## Modeling

## Opening

# Modeling

- Watch the video.
- Discuss how this architect uses mathematical modeling in his work.

VIDEO: Architect

- Watch the video.
- Discuss how this architect uses mathematical modeling in his work.

VIDEO: Architect

This is a city view of One World Trade Center in New York City.

- How tall do you think the building is (including the antenna)?

Find measurements using scale drawings.

Scale is difficult to determine with nothing to refer to. The One World Trade Center building has a cube-shaped base that is 200 ft in height, with trapezoid and triangle faces rising above the cube. You can use the picture of the One World Trade Center, as well as what you know about the height of its cube base, to approximate the height of the building.

- Approximately how many 200-ft sections is the building in height?
- How tall do you think the building is?

- What do you need to measure on the drawing to find the scale of the drawing?
- To find the height of the building, think about what you need to solve for.
- How can you set up the equation?

Villa Savoye is a house designed by the Swiss architect Le Corbusier. It was built between 1928 and 1931 and is considered a prime example of modern architecture and the International Style.

Look at the photo and the floor plans of the house.

- If the columns are 4.75 m apart, what are the length and width of the house?
- What is the area of the living room (the gridded area in the middle drawing of the second floor)?

- What is the scale expressed as a ratio?
- What are you solving for?
- How can you set up the equation?
- How can you estimate area?

This is a map of Rhode Island, the smallest state in the United States.

- What is the scale of the map?
- What is the distance between Providence (the state capital) and Newport?
- Excluding Block Island, what is the distance from the top of the state to the bottom of the state at its southernmost point?

- What is the scale expressed as a ratio?
- How can you use the scale to determine distances?

This globe has a diameter of 12 in.

- If the earth has a diameter of about 7,900 mi at the equator, what is the scale of the globe?
- About how wide is Africa in miles at its widest point?

In this drawing of an amoeba, the scale is in µm, which stands for micrometer; 1 micrometer is $\frac{1}{\mathrm{1,000,000}}$ of a meter.

- What is the approximate length of the amoeba in micrometers?
- About how long is the nucleus in micrometers?

The Burj Khalifa in Dubai is currently the tallest building in the world at 2,717 feet—which is a little more than half of a mile.

- If a model of the building were made at a scale of 50 : 1—that is, 50 ft to 1 in.—how tall would the model be?

Take notes about other students’ approaches to using scale drawings to find measurements.

As your classmates present, ask questions such as:

- How accurate do you think your results are? Explain.
- How is the image on your screen different from the actual drawing or model?
- Why is scale used?
- How did you make sense of the problem? What did you do first?
- How could you measure more accurately?

Write a summary about scale drawings.

Check your summary:

- Do you explain why scale drawings are used?
- Do you provide an example of scale and explain what it means?
- Do you explain how to use the scale in a scale drawing to find measurements of the thing that the drawing represents?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**Some places that I have seen scale used are …**