Illustrative Math Alignment: Grade 6 Unit 1

In this program we look at applications of area and volume. We do this in the context of three real-world applications. In the first, we look at the sinking of the Titanic in the context of volume and density. In the second application we look at the glass pyramid at the Louvre Museum and calculate its surface area. In the third application we look at the Citibank Tower in New York City to study the ratio of surface area to volume to learn about heat loss in tall buildings.

The sinking of the Titanic provides an opportunity to explore volume, density, and buoyancy. Students construct a mathematical model of the Titanic to determine why it sank and what could have been done to prevent it from sinking.

The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid.

The Citibank Tower in New York City presents some unique design challenges. In addition it has to cope with a problem that all tall structure have to deal with: heat loss. By managing the ratio of surface area to volume, a skyscraper can effective manage heat loss.

Topic

3D Geometry

Definition

Surface area is the total area that the surface of a three-dimensional object occupies.

Description

In the realm of three-dimensional geometry, surface area is a fundamental concept that quantifies the extent of a 3D shape's exterior surface. This measure is crucial for various applications, including engineering, architecture, and everyday tasks. For example, when painting a room, the surface area of the walls, ceiling, and floor must be calculated to determine the amount of paint required.

The formula for the Surface Area of a Cube.

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The formula for the Surface Area of a Cylinder.

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The formula for the Surface Area of a Rectangular Prism.

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The formula for the Surface Area of a Sphere.

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The formula for the Surface Area of a Square Pyramid.

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The formula for the Surface Area of a Triangular Prism.

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The formula for the Surface Area of a Triangular Pyramid.

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Topic

Geometric Models

This set of tutorials provides an overview of the 24 worked-out examples that show how to calculate the surface area of different three-dimensional figures.

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Topic

Geometry Concepts

Description

This image presents an irregular polygon superimposed on a square grid. The grid serves as a crucial tool for estimating the area of the polygon by providing a systematic method of counting squares.

To estimate the area, students should count the number of full squares entirely contained within the irregular polygon. For partial squares intersected by the polygon's edges, they need to approximate what fraction of each square is covered. By summing these full and partial square counts, students can arrive at a reasonable estimate of the polygon's area.

Topic

Geometry Concepts

Description

This image showcases another closed curve area superimposed on a square grid. The grid acts as a vital tool for estimating the area enclosed by the curve through a square-counting method.

To estimate the area, students should begin by counting the number of whole squares that are completely enclosed within the closed curve. For squares that are partially covered by the curve, students need to approximate what fraction of each square is included. By combining these full and partial square counts, students can arrive at a reasonable estimate of the area within the closed curve.

Topic

Geometry Concepts

Description

This image showcases another irregular polygon overlaid on a square grid. The grid functions as an essential tool for estimating the area of the polygon through a square-counting method.

To estimate the area, students should first count the number of complete squares that fall entirely within the boundaries of the irregular polygon. For squares that are only partially covered by the polygon, students need to assess what fraction of each square is included. By adding these full and partial square counts, students can develop a reasonable estimate of the polygon's total area.

Topic

Geometry Concepts

Description

This image depicts an irregular polygon placed on a square grid. The grid acts as a vital tool for estimating the area of the polygon using a square-counting approach.

To estimate the area, students should begin by counting the number of whole squares that are completely enclosed within the irregular polygon. For squares that are partially covered by the polygon's edges, students need to approximate what portion of each square is included. By combining these full and partial square counts, students can arrive at a reasonable estimate of the polygon's total area.

Topic

Geometry Concepts

Description

This image features an irregular polygon superimposed on a square grid. The grid serves as a crucial tool for estimating the area of the polygon through a square-counting method.

To estimate the area, students should first count the number of complete squares that fall entirely within the boundaries of the irregular polygon. For squares that are only partially covered by the polygon, students need to assess what fraction of each square is included. By summing these full and partial square counts, students can develop a reasonable estimate of the polygon's total area.

Topic

Geometry Concepts

Description

This image showcases a closed curve area outlined on a square grid. The grid functions as an essential tool for estimating the area enclosed by the curve through a square-counting approach.

To estimate the area, students should first count the number of complete squares that fall entirely within the closed curve. For squares that are only partially enclosed by the curve, students need to assess what fraction of each square is included. By adding these full and partial square counts, students can develop a reasonable estimate of the total area within the closed curve.

Topic

Geometry Concepts

Description

This image presents a closed curve area superimposed on a square grid. The grid serves as a crucial tool for estimating the area enclosed by the curve using a square-counting method.

To estimate the area, students should begin by counting the number of whole squares that are completely enclosed within the closed curve. For squares that are partially covered by the curve, students need to approximate what portion of each square is included. By combining these full and partial square counts, students can arrive at a reasonable estimate of the total area within the closed curve.

Topic

Geometry Concepts

Description

This image features a closed curve area outlined on a square grid. The grid acts as a vital tool for estimating the area enclosed by the curve through a square-counting approach.

To estimate the area, students should first count the number of complete squares that fall entirely within the closed curve. For squares that are only partially enclosed by the curve, students need to assess what fraction of each square is included. By summing these full and partial square counts, students can develop a reasonable estimate of the total area within the closed curve.

Topic

Geometry Concepts

Description

This image depicts a radiating figure superimposed on a square grid. The grid serves as an essential tool for estimating the area of the figure using a square-counting method.

To estimate the area, students should begin by counting the number of whole squares that are completely enclosed within the radiating figure. For squares that are partially covered by the figure's edges, students need to approximate what portion of each square is included. By combining these full and partial square counts, students can arrive at a reasonable estimate of the figure's total area.

Topic

Geometry Concepts

Description

This image presents a closed curve area outlined on a square grid. The grid functions as a crucial tool for estimating the area enclosed by the curve using a square-counting approach.

To estimate the area, students should first count the number of complete squares that fall entirely within the closed curve. For squares that are only partially enclosed by the curve, students need to assess what fraction of each square is included. By summing these full and partial square counts, students can develop a reasonable estimate of the total area within the closed curve.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This Teacher's Guide provides an overview of the 24 worked-out examples that show how to calculate the surface area of different three-dimensional figures.

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11/14/11. In this issue we commemorate the 125th anniversary of the Statue of Liberty. We also look at the geometry and architecture of this monument.

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