Modeling Prompt 6
A New Town
Integrated Math 1
In-Class Launch
Use after Unit 5, Lesson 8
Show students an aerial image of a city. This example is Cambridge, Massachusetts.
Ask students, “What shapes do you see?” (Polygons, triangles, circles, straight lines, curves.) Choose a feature on the map such as a group of buildings or a bridge, and ask students what they would need to know in order to figure out the size of that feature. (If I knew the scale of the map, then I could take measurements and multiply them by the scale factor to find the real size.)
Tell students that, in this task, they will make a town of their own.
Teacher Instructions
The location of the new town should be customized, based on students’ interest, if possible. For example, each group could choose a location, or the location could be somewhere nearby.
Provide each group access to a device that students can use to view mapping software and zoom in and out on the map as needed. Give students the GPS coordinates of the land so that they can easily find the location on an online map. The land shown in the Task Statement has GPS coordinates (35.620371, –104.277026).
Graphing applications, such as Desmos, also can be helpful when students are making their grids, because it’s easier to zoom in and out. Students may want to print out views of the town at different zoom levels, and then draw their plots on the grid by hand.
Here is a piece of land that will be developed into a town.
Your job is to divide up the land into plots that will be sold to people and businesses.
- Decide what you want the town to look like. For example, where will you put the major roads? Will there be a downtown business district surrounded by neighborhoods, or will businesses and houses be mixed together? Where will you mark the boundaries of the town? You do not have to use all the land on the map.
- Many people, such as architects and construction crews, will use your plan to communicate with each other while they work on their building projects. Sketch the town on a coordinate grid so that everyone can communicate about where buildings and other features should go.
- Choose the locations for important buildings in the town, such as a school, a fire station, and a grocery store, as well as any other features you want to plan in advance.
- Break up the remaining land into plots. These plots will be sold so that other people can build on them. Small plots are good for houses, and larger plots could become farms or warehouses.
- Calculate the sizes of the plots. You do not need to calculate the size of each individual plot, but you should record the size of each type.
Your final product will be a map showing how you divided the land, along with calculations that prove the size of each type of plot.
Teacher Instructions
The location of the new town should be customized, based on students’ interest, if possible. For example, each group could choose a location, or the location could be somewhere nearby.
Provide each group access to a device that students can use to view mapping software and zoom in and out on the map as needed. Give students the GPS coordinates of the land so they can easily find the location on an online map. The land shown in the Task Statement has GPS coordinates (35.620371, –104.277026).
Graphing applications, such as Desmos, also can be helpful when students are making their grids, because it’s easier to zoom in and out. Students may want to print out views of the town at different zoom levels, and then draw their plots on the grid by hand.
If students struggle to design the whole town, divide the work among several small groups or pairs. For example, a group of 6 could make the grid and choose the overall structure of the town. Dividing the group into three pairs, each pair could then work on a different area of the town and decide on the size of the plots in that area.
Here is a piece of land that will be developed into a town.
Your job is to divide up the land into plots that will be sold to people and businesses.
- Sketch the town on a coordinate grid. Many people, such as architects and construction crews, will use your plan to communicate with each other while they work on their building projects, so they need a consistent way to talk about locations. Making a grid also will help you see how much space is in the town and decide how to divide it into plots. Choosing a scale for your grid is also important. It will help if each unit on the grid represents a quantity that is easy to work with, such as 50 feet or 100 feet.
- Decide what you want the town to look like. For example, where will you put the major roads? Will there be a downtown business district surrounded by neighborhoods, or will businesses and houses be mixed together? Where will you mark the boundaries of the town? You do not have to use all the land on the map.
- Choose the locations for important buildings in the town, such as a school, a fire station, and a grocery store, as well as any other features you want to plan in advance. Before you decide where to place the buildings, research or estimate the average size of each type of building. Towns usually are divided into blocks, so it also will help to know the average size of a city block.
- Break up the remaining land into plots. These plots will be sold to other people so they can build on them. Small plots are good for houses, and larger plots could become farms or warehouses. Make sure your plots are a reasonable size for their intended use.
- Show how you know the sizes of the plots. You do not need to calculate the size of each individual plot, but you should record the size of each type.
Your final product will be a map showing how you divided the land, along with calculations that prove the size of each type of plot.