Download presentation

Presentation is loading. Please wait.

Published byPrincess Lowry Modified over 3 years ago

1
Quantitative Reasoning A quantity is anythingan object, event, or quality thereofthan 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. 1 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. 2 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 MTE 494 Arizona State University 3 Understanding a problem situation quantitatively means: 1.Understanding the quantities embedded in the situation, and 2.Understanding how these quantities are related to each other

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? MTE 494 Arizona State University 4 Some relevant quantities embedded within this scenario: Dieter As weight before the diet; Dieter As weight after the diet Dieter Bs weight before the diet; Dieter Bs 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

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

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

7
MTE 494 Arizona State University 7 Reasoning about quantities and solving-by-reasoning So DBs after weight is [(7 x 19) + 2] lbs and that is 5/6 as much as his before weight. This means that DBs 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.

Similar presentations

Presentation is loading. Please wait....

OK

Kitchen Calculations.

Kitchen Calculations.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on artificial intelligence download Ppt on eia report oil Ppt on conservation of natural vegetation and wildlife Ppt on computer manners Ppt on railway track and structures Ppt on natural vegetation and wildlife of the world Ppt on file system in linux Ppt on object-oriented programming vs procedural programming Ppt on cmos image sensor Ppt on water cycle for class 9