Quantitative Literacy Quantitative Literacy Sherry-Anne McLean Sherry-Anne McLean Lake Washington Institute of Technology Kirkland, WA ©2014 Copyright © 2014 Sherry-Anne McLean This book was edited by Sherry-Anne McLean, Lake Washington Institute of Technology The Quantitative Literacy Toolkit, Working With Data, and Algebraic Reasoning chapters are largely based on: Quantway Version 1.0. The original version of this work was developed by the Charles A. Dana Center at the University of Texas Austin under sponsorship of the Carnegie Foundation for the Advancement of Teaching. This work is used (or adapted) under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC- SA 3.0) license: creative commons.org/licenses/by-nc-sa/3.0. For more information about Carnegie’s work on Quantway I, www.carnegiefoundation.org/quantwaysee ; for information on the Dana Center’s workThe onNew Mathways Project, see www.utdanacenter.org/mathways. The Skills Quiz review chapters (A through E) contain portions taken and derived from: Worksheets created by David Lippman and released under a Creative Commons Attribution license. The worksheets were created to supplement the textbook Arithmetic for College Students. This work by Monterey Institute for Technology and Education (MITE) 2012 and remixed by David Lippman is licensed under a Creative Commons Attribution 3.0 Unported License This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. To view a copy of this license, visithttp://creativecommons.org/licenses/by -nc-sa/3.0/ or send a letter to Creative Commons,444 Castro Street, Suite900, Mountain View, California, 94041, USA. 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Contents Module 1: The Quantitative Literacy Toolkit…………… 1 Module 2 Working with Data…………………………... 113 Module 3: Algebraic Reasoning………………………… 215 Strengthening Skills A: Order of Operations…………….……………... 302 Strengthening Skills B: Fractions…………………………………..…… 312 Strengthening Skills C: Signed Numbers…………………………..…… 328 Strengthening Skills D: Percentages and Proportions………………..…. 338 Strengthening Skills E: Solving Equations…………………………..….. 346 1 Quantway Student Handout November 18, 2011 (Version 1.0) Lesson 1.1.1: 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: Every year since 1950, the number of American children gunned down has doubled. (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. The Carnegie Foundation for the Advancement of Teaching Quantway frontmatter available at www.quantway.org/kernel and The Charles A. Dana Center at the University of Texas at Austin or www.utdanacenter.org/mathways/index.php 1 2 Quantway Student Handout November 18, 2011 (Version 1.0) Lesson 1.1.1: Introduction to Quantitative Reasoning Theme: Citizenship (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. 1Best, J. (2001). Damned lies and statistics. University of California Press: Berkeley and Los Angeles. The Carnegie Foundation for the Advancement of Teaching Quantway frontmatter available at www.quantway.org/kernel and The Charles A. Dana Center at the University of Texas at Austin or www.utdanacenter.org/mathways/index.php 2 3 Quantway Student Handout November 18, 2011 (Version 1.0) Lesson 1.1.1: Introduction to Quantitative Reasoning Theme: Citizenship 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. The Carnegie Foundation for the Advancement of Teaching Quantway frontmatter available at www.quantway.org/kernel and The Charles A. Dana Center at the University of Texas at Austin or www.utdanacenter.org/mathways/index.php 3 4 Quantway Out-of-Class Experience November 18, 2011 (Version 1.0) Lesson 1.1.1: 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.