1 / 7

Quantitative Reasoning

Quantitative Reasoning. A quantity is anything—an object, event, or quality thereof—than can be measured or counted. . A value of a quantity is its measure or the number of items that are counted . A value of a quantity involves a number and a unit of measure. .

kellan
Download Presentation

Quantitative Reasoning

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Quantitative Reasoning Aquantity is anything—an object, event, or quality thereof—than can be measured or counted. • Avalue of a quantity is its measure or the number of items that are counted. A value of a quantity involves a number and a unit of measure. MTE 494 Arizona State University

  2. An important distinction: A quantity is not the same thing as a number or a value of the quantity One can think of a quantity without knowing its value. For example: the amount of snowfall on a given day is a quantity, regardless of whether someone actually measured this amount. One can think/speak about the amount of snowfall without knowing a value of this amount. MTE 494 Arizona State University

  3. Quantitative Analysis • Analyzing problem situations is key to be a skilled problem solver • Quantitative analyses of problem situations should be a first step toward helping students develop a deep understanding of such situations Understanding a problem situation quantitatively means: • Understanding the quantities embedded in the situation, and • Understandinghow these quantities are related to each other MTE 494 Arizona State University

  4. Example: Two dieters were overheard having the following conversation at a Weight Watchers meeting: • Dieter A: “I lost 1/8 of my weight. I lost 19 lbs.” • Dieter B: “I lost 1/6 of my weight, and now you weigh 2 pounds less than I do.” • How much weight did Dieter B lose? Some relevant quantities embedded within this scenario: • Dieter A’s weight before the diet; Dieter A’s weight after the diet • Dieter B’s weight before the diet; Dieter B’s weight after the diet • The amount of weight lost by Dieter A; The amount of weight lost by Dieter B • The difference in their weights before the diets; The difference in their weights after the diets MTE 494 Arizona State University

  5. This scenario can be seen as having a quantitative structure depicted below: MTE 494 Arizona State University

  6. Reasoning about quantities and solving-by-reasoning • We want to know how much weight Dieter B (DB) lost—it is the difference between his before-and-after diet weights. • We know about DA’s before and after weights: • DA losing 1/8 of his weight means that his after weight must be 7/8 as much as his before weight. • We also know that DA lost 19 lbs, which is the amount equal to 1/8 of his before weight. Since 7/8 of his weight is 7 times as much as 1/8 of it, DA’s after weight must equal (7 x 19) lbs • We also know about Dieter B’s (DB) weight loss: • DB losing 1/6 of his weight means that his after weight is 5/6 as much as his before weight • DA’s after weight being 2 lbs less than DB’s after weight means that DB’s after weight must be 2 lbs more than DA’s after weight, or [(7 x 19) + 2] lbs MTE 494 Arizona State University

  7. Reasoning about quantities and solving-by-reasoning • So DB’s after weight is [(7 x 19) + 2] lbs and that is 5/6 as much as his before weight. • This means that DB’s after weight is 5 times as much as 1/6 of his before weight. • So it must be that 1/6 of his before weight is 1/5 as much as his after weight (using our meaning of fractions). • That is, DB lost (1/5) x [(7 x 19) + 2] lbs = 27 lbs. MTE 494 Arizona State University

More Related