# MiddleSchoolPortal/Quantitative Literacy

<keywords content="middle school mathematics quantitative literacy science lessons activities project real world contexts data analysis numeracy probability measurement" /> <metadescription content="This free, standards-based, online publication developed for teachers features resources that support an approach to decision-making and an ability to see problems through quantitative lens and apply numerical insight to their solution." />

## What is Quantitative Literacy?

Quantitative literacy is not a new code name for mathematics, nor even a euphemism for statistics. While quantitative literacy uses both disciplines, it is not either of these. Rather, it is an approach to decision-making and an ability to see problems through quantitative lens and apply numerical insight to their solution. Quantitative literacy, also termed numeracy, is the capacity “to be comfortable with numerical data and to use them in meaningful ways, in particular to make well-reasoned decisions” (Manaster 2009, 68). To operate in today’s world, where every major public issue --- from health care reform to the international economy --- and many everyday decisions, such as buying a car, depend on interpreting quantitative data, informed citizens need the ability to reason and communicate not only verbally but also numerically.

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## What Does Quantitative Literacy Mean for the Middle School Curriculum?

Contrary as it may seem, taking more math or higher math courses does not necessarily improve a student’s level of quantitative literacy. It is not a direct by-product of taking math courses; it must be facilitated, it must be taught, not only by math teachers.

Quantitative literacy is the responsibility of all teachers, in the same way that reading and writing are. Lynn Arthur Steen, a professor of mathematics at St. Olaf College, observes (1999):

Educators know all too well the common phenomenon of compartmentalization, in which skills or ideas learned in one class are totally forgotten when they arise in a different context. Students need to learn numeracy in multiple contexts—in history and geography, in economics and biology, in agriculture and culinary arts. . . . All teachers need to help students think of mathematics not just as tasks on school worksheets but as something that arises naturally in many contexts.

Mathematical skills and concepts should be taught in contexts that make sense to students. Students need to model real-world situations, collecting and analyzing data to reach a reasoned conclusion. Finally, our middle school program needs to broaden, according to Steen, to encompass more than the basic arithmetic and algebra skills. He sees a need for higher arithmetic (ratio, percentage, proportion), measurement in 2-D and 3-D, data analysis, and probability.

## Overview

You will find here online lessons, activities, and projects that allow students a range of real-world contexts. The Content Collections section contains sites that offer sets of problems and illustrations that connect middle school math to down-to-earth settings. The Interdisciplinary Lessons and Activities section offers activities and projects ready for interdisciplinary teaching. Each of the following sections focuses on a math topic: Data Analysis and Display, Probability, Measurement, Number and Operations. The resources offer mathematics in settings that deliberately cross over into other areas of the curriculum. Finally, for teachers looking for support in teaching quantitative literacy, a new approach for us all, Background Information for Teachers presents a select set of professional resources.

## Background Information for Teachers

This section is a collage of professional resources that I found useful in developing my own understanding of quantitative literacy and impressed me as general resources in teaching the material. I believe you will find here a workshop, a video or a book that will intrigue you as well. First we direct you to the NSDL Strand Map Service. These maps illustrate connections between concepts and across grade levels. An image of the middle grades (6-8) only part of the Mathematical Models map appears below. This map is one of three under the heading The Nature of Mathematicsand it includes interpreting results. Clicking on a concept within the maps will show NSDL resources relevant to the concept, as well as information about related AAAS Project 2061 Benchmarks and National Science Education Standards. Move the pink box in the lower right hand corner of the page to see the grades 6-8 learning goals.

Mathematical Models

Learning Math: Data Analysis, Statistics, and Probability With these online workshops, developed for elementary and middle school teachers, you can build your skills through investigations of different ways to organize, analyze, and represent data. Practical examples open up exploration of probability, random sampling, estimation, measurement biases, and other topics of data analysis. The concluding case studies illustrate how to apply what you have learned in your own classroom.

Principles for Principals: Workshop 3. Math/Science Skills—What's Important? When does data analysis make a difference? An inspiring 11-minute video offers a look at how a teacher, with help from a local college, engaged his 5/6 class in exploring the safety of well water in their community. The students collected the actual data themselves as they took samples from 63 wells to test for contamination. Using spreadsheets, they analyzed the data and presented the surprising results to their community.

Mathematics and Democracy: The Case for Quantitative Literacy Compelling chapters on the need for quantitative literacy in the school curriculum. The book, edited by Lynn Steen and available complete and free online, argues that “the world of the twenty-first century is a world awash in numbers. . . . Unfortunately, despite years of study and life experience in an environment immersed in data, many educated adults remain functionally innumerate. Most U.S. students leave high school with quantitative skills far below what they need to live well in today’s society.”

U.S. Census Bureau A large collection of government statistics and articles on census controversies, population growth, and demographics. Don't miss the up-to-the-minute U.S. and world population clocks.

Ratios in Children’s Books This page presents three picture books that focus on ratios in accurate mathematical terms. Even older middle school students will enjoy and learn from the stories and problem scenarios. You can find the books in school or public libraries, or from online booksellers.

## Content Collections

These collections offer a rich variety of problems that demand a quantitative lens. As students confront the numerical in their everyday world, they sharpen that lens and gain facility in dealing with problems in real contexts.

Math in Daily Life This set of problems introduces mathematical concepts through everyday decision-making scenarios. A cooking exercise involves ratios and proportion; an essay on population introduces exponential growth and bar graphs; a home decorating exercise explains how to calculate area; and a banking and credit card scenario introduces simple and compound interest.

Figure This! Math Challenges for Families Here you have 80 mathematical challenges designed to encourage problem-solving with students in grades 6 to 8. The problems focus on concepts and objects found in everyday life, such as how fast your heart beats and what shape container holds the most popcorn. A complete explanation of the solution follows, plus additional problems related to the same challenge.

Ohio Math Works These activities and problems for grades 7 to 9 involve students in the mathematics used by professionals in journalism, meteorology, the snack food industry, the amusement park industry, and the fashion world. The site has interactive quizzes, animated diagrams, and background on various industries.

New York Times Daily Lesson Plan: Mathematics What better way to make mathematics real than to use the daily newspaper? Here are interdisciplinary lesson materials based on New York Times articles. The stories offer ways to draw on real-world situations to develop lessons in mathematics. For example, in one lesson, "students convert statistics about gun injuries into visual presentations, then use these as the basis for a poster campaign to teach children about the dangers of guns in the home."

The Mathematical Art of M.C. Escher Art seen through a geometric lens! Tessellations, polyhedra, logic of shape, logic of space---an essay introducing these topics states that Escher “created unique and fascinating works of art that explore and exhibit a wide range of mathematical ideas.” You will find these works well illustrated here.

CIESE: K-12 Online Classroom Projects The Center for Innovation in Engineering and Science Education (CIESE) sponsors and designs unique projects that link classrooms throughout the world. In collaborative exploration, students and teachers share in interdisciplinary projects that offer rich opportunities for data collection, data display, and analysis. One example: determining the factors that affect the boiling temperature of water. Each project includes lesson plans, handouts, and teacher guidance.

## Interdisciplinary Lessons and Activities

The activities and projects below are ready for interdisciplinary teaching in quantitative literacy.

Building BIG Through this PBS television series, students in grades 5 through 8 explore large structures and what it takes to build them. The material, including interactive online labs and challenging problems, is divided into five sections: bridges, domes, skyscrapers, dams, and tunnels.

Technology and the Environment: A Middle School Mix In this publication, middle school technology, science, and math teachers will find high-quality digital resources that they can use when building or freshening a unit about the environment. Excellent opportunities for interdisciplinary collaboration! The featured activities were selected to help equip students to assess the risks and benefits of individual and industrial uses of technology.

Mathematics of Cartography This web site, appropriate for the middle school level, opens with the question “What exactly is a map?” The site contains the history of maps, math lessons involving maps, teacher notes, map-related careers, and links to ancient maps and biographies of early mapmakers.

Musical Plates Let’s interpret real-time earthquake and volcano data and use the information to solve a real-world problem! Through this series of lessons, students study the correlation between earthquakes and tectonic plates, and determine whether there is a relationship between volcanoes and plate boundaries. Included are enrichment lessons and a final project that could be used for assessment.

The King of Tides This well-constructed WebQuest begins with an announcement: “The moon has been accused of causing the tides! Using real data collected from the Internet, your team’s job is to bring proof one way or another!” The group task, the process for finding data and establishing proof, and the evaluation are outlined and explained clearly. However, as on all WebQuests, you will have to check the site addresses given, since web addresses change or disappear over time. The two-week project, which depends on analysis of real data, culminates in a final report to the court.

Project SkyMath: Making Mathematical Connections Activities in this middle school module include collecting temperature data, identifying various statistics of that data, and reading and interpreting temperature maps. Developed by the University Corporation for Atmospheric Research (UCAR), all activities are solidly connected to data analysis, patterns, statistics and measurement. The web site includes all of the background information needed for teachers to use the module, as well as lesson plans, student handouts, and assessments.

Size and Scale This is a challenging and thorough activity on the physics of size and scale. Using information on the diameters of the Earth and the moon and the distances between the bodies, students construct scale models of the Earth-moon system. But the main objective here is understanding the relative sizes of bodies in our solar system and the problem of making a scale model of the entire solar system. The site contains a complete lesson plan, including motivating questions for discussion and extension problems.

## Data Analysis and Display

How can we guide our students to understand and make sense of data? They need to know how data are collected, analyzed, and, perhaps most crucially, interpreted and depicted to the public. Each activity below involves middle school students in hands-on work with data in its many representations.

Count on Math: Every Breath You Breathe In an activity designed to help students develop number sense, each student estimates the number of times she or he breathes in one hour, and the class graphs the estimates, finds the mean and median of the estimates, and discusses outliers. Students then brainstorm how they could find out how many breaths a person actually takes in a day—and implement their strategies.

Accessing and Investigating Population Data In these activities, students use census data available on the web to examine questions about population. They also formulate their own questions. For example, in one section they analyze statistics from five states of their choice, develop specific research questions using the data, and create three graphs to compare and contrast the information.

The International Boiling Point Project People from all over the world collaborate in this investigation. They simply boil water and post data to discover which factor in the experiment (room temperature, elevation, volume of water, or heating device) has the greatest influence on boiling point. Students can analyze all the data collected to reach their own conclusions.

Capture - Recapture In this lesson, students experience an application of proportion that scientists actually use to solve real-life problems. They learn how to estimate the size of a total population by taking samples and using the fact that the ratio of “tagged” items to the number of items in a sample is the same as the ratio of tagged items to the total population.

May You Live Long: Do Men Live Longer than Women? “Men live longer than women.” Students are first asked: What do you make of this statement? Exactly what does it mean? Then the exploration begins as they try to determine whether it is true, using actual data they must collect.

RoadKill: Collision in the Wildlife Corridors For this online data collection project, students monitor and report the number and type of animals killed by motor vehicles in their locale, along with information about the environmental conditions that may have contributed to an animal's death. The site provides a detailed protocol for collecting data on roadkill, a method of reporting data online, and access to data collected by all participants. You’ll find that the project crosses many disciplines, including environmental science.

Mathematics as Communication This grades 6-8 activity was created to encourage students to observe and examine the world around them. In particular, it helps them read and interpret graphs and organize and describe data. They will enjoy and be challenged by the time versus speed graphs given on the activity sheets.

Representation of Data: Cholera and War This rich problem has students study excellent examples of the presentation of data. Students analyze (1) a map of cholera cases plotted against the location of water wells in London in 1854 and (2) a map of Napoleon's march on Moscow in 1812-1813 to see what inferences they can draw from the data displays.

Gallery of Data Visualization: Historical Milestones As the site’s author states, “The history of statistical graphics reveals some graphics so breathtaking in information design and artistic beauty that it is hard to imagine how they might be reproduced today.” This gallery of images includes some of the best examples of data representation.

Cast Your Vote! This web site by Annenberg/CPB addresses issues in statistics and polling. Once inside the exhibit, you are taken through a year in a fictitious election campaign for an inside look at the mathematics behind the polls. The web site reviews concepts such as random sampling, margin of error, confidence intervals, and ways in which surveys can go wrong.

## Probability

Probability theory began with a question related to a game—and so do these lessons. What probability means and how it affects outcomes can seem inconsequential to middle school students, but when they see its connection to decisions in game playing, probability takes on real meaning. In these lessons, games serve to both motivate learning and connect the mathematics to actual experience.

Rescue Mission Game This two-day lesson introduces probability as well as forces used in flight. To guide a helicopter to stranded hikers on a mountaintop, students learn about lift, drag, thrust, and gravity. Spinners used in the game differ in the areas allotted to each of these forces. Which spinner should be used on the next turn? For each turn, students select the spinner with the greatest probability of helping them reach the lost hikers. An innovative introduction to the basics of probability!

The Game of Skunk In this lesson, students practice decision-making skills leading to a better understanding of choice versus chance and building the foundation of mathematical probability. Students make theoretical arguments and have discussions about differences between choice and chance, then do an experiment to show the difference. Discussion of the results can include how insurance rates are determined and why auto insurance is higher for teenagers.

Plinko: Probability from a Game Show This is a lesson plan that could profitably expand into a project. Besides all directions and needed diagrams, the resources include an online simulation of Plinko, a game of chance, as well as directions on how to make your own Plinko board. Playing the game, students gather data for investigation into experimental probability. Discussions also open to theoretical probability, including tree diagrams and counting paths that give insight into why game shows arrange the payoffs the way they do.

## Measurement

To understand measurement and the units that we use to figure length, area, or volume requires hands-on practice. These projects offer students the opportunity to develop a meaningful sense of measurement.

Floor Plan Your Classroom Students draw by hand a floor plan of their classroom to scale and use software to draft a computer-aided design from the drawing. What’s unique here is the well-designed set of directions to assist students in the process, including examples of floor plans and guidelines for creating scale drawings.

The Stowaway Adventure In this multidisciplinary project, students use real-time data from the Internet to track a real ship at sea, determine its destination, and predict when it will arrive. Complete lesson plans are included, as well as detailed directions for teachers on how to access maritime data online. The enrichment lessons include three interdisciplinary writing/ research activities, which the students can complete independently.

Meeting in the Middle With this hands-on activity, students apply measurement and communication skills to describe the location of the end of a tunnel they plan to construct. The goal is for a student to form a precise location description so that a second student planning to construct from the other side can determine the location of the tunnel end. Background information for the activity and a student handout are included.

The Noonday Project: Measuring the Circumference of the Earth In the course of this project, students learn about Eratosthenes and his experiment, do a similar experiment by collaborating with other schools, and analyze and reflect on the collected data to determine the accuracy of their measurements and what they learned. The project provides instructions, activities, reference materials, online help, and a teacher area. My all-time favorite project!

## Number and Operations

Critical to quantitative literacy is facility with simple mental arithmetic, estimation, calculations, and reasoning with proportions. These lessons offer your students opportunities to work with ratio, fractions and percent, and to deepen their concepts of large numbers.

Count on Math: Making Your First Million Do your students have a good grasp on the size of one million? In this activity, they will develop a sense of one million by working with blocks of 10 or 100 and then expanding the idea by multiplication or repeated addition until a million is reached. To help them relate to such a large quantity, students try to answer such questions as: Have you been alive a million days? Hours? Minutes? Seconds?

Too Big or Too Small? This lesson features three activities to promote number sense with large numbers, fractions, and decimal operations. In the first activity, students use proportional reasoning to determine whether \$1 million in \$1 bills would fit in a suitcase and how much it would weigh. In the second activity, students use circular regions to develop their sense of the relative sizes of fractions between 0 and 1. In the third activity, students play a game that develops their sense of the effect that operations with decimal numbers have on the size of the answer.

Grid and Percent It Really understanding percent is a “must” for most financial transactions. This lesson presents a method of solving percent problems that focuses on the basic concept of percent, that of "parts per hundred.” A 10 × 10 grid, a common model for visualizing percents, is extended to solve various types of percent problems.

Nutrients by the Numbers: Using Math to Explore Nutrition Students strengthen their percentage and fraction skills by comparing the nutritional values of similar food products. They individually calculate their own daily intake of various nutrients and compare their diets to recommended daily percentages. Discussion questions, additional activities, and suggestions for assessment are included with the lesson plan.

Is It Really News? A newspaper has stated that the majority of the information contained in its pages is in the form of advertisements. To investigate this, portions of the local newspaper are distributed to students working in groups. The class first reaches consensus on their definitions of "news" and other general headings (sports, entertainment). Students then express the ratio of the area of each category to the area of the page as a fraction and a decimal. After analyzing the entire newspaper, students decide how much of it is really news.

## SMARTR: Virtual Learning Experiences for Students

Visit our student site SMARTR to find related math-focused virtual learning experiences for your students! The SMARTR learning experiences were designed both for and by middle school aged students. Students from around the country participated in every stage of SMARTR’s development and each of the learning experiences includes multimedia content including videos, simulations, games and virtual activities.

## References

Manaster, Alfred B. 2009. Mathematics and numeracy: Mutual reinforcement. In Mathematics and democracy: The case for quantitative literacy, ed. Lynn Steen. Woodrow Wilson National Fellowship Foundation. http://www.maa.org/ql/067-72.pdf

National Council of Teachers of Mathematics. 2000. Principles and standards for school mathematics. Reston, VA: Author.

Steen, Lynn Arthur. 1999. Numeracy: The new literacy for a data-drenched society. Educational Leadership 57, no. 2 (October 1999) http://www.ascd.org/publications/educational_leadership/oct99/vol57/num02/Numeracy@_The_New_Literacy_for_a_Data-Drenched_Society.aspx