Illustrative Math Alignment: Grade 6 Unit 1

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.

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 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 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 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 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 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.

All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms.

All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms.

In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine.

In this video, students see a derivation of the formula for the volume of a pyramid. This involves a hands-on activity using unit cubes, along with analysis, and a detailed algebraic derivation.

In this video, students see a derivation of the formula for the volume of a pyramid. This involves a hands-on activity using unit cubes, along with analysis, and a detailed algebraic derivation.

In this video, students see a derivation of the formula for the volume of a pyramid. This involves a hands-on activity using unit cubes, along with analysis, and a detailed algebraic derivation.

In this video, students see a derivation of the formula for the volume of a pyramid. This involves a hands-on activity using unit cubes, along with analysis, and a detailed algebraic derivation.

Topic

Polynomials

Description

A cubic example where the volume of a cube, A = x3 + 3x2 + 3x + 1, is used to find the side length.

Example 6: Given the volume A = x3 + 3x2 + 3x + 1, factor as (x + 1)3, so the side lengths are x + 1.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

Topic

Polynomials

Description

Another cubic example solving for side length with volume A = x3 - 3x2 + 3x - 1.

Example 7: For the volume A = x3 - 3x2 + 3x - 1, express as (x - 1)3 to determine side lengths of x - 1.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

Topic

Polynomials

Description

An example showing how to find the side lengths of a square given its area, A = x2+ 2x + 1.

Example 1: Given the area A = x2+ 2x + 1, find the side lengths. Solution: Express the area as a perfect square, (x + 1)2, so the side lengths are x + 1.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

Topic

Polynomials

Description

Another example of finding the side lengths of a square with area A = x2+ 4x + 4.

Example 2: Given A = x2+ 4x + 4, find the side lengths. Solution: Factor as (x + 2)2, so the side lengths are x + 2.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

Topic

Polynomials

Description

Shows how to determine the side lengths of a square with area A = x2 - 2x + 1.

Example 3: For A = x2 - 2x + 1, the solution expresses it as (x - 1)2, making the side lengths x - 1.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

Topic

Polynomials

Description

Example solving for side lengths of a square with area A = x2 - 4x + 4.

Example 4: Given A = x2 - 4x + 4, factor as (x - 2)2 to find side lengths x - 2.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

Topic

Polynomials

Description

Solves for side lengths of a square with area A = x2 + 6x + 9.

Example 5: With A = x2 + 6x + 9, factor as (x + 3)2, giving side lengths x + 3.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is part of a collection of math examples that focus on volume.

This is the transcript for video entitled: "Geometry Applications--Volume of a Pyramid."

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