 It's one of the most recognizable residences in the world, but just how big is the White House? Even if you've never visited, this lesson will give you a sense of its scale.

Students use a 1:480 scale model of the White House to find the surface area of the walls and how much it would cost to paint them. They figure out how many models it would take to fill up the building, and finally, how much it costs to heat in the winter. In the process, they confront misconceptions about how area and volume change as distance changes.

### Students will

• Measure lengths and calculate areas on a model's net, then scale them up using the scale factor
• Describe how a rectangle's area changes as its dimensions change by a scale factor
• Use the surface area of the White House's vertical walls to find the cost of painting them
• Build a scale model of the White House and find its volume
• Find how many models are equivalent to the interior space of the real White House
• Find the volume of the White House and calculate the cost of heating it in winter

### Before you begin

Students should be able to find the area of a rectangle and the volume of a rectangular prism given their respective dimensions. They should understand that a scale factor is a ratio of lengths between two similar figures. They should be able to measure a length to the nearest tenth of a centimeter, and convert lengths from centimeters to meters.

In this lesson, students work with a three-dimensional object composed of rectangular prisms and a half-cylinder. They build this object out of a 2D net. Prior experience with such objects is helpful but not necessary.

• Calculators
• Scissors
• Tape

James Hoban