General Problem Solving: Learn It 5

The Foundation of Problem Solving: Identifying Required Data

To solve a problem effectively, we need to first identify what information is necessary. This involves understanding the problem’s context, deciphering the given information, and determining what additional data we need to reach a solution.

Context is crucial for identifying what data we need. This involves understanding the problem’s real-world situation and identifying the variables at play. In a problem about bus scheduling, for instance, crucial variables might include the number of buses, the number of stops, and the average speed of the buses.

The next step is to analyze the information that’s already been given. This might be presented directly in the problem statement, or it might require interpretation. For instance, if a problem states that a car travels at [latex]60[/latex] miles per hour, we know that speed, distance, and time are all important variables.

Once we understand the context and the given information, we can determine what additional data we need. If we’re asked to calculate how long it takes the car to travel [latex]240[/latex] miles, for instance, we don’t need any additional data because we can use the given speed to calculate time. But if we’re asked how far the car can travel in [latex]5[/latex] hours, we need to know its fuel efficiency and how much fuel it has.

What data might you need to consider when trying to address the following?

  1. You want to determine the fastest route to drive from Los Angeles to San Francisco.
  2. A school is trying to reduce the amount of waste it produces.
  3. You’re designing a new park for your city.

Identifying the necessary data is an important step in solving a mathematical problem. With the right information in hand, you’re well-equipped to develop a mathematical model and find a solution.

The Language of Data: Graphs, Charts, and Tables

Data is the lifeblood of mathematics, a language in itself. It tells stories, reveals patterns, and guides decision-making. And just as stories are written in words, data is often written in graphs, charts, and tables. Being fluent in this language allows us to solve problems, make predictions, and understand the world around us.

There are different way data can be presented.

  1. Graphs translate numerical data into visual form, making trends and patterns easier to spot. Types of graphs include line graphs, bar graphs, histograms, and scatter plots, among others. Each type serves a particular purpose and conveys different types of information.
  2. Charts provide a structured presentation of data. Pie charts, for example, are used to show percentages or proportions, while flowcharts can illustrate processes or systems.
  3. Tables, on the other hand, are perfect for organizing data in a clear and concise manner. They can be used to display raw data, comparisons, or statistical information.

Whether you’re reading a graph, chart, or table, the first step is to understand what kind of data you’re dealing with. What variables are being represented? Over what time period? Are there any units of measurement? Next, look for patterns, trends, or anomalies. Are there any unexpected spikes or dips in a line graph? Does one category dominate in a pie chart? Is there a key value that stands out in a table?

Once you’ve understood the data’s story, you can use it to solve problems. For instance, you might use a bar graph of monthly rainfall to predict when the best time to plant crops would be, or a table of population data to plan public services.

Consider the following table of students’ grades. What’s the most common grade? What’s the range of grades?

Student Grade
1 A
2 B
3 A
4 C
5 B
6 A
7 B
8 B

Remember, data interpretation is about more than just reading numbers—it’s about understanding the story those numbers tell, and using that story to solve problems and make decisions.