City Digits is a project to develop and pilot integrated curriculum resources and web-tools that support high school students' learning of mathematics. The project is a collaboration between CUNY's Brooklyn College and MIT's Civic Data Design Lab.

The team has designed two curricular modules to investigate social justice themes related to the local, urban context. The curricular modules are enhanced by the integration of geo-spatial technologies that enable students to explore their local urban landscape, collect field data, and organize and visualize patterns. Our first module, Local Lotto, is about state lotteries and was pilot tested in two rounds in 2013. Our second module, Cash City, is about pawn shops and alternative financial institutions and was pilot tested in two rounds in 2014.

This material is based upon work supported by the National Science Foundation under Grant No. DRL-1222430 to the City University of New York. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Technology

City Digits uses a combination of mapping, data, and media technologies to bring learning and information into the classroom in fresh and exciting ways.

Integrating real-world data into the classroom brings an added level of authenticity and civic awareness, ultimately turning otherwise disconnected mathematical investigations into rich and connected learning experiences.

The primary way City Digits brings data into the classroom is by using mapping as a language to communicate a complicated issue. Students can explore familiar areas on a map, at various levels of scale, in terms of socioeconomic and other measures, toward the development of a data-informed understanding of the topic and its significance. For that reason, a mapping API is at the center of the City Digits tools. On top of this are a host of image, audio file, and text media-upload features that allow students to augment data presented to them with their own observations.

Technology Development

In choosing how to develop a technology that would allow for very rich but extensive datasets to be presented in a user-friendly manner to students, a number of choices needed to be made. The following are some of the main challenges faced in developing the platform.

Web Platform vs. Stand-Alone App

The decision to develop a web platform rather than a standalone smartphone or tablet app was made based on the requirement that the technology require the least amount of upkeep and compatibility effort, while still being versatile enough to use on a variety of technologies.

Based on these requirements a web app, which could be deployed from any internet browser, allowed for the project to be used in classrooms using laptops or desktops, or out in the field on tablets with 4G internet connection.

A standalone app would have required us to choose one operating system (i.e. iPhone, Android), and would subsequently require continuous compatibility updates, and ultimately reduce the number of technologies that could be used to explore content.

Mapping API

Mapbox

Mapbox API provided a strong and versatile background/base for displaying the variety of data collected for display. Its extensive documentation provided appreciated support in developing the application.

View the Mapbox Platform - http://www.mapbox.com

Student Submitted Content

As part of Local Lotto and Cash City, students add media to the platform and formulate opinions based on their field experiences, data analysis, and classroom discussions.

Images/Audio/Notes/Interviews

Students conduct interviews with local pedestrians and with shopkeepers in the school's neighborhood. In Local Lotto students gather data on who plays the lottery, with what frequency, and why; which stores sell lottery tickets; and investigate people’s opinions about the impact of the lottery on the local neighborhood. In Cash City students gather data on which financial institutions people use and why, and investigate people's opinions about the availability of financial institutions in their local neighborhood.

Student-collected data is then tagged to its location by the tool and becomes part of an aggregated, online map.

View User-Submitted Content Local Lotto Cash City

Opinions / Tours

As a summative component to each City Digits module, students develop an opinion and justify it with a variety of available media, data, and map screenshots. Exploring the topic using the data from the maps combined with the user-generated content collected by their group or their peers gives youth space to take a position on a civic issue, connect it to their local neighborhood, and justify that position with mathematical analysis.

View User-Generated Opinions Local Lotto Cash City

New York City Data

The project’s partner high schools are in New York City. Despite having a singular geographic focus, the datasets are derived from multiple sources.

Where does your data come from?

Cash City Data

The geocoded list of pawnshops, received by the NYC Dept. of Consumer Affairs (DCA) in February, 2014; this represents a list of all establishments that currently possess a "pawnbrokers" license from DCA; please note that a handful (10-15) of establishments have overlapping addresses and thus multiple licenses

  • Data Sources: Business Analyst/RefUSA/NYC DCA
  • All InfoShare.org demographic and socioeconomic data compiled from the 2007-2011 ACS 5 year estimates (downloaded March 2014)
  • McDonalds = locations of McDonalds fast food chain (identified through RefUSA in March 2014)
  • Check Cashing = Geocoded list of 'check cashing' establishments (RefUSA) using SIC Code 609903
  • Money Transfer Services = Geocoded list of 'money transfer services' establishments (RefUSA) using SIC Code 609910
  • Commercial Banks = Geocoded list of commercial banks (ESRI Business Analyst) using SIC Code 602110
Local Lotto Data

Demographic and household income is from the 2010 Census. All lottery data is from the NYS Lottery for 2010. Winnings data represents winning tickets of $5,000 or more, geo-coded by retailer store. Sales data represents total sales at a retailer store. We are also using a modified version of the Infoshare Neighborhood file. Base data was obtained from Open Street Maps and New York City Building Footprints, Roadbeds, and Subway Entrances come from New York City Department of Information Technology and Telecommunications (DOITT).

Curriculum

The City Digits modules were developed to support students’ learning of mathematics by investigating compelling phenomena in their local environments. These projects address mathematical content and skills as outlined by the Common Core State Standards by engaging students to use mathematics to understand how something works, like the chances of winning a lottery game or the structure of a pawn shop transaction. Integrating geospatial technology enhances and extends these mathematical investigations by inviting data-rich spatial analyses of the topic at hand.

Project Curriculum

Here are overviews to the Local Lotto and Cash City curricula and links to longer descriptions.

Cash City Curriculum

In Cash City, students use ratio tables to calculate percentage and figure out the cost of pawning; they also model the growth of the cost using tables, graphs, and equations. Students learn about Annual Percentage Rate (APR) to compare the cost of a pawn to other cash loan options, including credit card cash advances and personal bank loans. Students then analyze the distribution of various financial institutions by examining digital maps, and they also gather their own data (media) in the school’s neighborhood to learn about the role of these institutions in their community. Finally, students create and publish their opinions about pawn shops and other financial institutions, incorporating evidence from maps, media they gathered, and mathematical analyses as support.

Cash City Curriculum Go to Cash City Tool

Local Lotto Curriculum

In Local Lotto, students create a tree diagram model to figure out all permutations and combinations of possible picks on a lottery ticket and figure out the (im)probability of winning the lottery. Students also gather interview data in their school’s neighborhood and analyze New York City maps about lottery spending to understand the impact of the lottery on different neighborhoods. Students have a chance to voice their ideas about the lottery through posters speaking back to lottery advertisements and opinion slideshows utilizing their mathematical findings.

Local Lotto Curriculum Go to Local Lotto Tool

Publications and Presentations

Publications

Rubel, L., Hall-Wieckert, M., Lim, V., Williams, S. (2015, in press). Maps, mobile tools, and media boards: digital technologies for learning about pawnshops. In O. Lindwall & S. Ludvigsen (Eds.) Proceedings of 11th International Conference on Computer Supported Collaborative Learning. Gothenburg, Sweden: International Society of the Learning Sciences..

Click for Full Article

Rubel, L., Lim, V., Full, M.C., Hall-Wieckert, M. (2015, in press). Critical pedagogy of place in mathematics: text, tools, and talk. In Greer, B. and Mukhophadyay, S. (Eds.) Proceedings of the Eighth International Mathematics Education and Society Conference. Portland, Oregon: Mathematics Education and Society.

Click for Full Article

Lim, V., Deahl, E., Rubel, L., Williams, S. (2015). Local Lotto: Mathematics and mobile technology to study the lottery. In Polly, D. (Ed.), Cases on Technology Integration in Mathematics Education (pp. 43-67). Hershey, PA: IGI Global.

Click for Full Article

Deahl, E. (2015). Youth Data Literacy as a Pathway to Civic Engagement. Civic Media Project, MIT Press

Click for Full Article

Williams, S., Deahl, E., Rubel, L., Lim, V. (2014). City Digits: developing socially-grounded data literacy using digital tools' Journal of Digital Media Literacy.

Click for Full Article

Presentations

City Digits: learning mathematics of the city in the city (May, 2015). Presentation at Brooklyn College Faculty Day.

City Digits cyberlearning tools (January, 2015). Presentation at the Cyberlearning Summit. Arlington, VA.

Click to View Poster Click to View Handout

Rubel, L., Lim, V.Y., Deahl, E., Williams, S. (April, 2014). Critical, place-based mathematics education in urban schools: Design-based research to create a mathematics curriculum on the local lottery. Paper and poster presented at the Annual Meeting of the American Educational Research Association. Philadelphia, PA.

Click to View Poster

Workshops for Teachers

The Maps and Math of New York City Pawn Shops. Mini-Course at Math for America, New York, NY. Co-led with teacher. (Spring 2015).

CityDigits: Critical, place-based approaches to teaching & learning mathematics. TODOS Conference. Phoenix, AZ. Presentation with participating high school teachers. (June 2014).

LottaFacts: A critical analysis of the state lottery through mathematics. Professional Development Workshop at Math for America. New York, NY. Presentation with participating high school students and teachers. (March 2014).

LottaFacts: A critical analysis of the state lottery through mathematics. Presentation at the Creating Balance for an Unjust World Conference. Los Angeles, CA. Presentation with participating high school students and teachers. (January 2014).

View Powerpoint Presentation

Team

Laurie Rubel | laurie.rubel [at] gmail.com

Laurie Rubel is an Associate Professor of Secondary Education at Brooklyn College and the Graduate Center of the City University of New York. Laurie's interest in place-based mathematics teaching and learning extends from her previous work with New York City mathematics teachers on culturally relevant mathematics pedagogy. Laurie’s been on the CUNY faculty since 2003 and was formerly a high school mathematics teacher.

Sarah Williams | sew [at] mit.edu

Sarah Williams is an Assistant Professor of Urban Planning at MIT's School of Architecture and Planning and the Director of the Civic Data Design Project, which employs data visualization and mapping techniques to expose and communicate urban patterns and policy issues. Before coming to MIT Williams was Co-Director of the Spatial Information Design Lab at Columbia University.

Vivian Lim | viv.lim [at] gmail.com

Vivian Lim is a research assistant at CUNY. She is a doctoral candidate at the University of Pennsylvania Graduate School of Education with an interest in the role of mathematics curriculum in the civic engagement and development of youth. Vivian formerly worked as a high school mathematics teacher in Brooklyn, NY.

Pierre Beaudreau | pierre.beaudreau [at] gmail.com

Pierre is a Masters student at MIT in the City Design and Development program. He graduated with a degree in Urban Systems and Geography from McGill University where he was also introduced to computer programming and web development

Maren Hall-Wieckert | maren.hall.wieckert [at] gmail.com

Maren is a research assistant at Brooklyn College. He recently attended Oberlin College as an undergraduate and has worked in varying capacities within the field of education since graduating from there in 2013 with a BA in English Literature. His interests currently lie in Critical Geography and how notions of Place and Space impact educational research.

Researchers / Contributors

  • Alicia Roualt, Research Assistant, Civic Data Design Lab, MIT, 2012-2014
  • Benjamin Golder, Research Assistant, Civic Data Design Lab, MIT, Fall 2012
  • Christopher Rhie, MIT MCP Student, Spring 2013
  • Erica Deahl, Civic Data Design Lab, Project Manager, MIT 2013-2014
  • JD Godchaux, MIT Civic Data Design Lab, Fellow, Fall 2014
  • Jonah Rogoff, Research Assistant, Civic Data Design Lab, MIT 2013-2014
  • Jose Ojeda, Teaching Artist, CUP 2012 - 2013
  • Karuna Mehta, MIT Research Assistant, Civic Data Design Lab, MIT 2013-2015
  • Kat Hartman, MIT Civic Data Design Lab, Fellow, Fall 2014
  • Kellyn Farlow Morris, University of Maryland, 2012-2013
  • Lee Dwyer, Research Assistant, Civic Data Design Lab, MIT Fall 2013
  • Lela Prashad, MIT Civic Data Design Lab, Fellow, Fall 2014
  • Liqun Chen, Research Assistant, Civic Data Design Lab, MIT 2012-2013
  • Mary Candace Full, UCLA, Summer 2014
  • Mia Petkova, Research Assistant, Civic Data Design Lab, MIT 2013-2014
  • Mike Foster, GIS Data Visualization Specialist DUSP, MIT, 2014-2015
  • Pema Domingo-Barker, Program Assistant, CUP Summer 2013
  • Valeria Mogilevich, Deputy Director, CUP 2012-2013
  • Vikash Dat, MIT Civic Data Design Lab, Fellow, Summer 2013

NYC Department of Education & Math for America Teacher Partners

  • Alex Cristando, 2013-2015
  • Jordan Rosen, 2013-2015
  • Lauren Shookhoff, 2013-2015
  • Mathew Sullivan, 2013-2015
  • Phiola McFarlane, 2013-2015
  • Sara Katz, 2014-2015
  • Soledad Fernandez, 2013-2014
  • Tricia Stanley, 2014-2015

Other Thanks

Some of the icons used on this page were generously designed and made available by the following people:

Local Lotto Curriculum

Here is a general outline of the curriculum used in the classrooms to introduce students to the general ideas surrounding lottery tickets and probabilities. You can download the PDF version of the curriculum and/or the Powerpoint slides used to present the material here.

1 - Introduction to the Lottery: What do we know, what don't we know?

The unit begins with a collective brainstorm of students' knowledge about the lottery and having students share their ideas about what they might do if they won. Students then visualize what they already know about how the lottery works by creating images that represent their understanding of the lottery system. This helps students identify gaps in their shared knowledge and develop questions about how the lottery works as a system.

2 - Chances

2.1 - Exploring Games of Chance

Why do we win more in some games of chance than in others? In this lesson, students play a series of games of chance: 1) straight-bet roulette, 2) a "color pick" game involving choosing three colors from a set of 5 colors, and 3) Sweet Millions, a local lottery game. Students compare win and loss data from aggregated classroom trials of each game. They formulate ideas about the probability of winning each game, paying specific attention to the role of parameters.

2.2 - Counting Outcomes

Counting Outcomes Lesson Plan

Is it necessary to play a game many times to figure out the likelihood of winning? If not, how can we measure this likelihood? In this lesson, students learn that they can find the probability of winning a game by finding the ratio all the possible ways to win to all the possible outcomes for the game. Students work in groups to create a collective probability tree representing all possible outcomes in the "color pick" game. Using features of the tree model, students identify patterns to come up with the probability of winning the game.

2.3 - Winning the Jackpot

Summary Sheet Handout Summary Sheet Student Work

What is the probability of winning the jackpot lotteries in New York? And how can we calculate them without drawing a tree diagram? In many cases, the number of choices to consider for calculating probability is too large to be able to draw as a tree diagram. In this lesson, students reflect upon the "color pick" probability tree from the previous lesson to draw out the mathematical principles of combinatorics and probability including the multiplication principle, permutations, and combinations. Students then apply these principles to find the probability of winning various local lottery game jackpots.

2.4 - What is 4 million?

Students compare the probability of winning the various jackpot lotteries in New York and consider what the probabilities mean. Students scale very large numbers to familiar, smaller numbers.

2.5 - "Hey, Now You Know!"

The New York Lottery's slogan is "Hey, You Never Know." In this lesson, students use mathematics to respond to this slogan by revealing and explaining the unsaid facts about the lottery that are not given on their website. Students create posters that illuminate the mathematics of various local lottery games.

3 - Lottery in our City

3.1 - Interviews

In this session, students conduct interviews with people and with shopkeepers in the school's neighborhood. They gather data on who plays or does not play the lottery and why as well as which stores sell or do not sell lottery tickets. The interviews are recorded with photographs and audio. Each interview is tagged to its location and becomes part of an online map that displays all of the interviews that were conducted.

View interviews at citydigits.mit.edu/locallotto.

3.2 - Analyzing Interviews

Interview Scavenger Hunt Cards

What kind of information did we get from our interviews? In this lesson, students seek out examples of different perspectives on the lottery from their interviewees and share interview results with the rest of the class.

3.3 - Local Lottery Spendings as a Percentage of Income

Students become familiar with maps and mapping conventions by exploring the Lotta Facts digital choropleth maps of New York City showing median family income by neighborhood. Students embody the concept of median household income by playing the role of households with differing incomes, lining up, and identifying the median family income. Students are introduced to ratio tables as a way to compare lottery spending to household income across neighborhoods with varying incomes. Students use the percentage of income map on the Lotta Facts tool to compare lottery spending across neighborhoods relative to median family household income.

Who Spent More - Student Work

View maps at citydigits.mit.edu/locallotto.

3.4 - Aggregated Neighborhood Losses (or State Profits?)

Students analyze maps with data on percentage of income spent on the lottery and median household incomes to understand financial losses at the neighborhood level. Students locate map data containing median household income per day and scale household income to weekly and monthly values for a specific neighborhood. Students use map statistics on the percentage of income spent on lottery in a day for their neighborhood to calculate money spent on the lottery in a week, and a month. Students are presented with actual distribution of lottery profits. Students discuss how data and information from today's session could support an argument that the lottery is a regressive tax.

View maps at citydigits.mit.edu/locallotto.

4 - Opinions with Justifications - Student Lottery "Tours"

In small groups, students prepare a digital story board presentation to demonstrate their understanding of the lottery. The story board is an opinion story with evidence from mathematical analyses (Hey, Now You Know!), interviews, and map analyses. Students formulate their opinion statements and plan their story boards with sketches and notes on worksheets. Next, students finalize their storyboards and create their Lottery Tour storyboards on tablets/laptops. The tool archives student presentations for sharing with classmates and others.

View tours at citydigits.mit.edu/locallotto.

Local Lotto Technology

Overview

In choosing how to develop a technology that would allow for very rich but extensive datasets to be presented in a user-friendly manner to students, a number of choices needed to be made. The following are some of the main challenges faced in developing the platform.

Web Platform vs. Stand-Alone App

The decision to develop a web platform rather than a standalone smartphone or tablet app was made based on the requirement that the technology require the least amount of upkeep and compatibility effort, while still being versatile enough to use on a variety of technologies.

Based on these requirements a web app, which could be deployed from any internet browser, allowed for the project to be used in classrooms using laptops or desktops, or out in the field on tablets with 4G internet connection.

A standalone app would have required us to choose one operating system (i.e. iPhone, Android), and would subsequently require continuous compatibility updates, and ultimately reduce the number of technologies that could be used to explore content.

New York City Data

The project’s partner high schools are in New York City. Despite having a singular geographic focus, the datasets are derived from multiple sources.

Where does your data come from?

The geocoded list of pawnshops, received by the NYC Dept. of Consumer Affairs (DCA) in February, 2014; this represents a list of all establishments that currently possess a "pawnbrokers" license from DCA; please note that a handful (10-15) of establishments have overlapping addresses and thus multiple licenses

  • Data Sources: Business Analyst/RefUSA/NYC DCA
  • All InfoShare.org demographic and socioeconomic data compiled from the 2007-2011 ACS 5 year estimates (downloaded March 2014)
  • McDonalds = locations of McDonalds fast food chain (identified through RefUSA in March 2014)
  • Check Cashing = Geocoded list of 'check cashing' establishments (RefUSA) using SIC Code 609903
  • Money Transfer Services = Geocoded list of 'money transfer services' establishments (RefUSA) using SIC Code 609910
  • Commercial Banks = Geocoded list of commercial banks (ESRI Business Analyst) using SIC Code 602110

Mapping API

Mapbox

Mapbox API provided a strong and versatile background/base for displaying the variety of data collected for display. Its extensive documentation provided appreciated support in developing the application.

View the Mapbox Platform - http://www.mapbox.com

Student Submitted Content

As part of Local Lotto and Cash City, students add media to the platform and formulate opinions based on their field experiences, data analysis, and classroom discussions.

Images/Audio/Notes/Interviews

Students conduct interviews with local pedestrians and with shopkeepers in the school's neighborhood. In Local Lotto students gather data on who plays the lottery, with what frequency, and why; which stores sell lottery tickets; and investigate people’s opinions about the impact of the lottery on the local neighborhood. In Cash City students gather data on which financial institutions people use and why, and investigate people's opinions about the availability of financial institutions in their local neighborhood.

Student-collected data is then tagged to its location by the tool and becomes part of an aggregated, online map.

View User-Submitted Content - http://citydigits.mit.edu/locallotto#interviews-tab

Opinions

As a summative component to each City Digits module, students develop an opinion and justify it with a variety of available media, data, and map screenshots. Exploring the topic using the data from the maps combined with the user-generated content collected by their group or their peers gives youth space to take a position on a civic issue, connect it to their local neighborhood, and justify that position with mathematical analysis.

View User-Generated Opinions - http://citydigits.mit.edu/locallotto#tours-tab Go to Local Lotto Tool

Cash City Technology

Overview

In choosing how to develop a technology that would allow for very rich but extensive data to be presented in userfriendly manner to students in the classroom, a number of choices needed to be made. The following are some of the main challenges faced in developing the platform.

Web Platform vs. Stand-Alone App

The decision to develop a web platform rather than a standalone smartphone or tablet app was mas taken based on the requirement for a technology that requires the least amount of upkeep and compatibility effort, while still being versatile enough to use on a variety of technologies.

Based on these requirements, a web app, which could be deployed form any internet browser, allowed for the project to be used in classrooms using laptops or desktops, or out in the field on tablets with 4G internet connection.

A standalone app would require for us to choose one operating system (i.e. iPhone, Android), and would subsequently require continuous compatibility updates, and ultimately reduce the number of technologies that could be used to explore content.

New York City Data

With the high schools we were partnering with being in New York City, the data we needed to acquire was obviously that of New York as well. That said, the data required for communicating the right data doesn't always come from the same place requiring it to be acquired from mulitple sources.

Where does your data come from?

The geocoded list of pawnshops, received by the NYC Dept. of Consumer Affairs (DCA) in February, 2014; this represents a list of all establishments that currently possess a "pawnbrokers" license from DCA; please note that a handful (10-15) of establishments have overlapping addresses and thus multiple licenses

The unit begins with a collective brainstorm of students' knowledge about the lottery and having students share their ideas about what they might do if they won. Students then visualize what they already know about how the lottery works by creating images that represent their understanding of the lottery system. This helps students identify gaps in their shared knowledge and develop questions about how the lottery works as a system.

  • Data Sources: Business Analyst/RefUSA/NYC DCA
  • All InfoShare.org demographic and socioeconomic data compiled from the 2007-2011 ACS 5 year estimates (downloaded March 2014)
  • McDonalds = locations of McDonalds fast food chain (identified through RefUSA in March 2014)
  • Check Cashing = Geocoded list of 'check cashing' establishments (RefUSA) using SIC Code 609903
  • Money Transfer Services = Geocoded list of 'money transfer services' establishments (RefUSA) using SIC Code 609910
  • Commercial Banks = Geocoded list of commercial banks (ESRI Business Analyst) using SIC Code 602110

Mapping API

Mapbox

Mapbox API provided a strong and versatile background/base for displaying the variety of data to be displayed. Its extensive documentation also meant much appreciated support for developing the application.

View the Mapbox Platform - http://www.mapbox.com

Student Submitted Content

With the technology finalized and working, students were then able to add media to the platform and begin formulating opinion based on their observations and discussions with peers.

Images/Audio/Notes/Interviews

In this session, students conduct interviews with people and with shopkeepers in the school's neighborhood. They gather data on who plays or does not play the lottery and why as well as which stores sell or do not sell lottery tickets. The interviews are recorded with photographs and audio. Each interview is tagged to its location and becomes part of an online map that displays all of the interviews that were conducted.

View User-Submitted Content - http://citydigits.mit.edu/cashcity/media

Opinions

With all the media added to the platform, students were then asked to compile a variety of the content into opinion pieces. By asking students to explore the topics using the data from the maps, and the user-generated content collected by their group or their peers, this helped bring the topic from simple information to internalizing it and trying to take a position/opinion on it.

View User-Generated Opinions - http://citydigits.mit.edu/cashcity/opinion Go to Cash City Tool

Cash City Curriculum

Here is a general outline of the curriculum used in the classrooms to introduce students to the general ideas surrounding alternative financial institutions (i.e. pawn shops, check cashing) and their financial implications. You can download the PDF version of the curriculum and/or the Powerpoint slides used to present the material here.

1 - Introduction: How do pawn shops work?

The unit begins with a collective brainstorm of students' knowledge about pawn shops. Students then watch and discuss a skit simulating a pawn shop transaction to learn about how a pawn shop loan works and to build a shared understanding about the terms of a pawn. Finally, students create a poster that serves as a visual display of their knowledge and questions about pawn shops.

Pawn shop skit

2 - The Cost of Pawning

2.1 - How much does it cost to pawn?

Students are presented with scenarios in which they must figure out the cost of pawning an item, including interest and fees. Students calculate interest using ratio tables to perform percentage calculations (without a calculator). Students consider and discuss the value of obtaining a loan this way.

EZ Pawn handout

2.2 - Modeling the growth of the cost of a pawn

Students match tables and graphs modeling how the cost of various pawn shop loans grow over time. Through this activity, students are introduced to the idea of linear growth as students observe that the amount owed increases at a constant rate, which leads to writing linear equations.

Tables and graphs matching activity

2.3 - Cash loan options and APR

What other cash loan options are available besides pawning? This lesson introduces students to the idea of Annual Percentage Rate (APR) to compare the cost of various types of cash loans, including credit card cash advances, credit union loans, and secured/unsecured personal bank loans. Students are introduced to APR through a scenario in which someone pawns an item and renews it multiple times such that she has taken out her loan for one year. Students then compare loans by considering their terms and APR.

Loan comparison chart Loan comparison role playing activity

3 - Financial Insitutions in our City

3.1 - How are financial institutions distributed across the boroughs of NYC? (Floor map)

In this lesson, students begin to explore the idea of fair vs. equal distribution of resources (i.e. financial institutions including pawn shops and banks) across the five boroughs of New York City. The lessons starts with students exploring a giant floor map of New York City, walking on the map and marking landmarks and other locations they recognize. After students are oriented to the map, the teacher guides the students in a physical demonstration of what the distribution of pawn shops and banks across the boroughs might look like if they were divided equally vs. proportionately to the number of households. Students compare these means of distribution to the actual numbers and discuss what they consider to be “fair.”

Distribution across boroughs lesson plan Distribution across boroughs teacher presentation

3.2 - Patterns of locations of financial institutions in NYC (Digital maps)

Students explore the Cash City tool’s digital maps showing the locations of banks and alternative financial institutions (AFIs, including pawn shops, check cashing, and wire transfers) in order to learn about the distribution of various financial services across New York City. Students also examine demographics maps on the tool (% population in poverty, median household income, % unemployment, and % foreign born) to make observations about relationships between neighborhood characteristics and availability of financial services.

Map exploration handout

View maps at citydigits.mit.edu/cashcity.

3.3 - Comparing the distribution of financial institutions in NYC using ratio maps (Digital maps)

In this lesson, students continue their exploration of the Cash City tool’s digital maps, extending their thinking to consider the density of institutions relative to another variable (e.g. banks per AFIs, banks per square mile, or households per bank). Students choose and make sense of ratio maps to make comparisons between neighborhoods.

Ratio map handout

View maps at citydigits.mit.edu/cashcity.

3.4 - Data from the field

In this lesson, students go on a field trip outside of school walls to gather digital media including photos of financial institutions as well as interviews with shopkeepers/employees of financial institutions and pedestrians in the school's neighborhood. Students gather information about the services and fees offered by financial institutions and talk to people about their reasons for using/not using certain services. Each photo and interview is tagged to its location and becomes part of an online map that displays all of the data that was uploaded.

Question writing handout

View media at citydigits.mit.edu/cashcity/media.

4 - Conclusion: Student Opinions

To conclude the project, students create and publish their opinions about banks, pawn shops, and other AFIs on the Cash City tool. They use the mathematics they have learned, snapshots of digital maps from the tool, as well as media they gathered during the field trip to support their opinions. Students look at and make comments on each other’s opinions and discuss their final reflections on the project.

View opinions at citydigits.mit.edu/cashcity/opinion.

All Rights Resrved © City Digits 2015