4.1: Corequisite- Estimation Vs Calculation
- Page ID
- 148599
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)SPECIFIC OBJECTIVES
By the end of this lesson, you should understand that
- you are a necessary and integral part of the classroom community.
- you should feel comfortable asking questions and participating in classroom discourse, no matter your language background.
- quantitative reasoning is the ability to understand and use quantitative information. It is a powerful tool in making sense of the world.
- relatively simple math can help make sense of complex situations.
- 1 billion = 1,000 × 1,000 × 1,000.
- the representations 1 billion, 1,000,000,000, and 109 have the same meaning.
By the end of this lesson, you should be able to
- work effectively in groups.
- understand the course expectations and what is necessary to succeed in the course.
- identify quantitative information.
- convert units from feet to miles.
- round numbers.
- name large numbers.
- work in groups and participate in discussion using the group norms for the class.
ESTIMATION
In this course, you will talk about different types of estimation.
- Educated guess: One type of estimation might be called an educated guess about something that has not been measured exactly. You could estimate the world population. This quantity cannot be measured exactly—it would be impossible to count how many people live on the earth at any given time. Scientists can use good data and mathematical techniques to estimate the population, but it will always be an estimate.
- Convenient estimation: Sometimes estimations are used when it is inconvenient or not worthwhile to make an exact count. Imagine that you need to know how much paint to buy to paint the baseboard trim in your house. (The baseboard trim is the piece of wood that follows along the bottom of the walls.) You need to know the length of the baseboard. You could measure the length of each wall to the nearest 1/8 inch and carefully subtract the width of halls and doors. It would be much quicker and just as effective to measure to the nearest foot or half foot. If you were cutting a piece of baseboard to go along the floor, however, you would want an exact measurement.
- Estimated calculation: This usually involves rounding numbers to make calculations simpler. You will find in this course that percentages are used in many contexts. One of the most important skills you will develop is understanding and being comfortable working with percentages in a variety of situations.
PROBLEM SITUATION: DOES THIS INFORMATION MAKE SENSE?
During this course, you will be presented with a number of problem situations. These problem situations will help you learn how to evaluate the types of quantitative information you may encounter in everyday life.
This problem situation asks you to use quantitative information to figure out if a statement makes sense.
Imagine that you just received a flier in the mail with the following statement:1
(1) What groups might have wanted to mail a flier like this? What are some social issues or political ideas that this statement might support?
Is the Information Reasonable?
The flier above includes quantitative information. Quantitative information uses concepts about quantity or number (this can be specific numbers or a pattern based on numerical relationships such as doubling).
You hear and see statements that include quantitative information every day. People use these statements as evidence to convince you to do things like
- vote a certain way;
- donate or give money to a cause; or
- understand a health risk.
You often do not know whether these statements are true. You may not be able to locate the information that supports these statements, but you can start by asking if the statements are reasonable. This means asking if the statements make sense. You will be asked if information is reasonable throughout this course. This lesson will help you to understand what is meant by this question.
(2) Do you think the statement, “Every year since 1980, the number of children gunned down has doubled” is a reasonable statement? Discuss with your group and write your reasoning below.
(3) Using only the information that was included in the flier, how can you decide if the statement was reasonable? Talk with your group about the different ways in which you might answer this question. Record some strategies below.
(4) In Question 3, you thought about how to decide if the statement below was reasonable.
"Every year since 1980, the number of American children gunned down has doubled."
For this problem, choose a starting number for gun deaths in 1980. Put this number into the table below in cell (a). Work in your group to complete the other values in the second column of the table (b) – (f). Enter the numbers in words in (g) – (l).
For example, if “1000” is in column 2, “one thousand” would be entered in the corresponding space in column 3.
| Year | Number of Children Gunned Down | Rounded (using words) |
| 1980 | (a) | (g) |
| 1990 | (b) | (h) |
| 2000 | (c) | (i) |
| 2010 | (d) | (j) |
| 2015 | (e) | (k) |
| 2020 | (f) | (l) |
(5) Refer to the table you created in Question 4. Does the number of children gunned down in the year 2020 seem reasonable? What kind of information might help you decide?
About This Course
This course is called a quantitative reasoning course. This means you will learn to use and understand quantitative information. It will be different from many other math classes you have taken. You will learn and use mathematical skills connected to situations like the one you just discussed in this lesson. You will talk, read, and write about quantitative information.
The lessons in this course will focus on three themes.
- Social and Environmental: You will learn how to understand information about your society, government, and world that can impact many decisions you make.
- Financial: You will study how to understand financial information and how to use it to make decisions in your life.
- Health and Risk: You will learn how to understand information about health issues and medical treatments.
This lesson is part of the “Social” theme. In this lesson, you learned about ways to decide if information is reasonable. This can help you form an opinion about an issue.
Today, the goal was to introduce you to the idea of quantitative reasoning. This will help you understand what to expect from the class. Do not worry if you did not understand all of the math concepts. You will have more time to work with these ideas throughout the course.
In this course you will learn to do the following things:
- Understand and interpret quantitative information.
- Evaluate quantitative information. Today you did this when you answered if the statement was reasonable.
- Use quantitative information to make decisions.
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1 Adapted from Joel Best, Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists (Berkeley: University of California Press, 2001).