Illustrative Math Alignment: Grade 7 Unit 9

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. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume]: https://www.media4math.com/library/geometry-applications-area-and-volume-segment-3-ratio-surface-area-volume

Frank Lloyd Wright’s architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes. Some of the rectangular forms in this building seem to defy gravity, as we explore the properties of squares and rectangles that allowed Frank Lloyd Wright to push the envelope of design and structure. Note: The download for this resources is the Promethean Flipchart.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-quadrilaterals-segment-2-squares-and-rectangles

The Puerta de Europa towers in Madrid bring parallelograms front and center. These tilted towers, looking like modern-day towers of Pisa seem to defy gravity, but rely on the stability brought about by its quadrilateral structure. The underlying parallelogram and trapezoidal designs are explored and analyzed. Note: The download for this resources is the Promethean Flipchart.

The full video can be found here: https://media4math.com/library/geometry-applications-quadrilaterals-segment-3-parallelograms-and-trapezoids

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-quadrilaterals-segment-3-parallelograms-and

This 45-minute SAT Math lesson helps students master the art of translating real-world scenarios into solvable math problems. Focused on the Problem Solving and Data Analysis domain—which accounts for approximately 29% of SAT Math questions—this lesson provides strategies for tackling multi-step word problems involving algebra, geometry, statistics, ratios, and percent reasoning. Students will learn how to analyze word problems, identify key quantities and relationships, and solve problems using equations, proportions, and logical reasoning.

In SAT Math Lesson 27, students explore the properties of quadrilaterals and other polygons. This lesson covers:

This 45-minute SAT Math prep lesson focuses on ratios, proportions, and percents—key concepts that appear throughout the Problem Solving and Data Analysis domain of the SAT. These topics account for approximately 29% of the SAT Math section and often appear in real-world scenarios involving recipes, maps, discounts, and data comparisons. In this lesson, students will learn to simplify ratios, solve proportions using cross multiplication, calculate percent increase and decrease, and solve percent-based equations involving unknowns.

This 45-minute SAT Math lesson focuses on mastering percents, percent increase and decrease, percent error, and reverse percent problems. Students will learn to convert between fractions, decimals, and percents, and apply key percent formulas to real-world and test-style problems. The lesson includes a warm-up activity, five instructional examples, a five-problem review section, and a 10-question SAT-style quiz with detailed solutions. Students also learn how to recognize percent-related language on the SAT and determine the correct solving strategy.

What Are Algebra Tiles?

This is the transcript for the video of same title. Video contents: In this program we explore the properties of three-dimensional figures. We do this in the context of two real-world applications. In the first, we look at the three-dimensional structure of Mayan pyramids. These stair-step structures provide a unique opportunity to also explore sequences and series. In the second application we look at the Shanghai Tower as an example of cylindrically shaped structures.

This is the transcript for the video of same title. Video contents: We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the video of same title. Video contents: Rectangular Prisms. Mayan pyramids are essentially stacks of rectangular prisms. The volume of each successive level is a percentage decrease of its lower neighbor. This introduces the notion of a geometric sequence and series, including an infinite series.

This is the transcript for the video of same title. Video contents: The Shanghai Tower in China is a stack of cylindrical shapes, where each successive layer is a percentage decrease of its lower neighbor. As with the previous section, this introduces the notion of a geometric sequence and series.

This is the transcript for the video of same title. Video contents: In this program we explore the properties of quadrilaterals. We do this in the context of two real-world applications. In the first, we explore the architecture of Frank Lloyd Wright as an application of squares and rectangles; in particular, we look at his Fallingwater house. In the second application we look at a unique parallelogram-shaped building in Spain, known as the Puerta de Europa. It provides an opportunity to explore the properties of parallelograms and trapezoids.

This is the transcript for the video of same title. Video contents: Stonehenge is best known as a circular structure. But it's the post and lintel construction used that is noteworthy, and this type of construction involves quadrilateral shapes. From the familiar door frames of houses to the majestic entryways of ancient temples, post and lintel construction provides a clear introduction to the nature of quadrilaterals. This segment also describes the key concepts developed throughout the program.

This is the transcript for the video of same title. Video contents: Frank Lloyd Wright's architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes. Some of the rectangular forms in this building seem to defy gravity, as we explore the properties of squares and rectangles that allowed Frank Lloyd Wright to push the envelope of design and structure.

This is the transcript for the video of same title. Video contents: The Puerta de Europa towers in Madrid bring parallelograms front and center. These tilted towers, looking like modern-day towers of Pisa seem to defy gravity, but rely on the stability brought about by its quadrilateral structure. The underlying parallelogram and trapezoidal designs are explored and analyzed.

This is the transcript for the video: Geometry Applications—Antiprisms. In this video students learn the basics of antiprisms, in the context of New York’s Freedom Tower, which has an antiprism design. They learn the properties of antiprisms, with the focus on those with a square base.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the video: Geometry Applications--What Are Prisms? In this video students learn the basics of prisms and anti prisms. They learn the properties of triangular prisms, rectangular prisms, triangular antiprisms, and rectangular antiprisms.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Integers: Variable Expressions with Integers.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Variable Expressions with Rational Numbers.

To see the complete collection of video transcriptsy, click on this link.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

Topic

Expressions and Equations

Description

The video explains how to simplify variable expressions like (x + 3) + (x + 1) using algebra tiles. It demonstrates combining like terms and using zero pairs for simplification. Key vocabulary includes simplifying, variable expressions, and zero pairs.

Topic

Integers

Description

This video introduces variable expressions with integers, focusing on simplifying and evaluating expressions. Key concepts include distributive property, combining like terms, and factoring. Vocabulary: variable expression, distribute, like terms. Applications involve calculating areas and volumes using expressions with variables.

In this video tutorial learn about perimeter in the context of triangles. Several examples of calculating a perimeter are shown: whole number sides, decimal sides. Then we look at triangles one of whose sides is a variable. The resulting perimeter is an algebraic expression. Finally, explore a situation where the perimeter is known but one of the side lengths is a variable. This results in an equation that can be solved for the variable.

Topic

Rational Numbers

Description

The video explores variable expressions involving rational numbers. Examples include finding combined areas of rectangles using algebraic expressions and analyzing the trajectory of a ball using a formula with time as a variable. It demonstrates real-world applications of rational number operations in algebra and physics.

Topic

Ratios

Description

The video focuses on unit rates, where the denominator equals one. It includes practical examples like finding the cost per pound of bananas or determining hourly wages. Applications extend to conversions and scaling calculations for various real-world tasks.

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

In this Brief Review, we explore simplifying variable expressions using algebra tiles.

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things.

Topic

3D Geometry

Topic

3D Geometry

Description

This segment introduces Platonic solids, including tetrahedron, cube, and dodecahedron, emphasizing their congruent edges, vertices, and angles. It connects these geometric figures to both natural and man-made structures, setting the stage for exploring 3D geometry applications.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

Topic

3D Geometry

Description

This segment explores pyramids, particularly Mayan and Egyptian structures, to distinguish rectangular and square bases. It discusses the volume of truncated pyramids using proportional relationships and introduces the concept of tiered volume reduction through geometric sequences.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

Topic

3D Geometry

Description

This segment examines cylinders, using the Shanghai Tower as a case study. It highlights how adjustments to height and radius affect volume and surface area, demonstrating these principles with geometric calculations and their architectural applications in energy efficiency.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

Topic

3D Geometry

Description

This video focuses on antiprisms, with One World Trade Center serving as a striking example. An antiprism is a polyhedron with two congruent polygonal bases rotated relative to each other and triangular sides connecting them. Key vocabulary includes antiprism, square base, triangular sides, and octagon. The geometry of the Freedom Tower is discussed, including its octagonal slices and symbolic height of 1776 feet. Applications highlight the dual role of the building as both an office space and a monument, emphasizing how its antiprism structure represents unity and homage to the Twin Towers.

Topic

3D Geometry

Topic

3D Geometry

Topic

3D Geometry

Topic

Quadrilaterals

Topic

Quadrilaterals

Description

Description: Quadrilaterals are fundamental in structural design, as seen in examples like Stonehenge and home layouts. Their prevalence in construction stems from properties like parallel sides and stability, making them ideal for creating functional spaces.

Topic

Quadrilaterals

Description

Description: This segment examines quadrilaterals in modern architecture, such as Frank Lloyd Wright’s Fallingwater. It explores how rectangles derive stability and maximum area from right triangles, offering applications in both aesthetic and structural design.

Topic

Quadrilaterals

Description

Description: Focused on tilted parallelograms in architecture, such as Madrid’s Puerta de Europa towers, this segment discusses balance, center of gravity, and how slanted shapes maintain stability. Applications include structural engineering and innovative design.

This is part of a collection of math worksheets on the topic of analyzing linear and quadratic expressions to identify specific terms based on a description.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of analyzing linear and quadratic expressions to identify specific terms based on a description.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of analyzing linear and quadratic expressions to identify specific terms based on a description.

Related Resources

Worksheet Library