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SPECIFIC OBJECTIVES
By the end of this collaboration, you should understand that
- 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 collaboration, you should be able to
- identify quantitative information.
- convert units from feet to miles.
- round numbers (based on homework).
- name large numbers (based on homework).
- work in groups and participate in discussion using the group norms for the class.
PROBLEM SITUATION 1: 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.
Problem Situation 1 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 in Problem Situation 1 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
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.
(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. Write some strategies below.
(4) In Question 3, you thought about how to decide if the statement was reasonable. 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). Write the numbers in words in (g)-(l). For example, if “1000” is in column 2, “one thousand” would be written in the corresponding space in column 3.
| Year | Number of Children Gunned Down | Number in words (rounded) |
| 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 material in this course will focus on three themes.
- Citizenship: You will learn how to understand information about your society, government, and world that can impact many decisions you make.
- Personal Finance: You will study how to understand financial information and how to use it to make decisions in your life.
- Medical Literacy: You will learn how to understand information about health issues and medical treatments.
This collaboration (1.1) is part of the “Citizenship” theme. In this collaboration, you learn about ways to decide if information is reasonable. This can help you form an opinion about an issue.
Today, the goal is 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.
PROBLEM SITUATION 2: HOW BIG IS A BILLION?
Scientists have worried about human population growth for nearly 200 years. The population of Earth has grown over time and is still growing. We do not know how many people Earth can support. (In Lesson 1.2, you will get a sense of how many people there are and how that number has changed over time.)
The world population is estimated to be about 7 billion people. That is seven times as many people as there were 200 years ago.
It is difficult to understand just how big a billion is. Here is a way to help you think about it:
1 billion = 1,000 × 1,000 × 1,000 = 1,000,000,000 = 109
The following questions will also help you think about how big 1 billion is.
(6) Imagine a line of 1,000 people standing shoulder to shoulder. How long is the line? Complete the following steps to answer this question. For each step, write your calculations clearly so that someone else can understand your work.
(a) Estimate the shoulder width of an “average” person. Write your estimate in the space below.
(b) Use that estimate in the following calculations. Calculate how far a line of 1,000 people, standing shoulder to shoulder, would measure in miles (5,280 feet = 1 mile).
(c) Now imagine 1,000 lines of 1,000 people.
(i) How many people would be in the line?
(ii) How long would the line be measured in miles?
(d) Imagine 1,000 lines like the one in Question 6(c).
(i) How many people would be in line?
(ii) How long is the line measured in miles? Round to the nearest whole mile.
MAKING CONNECTIONS
Record the important mathematical ideas from the discussion.
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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).
