Sheryl A. DeCaprio
Students should eventually feel comfortable about designing flowcharts to complete tasks outside the realm of mathematics as they know it. Practice in this exercise will direct students to pay attention to the details and the order of events. Students can now apply this logical thinking process to solve the word problem that appear in math class. Below are three examples for flowcharting lessons. One for adding decimal numbers, one for finding Least Common Multiple, and one for finding area of a geometric figure. Students may develop general flowcharts to save and use again for similar problems or may write a chart to describe the solution to a specific problem. The choice is their own, although a collection of flowcharts describing basic mathematical operations and formulas can be used throughout the year and would be a tremendous resource for each student.
A. Addition of Decimals
Write a flowchart to describe the process of solving the following word problem. Find the given information, decide what must be done and how to accomplish the task.
Raul went to the grocery store and bought a loaf of bread for 69¢, a gallon of milk for $1.14, and a dozen of eggs for 97¢. He paid for the groceries with a ten dollar bill. What was his change?
Students must determine that this is a two part problem. First an addition problem to determine the total cost of the groceries and secondly, a subtraction problem to determine his change from the ten dollar bill. A possible flowchart of the problem is diagrammed in Figure I.
Although this may seem involved it is important for students to understand the process through which the numbers are placed as well as the computational skills needed to carry out the operation. The decision box may be omitted in this chart as it serves only to introduce and additional dimension to the problem, one of sufficient information.
FIGURE
I Flowchart the addition of decimals.
(figure available in print form)
B. Least Common Multiple
Write a flowchart to describe the process to find the Least Common Multiple of two numbers.
(figure available in print form)
In each case the task at hand is divided into smaller manageable steps that can be easily performed. Students now have a general method for finding Least Common Multiples. A flow diagram can be referred to whenever the students must solve a similar problem.
C. Flowchart a formula for a geometric figure.
Flowchart the following word problem:
Roberta wants to grow spaghetti in her back yard. She has cleared a rectangular patch of land with a width of one inch and a length of sixty inches. How much fertilizer does she need to cover the area of her garden.
Students must recognize that:
1) it is an area problem
2) the dimensions are given
3) the formula for area of a rectangle is length x width
(figure available in print form)
Again, students have a general chart how to find area of any rectangular figure. Students should be encouraged to keep a notebook of charts explaining how to perform certain tasks. The use of general flowcharting techniques, especially those used to find area and perimeter, also help students adapt to the concepts of using variables and formulas, an important concept for children to grasp and necessary for math literacy.
A child who is able to develop a process for solving problems will achieve success in school and develop a healthier attitude towards learning. Flowcharting gives the children a direction and a method to decipher and decode the problems they, at one time, would not attempt. Practice and reinforcement of these skills will enable our students to solve any problem, and build their confidence in their own problem solving skills. To “think like a computer” that is to approach a task in a logical, sequential order, is to reorganize their thinking patterns and achieve success in developing problem solving techniques.