Illustrative Math Alignment: Grade 6 Unit 1

Topic

Area and Volume

Description

This segment explores the surface area-to-volume ratio using the Citigroup Building as an example. It discusses how this ratio impacts energy efficiency in buildings and compares it to natural examples like polar bears and snakes for context.

Topic

Area and Volume

Description

This segment focuses on surface area, using the Louvre Pyramid to highlight geometric tessellations and triangular net calculations. It explains the surface area formula for pyramids and how these calculations are applied in architectural design and material efficiency.

Topic

Area and Volume

Description

This segment focuses on surface area, using the Louvre Pyramid to highlight geometric tessellations and triangular net calculations. It explains the surface area formula for pyramids and how these calculations are applied in architectural design and material efficiency.

Topic

Area and Volume

Description

This segment focuses on surface area, using the Louvre Pyramid to highlight geometric tessellations and triangular net calculations. It explains the surface area formula for pyramids and how these calculations are applied in architectural design and material efficiency.

Topic

Area and Volume

Description

This segment focuses on surface area, using the Louvre Pyramid to highlight geometric tessellations and triangular net calculations. It explains the surface area formula for pyramids and how these calculations are applied in architectural design and material efficiency.

Topic

Area and Volume

Description

This segment focuses on surface area, using the Louvre Pyramid to highlight geometric tessellations and triangular net calculations. It explains the surface area formula for pyramids and how these calculations are applied in architectural design and material efficiency.

Topic

Area and Volume

Description

This segment focuses on surface area, using the Louvre Pyramid to highlight geometric tessellations and triangular net calculations. It explains the surface area formula for pyramids and how these calculations are applied in architectural design and material efficiency.

Topic

Rational Functions

Description

Examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates.

This video provides a detailed explanation of examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates and its significance in understanding rational functions.

Topic

Rational Functions

Description

Examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates.

This video provides a detailed explanation of examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates and its significance in understanding rational functions.

Topic

Rational Functions

Description

Explains submarine pressure and volume relationships using rational functions, illustrating depth impacts on vessel integrity and scuba safety.

This video provides a detailed explanation of explains submarine pressure and volume relationships using rational functions, illustrating depth impacts on vessel integrity and scuba safety. and its significance in understanding rational functions.

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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