Module 1 Student Textbook

QuantwayTM I

Quantway™ I

Module 1

Student

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This Module is part of QUANTWAY™, A Pathway Through College-Level Quantitative Reasoning, which is a product of a Carnegie Networked Improvement Community that seeks to advance student success. The original version of this work, version 1.0, was created by The Charles A. Dana Center at The University of Texas at Austin under sponsorship of the Carnegie Foundation for the Advancement of Teaching. This version and all subsequent versions, result from the continuous improvement efforts of the Carnegie Networked Improvement Community. The network brings together community college faculty and staff, designers, researchers and developers. It is a research and development community that seeks to harvest the wisdom of its diverse participants through systematic and disciplined inquiry to improve developmental mathematics instruction. For more information on the QuantwayTM Networked Improvement Community, please visit carnegiefoundation.org.

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This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. (CC BY-NC)

Table of Contents

Module 1

E-Understanding Visual Displays of Information 5

G-Writing About Quantitative Information 6

Lesson / Title / Theme / Page
1.1 / Introduction to Quantitative Reasoning / Citizenship
Student Handout / 7
Out-of-Class Experience / 11
1.2 / Seven Billion and Counting / Citizenship
Student Handout / 22
Out-of-Class Experience / 28
1.3 / Percentages in Many Forms / Personal Finance
Student Handout / 36
Out-of-Class Experience / 41
1.4 / The Flexible Quantitative Thinker / Personal Finance
Student Handout / 51
Out-of-Class Experience / 56
1.5 / The Credit Crunch / Personal Finance
Student Handout / 67
Out-of-Class Experience / 73
1.6 / Whose Footprint Is Bigger? / Citizenship
Student Handout / 81
Out-of-Class Experience / 87
1.7 / A Taxing Set of Problems / Personal Finance
Student Handout / 93
Out-of-Class Experience / 98
1.8 / Interpreting Statements About Percentages / Medical Literacy
Student Handout / 105
Out-of-Class Experience / 110
1.9 / Percents and Probabilities / Medical Literacy
Student Handout / 115
Out-of-Class Experience / 120
Review / 127

Version 1.5

QuantwayTM Student Support Materials

Understanding Visual Displays of Information Strategy: Asking Questions
About Displays

Data are increasingly presented in a variety of forms intended to interest you and invite you to think about the importance of these data and how they might affect your lives. The following are some of the types of common displays:

· pie charts,

· scatterplots,

· histograms and bar graphs,

· line graphs,

· tables, and

· pictographs.

In your lessons, you will find a variety of such collections of data.

What questions should you ask yourself when you study a visual display of information?

· What is the title of the chart or graph?

· What question is the data supposed to answer? (For example: How many males versus females exercise daily?)

· How are the columns and rows labeled? How are the vertical and horizontal axes labeled?

· Select one number or data point and ask, “What does this mean?”

Use the following chart to help you understand what some basic types of visual displays of information tell you and what questions they usually answer.

This looks like a … / This visual display is usually used to … / For example, it can be used to show …
pie chart / · show the relationships between different parts compared to a whole. / · how time is used in a 24-hour cycle.
· how money is distributed.
· how something is divided up.
line graph / · show trends over time.
· compare trends of two different items or measurements. / · what seems to be increasing.
· what is decreasing.
· how the cost of gas has increased in the last
10 years.
· which of these foods (milk, steak, cookies, eggs) has risen most rapidly in price compared to the others.
histogram or bar graph / · compare data in different categories.
· show changes over time. / · how a population is broken up into different age categories.
· how college tuition rates are changing over time.
table / · organize data to make specific values easy to read.
· break data up into overlapping categories. / · the inflation rates over a period of years.
· how a population is broken into males and females of different age categories.

Version 1.5

QuantwayTM Student Support Materials

Writing About Quantitative Information: An Introduction

Background

You might be surprised that you are asked to write short responses to questions in Quantway. Writing in a math class? This course emphasizes writing for the following two reasons:

· Writing is a learning tool. Explaining things such as the meaning of data, how you calculated the data, or how you know your answer is correct deepens your own understanding of the material.

· Communication is an important skill in quantitative literacy. Quantitative information is used widely in today’s world in products such as reports, news articles, publicity materials, advertising, and grant applications.

Understanding the Task

One important strategy in writing is to make sure you understand the task. In this course, your tasks will be questions in assignments, but in other situations the task might be a question on a report form, instructions from your employer, or a goal that you set for yourself. To begin to write successfully, ask yourself the following questions:

· What is the topic of the writing task?

· What is the task telling me to do? Some examples are given below:

o Describe how you found the answer.

o Explain why you think you have the right answer.

o Reflect on the process of coming up with the answer.

o Make a prediction about the next data point.

o Compare two data points or the answers to two parts of the problem.

· What information am I given to help me with the task?

Look at this example and the answers it gives to these questions.

(12) In OCE 1.4, you read about self-regulating your learning during the plan phase. Explain briefly why it is important to evaluate your confidence before planning on working a problem.

· What is the topic of the writing task? (Answer: It is about self-regulating or evaluating confidence.)

· What is the task telling me to do? (Answer: It is asking me to explain why “evaluating confidence” is important.)

· What information am I given to help me with the task? (Answer: I can look back at the OCE for Lesson 1.4 if I need to remember what self-regulating is.)

A Basic Writing Principle for Quantitative Information

Writing Principle: Use specific and complete information. The reader should understand what you are trying to say even if he or she has not read the question or writing prompt. This includes

· information about context, and

· quantitative information.

Version 1.5

QuantwayTM Student Handout

Lesson 1.1: Introduction to Quantitative Reasoning

Theme: Citizenship

Specific Objectives

Students will 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.

Students will be able to

· identify quantitative information.

· 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: Does This Information Make Sense?

In this lesson, you will learn how to evaluate information you see often in society. You will start with the following situation.

You are traveling down the highway and see a billboard with this message:

(1) You do not see the name of the organization that put up the billboard. What groups might have wanted to publish this statement? What are some social issues or political ideas that this statement might support?

The information in this statement is called quantitative. 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 using 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

· understand a health risk

You often do not know whether these statements are true. You may not be able to locate the information, but you can start by asking if the statement is reasonable. This means to ask if the statements make sense. You will be asked if information is “reasonable” throughout this course.
This lesson will help you understand what is meant by this question.

(2) In 1995,[1] a group published the statement in the Problem Situation. Do you think this was a reasonable statement to make in 1995? Discuss with your group.

(3) You only have the information in the statement. Using only that information, how can you decide if the statement is reasonable? Talk with your group about different ways in which you might answer this question.

(4) In Question 3, you thought about ways to decide if the statement was reasonable. One approach is to start with a number for the first year. Put this number into the table below. Complete the other values in the second column of the table. Do not complete the third column right now.

Year / Number of Children / Rounded (using words)
1950
1960
1970
1980
1990
1995

(5) Does the number you predicted for the number of children shot in 1995 seem reasonable? What kind of information might help you decide?

Making Connections

Record the important mathematical ideas from the discussion.

About This Course

This course is called a quantitative reasoning course. This means that 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 discussed in this lesson. You will talk, read, and write about quantitative information. The lessons will focus on three themes:

· Citizenship: You will learn how to understand information about your society, government, and world that is important in many decisions you make.

· Personal Finance: You will study how to understand and use 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 lesson is part of the Citizenship theme. 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. You will learn the following things:

· You will understand and interpret quantitative information.

· You will evaluate quantitative information. Today you did this when you answered if the statement was reasonable.

You will use quantitative information to make decisions.

Student Notes

Version 1.5

QuantwayTM Out-of-Class Experience

Lesson 1.1: Introduction to Quantitative Reasoning

Theme: Citizenship

Introduction

Since this is your first assignment, the authors will be explaining how your daily assignments will be structured. An assignment is referred to as an Out-of-Class Experience (OCE). Each OCE has the same four sections:

· Making Connections to the Lesson

· Developing Skills and Understanding

· Making Connections Across the Course

· Preparing for the Next Lesson and/or Assessment

Making Connections to the Lesson

The purpose of this section is to help make sure you understand the most important ideas of the lesson. Sometimes it is hard to know what to focus on when you are in class. The authors have designed this curriculum to help you identify and remember important ideas through the following steps:

· Every lesson ends with a discussion. During this discussion, the class identifies the important mathematical ideas of the lesson.

· The Student Handout always ends with a section called Making Connections. In this section, you write down the important mathematical ideas.

· This section of your OCE always starts with a question that asks you to identify a main mathematical idea of the lesson. You are given four statements to choose from.

· In future OCEs, you will describe how mathematical ideas connect across lessons.

A main mathematical idea means that the idea is an important concept that helps explain how to do many different types of problems and helps connect different problems together. It may take you a while to be able to identify the main mathematical ideas of lessons. Your instructor will help you at first by making sure these ideas are discussed at the end of the lesson.

(1) Which of the following statements correctly illustrates one of the main mathematical ideas of the lesson?

(i) Asking good questions about quantitative information is important in quantitative reasoning.

(ii) Doubling means to multiply by 2.

(iii) Gun violence is a problem in the United States.

(iv) You should not use estimation.

Since this is your first time with this type of question, the authors are going to explain the answer to Question 1. The answer is (i) because asking questions about quantitative information is important in many different problem situations. The other answers may or may not be true, but they are not main mathematical ideas for this lesson. Specifically,