# Collapse Zone (AIG IRP)

## Overview

Students construct various buildings using centimeter cubes or inch cubes. Students cause the buildings to collapse in order to determine the appropriate collapse zone firefighters should mark off for any building in danger of collapse during a fire. This lesson was developed by NCDPI as part of the Academically and/or Intellectually Gifted Instructional Resources Project. This lesson plan has been vetted at the state level for standards alignment, AIG focus, and content accuracy.

# Lesson Overview

**Brief Description of Lesson/Task/Activity: **Students construct various buildings using centimeter cubes or inch cubes. Students cause the buildings to collapse in order to determine the appropriate collapse zone firefighters should mark off for any building in danger of collapse during a fire.

**Time Frame: **45 minutes-1 hour

**Type of Differentiation for AIGs:**

- Extension

**Adaptations for AIGs:**

- Content
- Process
- Product

**Explanation of How Resource is Appropriate for AIGs: **Gifted students will use their understanding of multiplication of fractions and whole numbers, finding regularity in repeated reasoning and experimenting in order to determine a standard collapse zone for firefighters to use when fighting fire on any building. Using the collapse zone they determined to be safe, students will find the area of collapse zones of various buildings given the length and width of the base and the height of the building. They will compare the areas they deemed safe to the areas of the standard collapse zone (1 ½ x height of the building).

**Needed Resources/Materials:**

- inch or centimeter cubes
- grid paper
- measuring tools (flexible meter sticks recommended)

**Sources:**

- (2000) Essentials of Fire Fighting 4th Edition. International Fire Service Training Association. p. 73-75

**Mathematical Practices:**

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

6. Attend to precision.

8. Look for and express regularity in repeated reasoning.

# Stage 1: Engage

Pose the task…

Today you will be firefighters. Your job is to determine a standard collapse zone for all members of your fire department to use when fighting fire on a building in danger of collapse. A collapse zone is the area around the base of a building that should not be occupied by any firefighting personnel, equipment, or civilians. There are many factors to consider when determining the size of the area that is unsafe around the base of the building. The collapse zones you create will be rectangular and will extend the same distance from the base of the building on all four sides.

You will begin the task by creating buildings (right rectangular prisms) of varying sizes, using centimeter or inch cubes, and causing them to collapse (The group should come to an agreement on how to cause the buildings to collapse, and this method should be used by all groups throughout the activity.). You will collect data (Grid paper, string for measuring distance, or meter sticks may be used.) on the location (distance from the base of the building) of the debris farthest from the building. Once you feel that you have adequate data, you will determine a standard way to find the collapse zone of any building.

Using grid paper provided by your teacher1, draw the collapse zone of a building with base dimensions 40 ft. by 22 ft. and a height of 45 ft. based on the collapse zone you chose for your fire department.

Once the task has been posed, facilitate a discussion about the task, making sure all students understand their goal. A video of a building collapsing may be shared in order to distinguish between collapsing and exploding or falling over. Come to an agreement on a method for causing their model buildings to collapse in the classroom. One method for causing buildings to collapse is to pull a cube from the bottom of the building. The following discussion questions may be asked throughout the class period to focus and deepen students’ thinking about the task at hand.

Discussion questions…

- What should be considered when determining the area that is unsafe for use?
- What are some consequences of making the collapse zone too small?
- If the base of the building and the collapse zone are both rectangular what points of the collapse zone will be equidistant from the building? What points will be farthest from the base of the building? Explain your thinking.
- Your fire department has tasked you and your team with determining a standard collapse zone to use on all fire scenes. This standard collapse zone will be recorded as a standard operating procedure, so precision is important for the safety of all personnel. How will you determine a standard collapse zone with the tools provided (cubes, measuring tools, grid paper)?
- How does your collapse zone compare to the collapse zones of other groups in the class? Why aren’t they identical?

Large grid paper should be created by taping or gluing pieces of grid paper together. Chart grid paper may be used if available.

# Stage 2: Elaborate

Once students have had ample time to experiment, identify the collapse zone they deem appropriate for their fire department, and represent the building and collapse zone in part 2 on the grid paper, pose the following…

The standard collapse zone for firefighters is 1 ½ times the height of the building. Firefighters must determine the height of the building (exact height from a preplan or estimate based on their judgment if no building plans are available), multiply the height by 1 ½ and measure that distance away from all sides of the building. Usually they create a circular collapse zone, but we will continue to use a rectangular collapse zone.

For the building and collapse zone you have represented on your grid paper, construct the actual collapse zone using the formula given (1 ½ x height of building). Represent the actual collapse zone in a way that is easily distinguished from your fire department’s collapse zone. Compare the areas of your collapse zone and the actual standard collapse zone.

Evaluate the students’ work based on their numerical findings and on the logic of their reasoning when answering the questions provided.

# Stage 3: Evaluate

Possible follow-up questions…

- Suppose the state of North Carolina decided that all fire departments in the state should increase the collapse zone to 2 ¼ times the height of the building. What events might cause the state to make the change? How would the new collapse zone area compare to the original collapse zone (1 ½ times the height)?
- How might fire-fighting organizations determine when a collapse zone is needed?
- Why do you think it’s important to have a standard collapse zone?
- How might the process of finding the actual standard collapse zone compare to the process you used in finding your fire department’s collapse zone?