About This Chapter
Numerical Ability: Reasoning & Data Interpretation - Chapter Summary
The lessons in this chapter provide an overview of numerical reasoning and data interpretation. You'll review connective reasoning, a 3-step process for solving problems, and techniques for personalizing word problems. You'll also look at how to eliminate fractions to solve problems. After completing the chapter, you should be prepared to:
- Describe the difference between inductive and deductive reasoning in mathematics
- Use Polya's four-step problem-solving process
- Detail mathematical principles that can be used to solve any problem
- Explain the correct way to set up a math problem
- Restate, personalize, simplify, and solve different types of word problems
- Relate distance to change in position and calculate average speed
- Organize and understand data by using tables and schedules
- Interpret bar graphs and pie charts
These lessons will help you quickly get up to speed on the topics covered. You can use the Help feature to submit questions to instructors if you get stuck on a topic. Video timelines let you easily navigate to specific topics. A brief multiple-choice quiz is available for each lesson to test your knowledge. Study offline by printing out the quiz/worksheet.
1. Reasoning in Mathematics: Inductive and Deductive Reasoning
Many people think that deductive and inductive reasoning are the same thing. It is assumed these words are synonymous. They are not. This lesson reveals the reality of these two types of reasoning.
2. Reasoning in Mathematics: Connective Reasoning
Connective reasoning is reasoning that has an operation, or a way to connect two phrases. The five main logic connectives will be reviewed in this lesson.
3. Polya's Four-Step Problem-Solving Process
Problem solving can be a problem. Any problem is solved easier with an action plan. Polya's 4-Step Problem-Solving Process is discussed in this lesson to help students develop an action plan for addressing problems.
4. Mathematical Principles for Problem Solving
Solving problems is not just a simple, straightforward process. There are a few principles that can help you as you approach any problem solving scenarios. This lesson covers those principles with examples.
5. What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions
When it comes to solving math word problems, there is a correct way of setting up the problem and labeling the various parts of the problem so that you can solve the problem easily. Watch this video lesson to learn how you can do it.
6. Solving Word Problems: Steps & Examples
Watch this video lesson to learn how you can solve word problems by following this 3-step process. Learn how to visualize your problem so you fully understand it. Then learn how to write and solve your equations.
7. Solving Word Problems with Multiple Steps
Not all word problems are so straightforward that they only require you to do one operation and you're done. Some are more complicated, requiring several steps. Watch this video lesson to learn how to solve these kinds of problems.
8. Restating Word Problems Using Words or Images
Watch this video lesson to learn how you can use sketches and notes to help you visualize a problem. Watch how easy it becomes to solve your problem once you have visualized it.
9. Personalizing a Word Problem to Increase Understanding
When it comes to word problems, being able to personalize a word problem with more familiar situations will help you a lot in your problem solving. Watch this video lesson to learn how you can restate the word problem in terms you understand.
10. How to Simplify Word Problems with Fractions Using Whole Numbers
Watch this video lesson to learn how to solve word problems with fractions in them easily by turning your fractions into whole numbers. Learn what you need to do to get rid of your fractions so you can easily solve your problem.
11. Distance, Time & Average Speed: Practice Problems
After watching this video, you will be able to explain what distance is, explain how it relates to change in position, and calculate the average speed in various situations. A short quiz will follow.
12. Organizing and Understanding Data with Tables & Schedules
In math, when we have to deal with a lot of data, having a visual format to present all the data becomes very useful. Watch this video lesson to learn how you can take advantage of two of these visual formats.
13. Understanding Bar Graphs and Pie Charts
In this lesson, we will examine two of the most widely used types of graphs: bar graphs and pie charts. These two graphs can provide the reader with a comparison of the different data that is displayed.
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