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Community Based Mathematics Project of Philadelphia

Penn's Map
Submitted By: Caroline Ebby (University of Pennsylvania)

Display Image
Sepia tone photo of an old map of Penn
Grade
Grade
5th Grade
Math Focus
Math Focus
Graphing on the coordinate plane
Context
Context
Maps
Common Core State Standards
Geometry
Graph points on the coordinate plane to solve real-world and mathematical problems: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). (Math.5.G.A.1)Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. (Math.5.G.A.2)
Overview / Lesson Summary

In this lesson, students look at historic and present day maps of Philadelphia to understand the importance of a grid system in defining locations. Students learn how to navigate and find locations on a coordinate grid.

Preparation and Materials
  • You will need the Penn's Map powerpoint for this lesson.
Introducing the Context

Use the Penn's Map PowerPoint to project the picture of map of Philadelphia from 1683 and give students the handout on Penn's Map.  After reading and or discussing the information on the handout about William Penn, ask students for their observation:

  • What do you notice about Penn's layout for the city streets? (This is an opportunity to review geometric vocabulary such as symmetry, rectangles, parallel and perpendicular lines, intersection, right angles)
  • Is this a good design for a city? Why or why not?

The next slide shows maps of London and Boston around the same time. What is different about the layouts of those cities?

Explain to students that Philadelphia was one of the first North American cities to use a grid system and that William Penn claimed that this design would help prevent overcrowding, fire and disease, which were common in many European cities at the time. Share some or all of the following historical facts to help explain why he decided to use a grid system:

  • Penn grew up in 17th century London which had no sensible pattern to its streets, houses that were built too close together, no open green spaces and a physical structure that made its citizens susceptible to spread of disease (Great Plague 1665-66), and its buildings at risk of destruction by fire (Great Fire 1666).
  • He wanted Philadelphia to be as fire safe as possible, after he witnessed the Great Fire of London. He laid out wide streets and planned green spaces for parks that would serve as fire breaks.
  • He envisioned it as a utopian city: organized in orderly geometric pattern, a rectangular grid divided into quadrants, each quadrant would contain a public park
  • He planned it as a collective of country estates: properties to be half-acre or one-acre lots, investors able to plant own garden

Finally, show the current map of Center City, Philadelphia and have students locate what is the same from Penn's Map:

  • Note the four "squares": Logan circle, Rittenhouse Square, Franklin Square and Washington Square with City Hall in the middle
  • Note the streets are in a grid system

Penn's original design had much larger blocks (one block would have been Walnut to Chestnut, with no Samson in between) but the block were too large for the rowhouses that were built at the time, so they ended up being subdivided. 

Note that if you pull up a map of Center City on Google Maps, it will appear to be skewed. This is because google maps uses true north to orient its maps.

 

Introducing the Mathematical Ideas

The remainder of the powerpoint is animated to show how the streets in Philadelphia are named:

  • the vertical, N-S streets begin at the Delaware with 2nd street and increase by one as you move West to the Schuylkill
  • The horizontal streets are mostly named for trees. You can point out that Race and Arch used to be named for Mulberry and Sassafrass (South St was Cedar St). Tell students that next time they go to the Ritz East movie theatre, look at the layout of the old streets in the plaza out front (see picture below)
  • Note that this rendering does not show all the horizontal streets, only the ones that define major blocks with the numbering system.

Explain how the numbering system works to locate addresses through the examples given on the slides

  • 1500 Walnut St is at 15th and Walnut
  • 876 Locust St would be on Locust, between 8th and 9th
  • 200 S 12 St would be on 12ths st, 2 blocks south of Market St. at Walnut
  • 150 N. 21st st would be on 21st, 1.5 blocks north of Market St or between Arch and Race
Exploration

Have students continue to find locations on the map. If you school is in the city, use a map of the local neighborhood around the school to have them find locations and addresses.

Extensions
Additional Images
Outside of the Ritz East
View Image at Full Size

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