dimes, and quarters
Output: US dollar amount

Solution:

Algorithm: (Hint: 1 penny = .01 dollars, 1 nickel = .05 dollars, 1 dime = .10 dollars, 1 quarter = .25 dollars)

Variables and Types:

Possible Solutions:

2. A program to convert inches (given as a whole number) to miles, feet, and inches.
Input: inches (as a whole number)
Output: miles, feet, and inches

Solution:

Algorithm: (Hint: 1 mile is equal to 5280 feet and 1 foot is equal to 12 inches)

feet = inches / 12
inches = inches % 12
miles = feet / 5280
feet = feet % 5280

Variables and Types:

feet, inches, and miles would all be of type int in order to use the % operator.

Solution:

Algorithm: (Hint: 1 penny = 1 cent, 1 nickel = 5 cents, 1 dime = 10 cents, 1 quarter = 25 cents)

total = num_pennies * .01 + num_nickels * .05 + num_dimes * .10 + num_quarters * .25

Variables and Types:

num_pennies, num_nickels, num_dimes, and num_quarters would be of type int since it doesn't make sense to have a fractional piece of a coin. total would of type double since dollars can be fractional (i.e. $3.27). When writing the C program, one would use a cast for the multiplication of num_pennies and .01 since num_pennies is an integer and .01 is a double.

Alternatively, one could use the following algorithm (making sure all multiplications are done on pairs on integers)

total_cents = num_pennies * 1 + num_nickels * 5 + num_dimes * 10 + num_quarters * 25
total_dollars = (double) total_cents / 100.00

Possible Uses of Activity:

Have students work in groups to complete this activity. The instructor may want to circulate throughout the groups to ensure that each group is making progress. After the groups have completed the problems, the instructor can ask for volunteers for each problem. Be sure to ask why the group chose variable types that they did.
Have students work individually on their problems and form a small group to discuss their answers. If two members in the group come up with two different solutions (both being correct), use this opportunity to explain that in most cases, there are several ways to solve a problem. In the future, they'll learn how to choose efficient ways to solve problems which is at the heart of computer science.