Linear Equations

NZ Level 7 (NZC) Level 2 (NCEA)

Town Planning (Investigation)

Lesson

- To explore uses of perpendicular and parallel lines in real life
- To practice finding parallel and perpendicular lines

- Pencil
- Crayons
- Graphing paper
- Straight edge
- Internet
- Printer

You have just been appointed city planner for a new town! You will need to decide what buildings go where and determine the placement of the streets as well.

- Draw in the four quadrants of the coordinate plane on your graph paper. Each of the quadrants will represent a section of the town (Northwest, Northeast, Southwest, Southeast).
- Decide on at least 10 buildings that you want to include in your town. These buildings can be residential, businesses, or town buildings (fire department, town hall etc.).
- Determine where you want to place the buildings that you have decided on. You can strategically place the buildings however you would like. Be sure to label each of the buildings. The buildings can take up a varying amount of boxes.
- Design a plan for the streets in your city. Each street will be represented by a line or line segment. Make sure that you can identify the equation of each of the streets you create. Try to create some streets that are parallel to one another and others that are perpendicular to one another. Avoid making streets that are horizontal or vertical.
- Color in your town. If you want you can add parks in any empty spaces left on your map.
- Don’t forget to name your town.

- How many parallel streets are there in your town? What are their equations?
- How many perpendicular streets are there in your town? What are their equations?
- Are there any streets in your town that intersect (or that would intersect if they were continued) in a non perpendicular way? What are their equations?
- In what situations did you use parallel lines for your town?
- In what situations did you use perpendicular lines in your town?
- What strategy did you use to plan the positioning of the buildings you chose?
- Compare with a friend!
- Compare and contrast the strategy they used to place their buildings to yours.
- Compare and contrast the amount of parallel and perpendicular lines in both of your towns.
- Are any of your streets parallel to any of their streets? Why or why not?
- Are any of your streets perpendicular to their streets? Why or why not?
- If you replied no to part (c) what is the equation of a line that would be parallel to one of their streets?
- If you replied no to part (d) what is the equation of a line that would be perpendicular to one of their streets?

- Work with a friend to lookup a map of your town and draw a grid over the top of it. Are there any streets in your town that are parallel? Are there any streets in your town that are perpendicular? Explain.

Apply co-ordinate geometry techniques to points and lines

Apply co-ordinate geometry methods in solving problems