Illustrative Math Alignment: Grade 7 Unit 7

This set of tutorials provides 23 examples of solving for the area and circumferences of circles and sections of circles.

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This set of tutorials provides 36 examples of how to classify polygons based on side and angle characteristics.

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This Teacher's Guide provides an overview of the 24 worked-out examples that show how to calculate the area and perimeter of different quadrilaterals.

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This set of tutorials provides 34 examples of the types of quadrilaterals and how to classify quadrilaterals based on the sides and angles.

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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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This set of tutorials provides 40 examples of how to find the area and perimeter of triangles.

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This set of tutorials provides 24 examples of how to find the volume of various 3-dimensional geometric figures.

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This set of tutorials provides 40 examples of how to find the area and perimeter of triangles. NOTE: The download is a PPT file.

This set of tutorials provides 24 examples of how to find the volume of various 3-dimensional geometric figures. NOTE: The download is a PPT file.

November 2014. In this issue of Math in the News we examine the historic landing of a spacecraft on an asteroid in space.

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6/13/11. In this issue we explore the volcanic eruption in Chile that resulted in a huge plume of smoke and ash that was miles high. We explore the viscosity of lava that makes such eruptions possible.

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6/27/11. In this issue we look at the technology of hydraulic fracking. In particular, we estimate the amount of drilling required for such wells.

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9/19/11. To commemorate the 10-year anniversary of the 911, we look at the geometry and architecture of the Freedom Tower, currently under construction.

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10/17/11. In this issue we look at the earthquake damage that the Washington Monument recently experienced. Some dramatic footage reveals cracks in the exterior of the monument.

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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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11/28/11. In this issue we look at the geometry of parade balloons.

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12/7/11. In this issue we look at the heroic work of salvaging and retrofitting many of the ships sunk during the attack on Pearl Harbor.

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12/12/11. In this issue we look at the MLK Memorial and the special properties of granite that presented some design challenges in the construction of the statue.

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January 2012. In this issue we look at the Burj Khalifa Tower, made popular with the release of the Mission Impossible movie.

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January 2012. In this issue of Math in the News we analyze how the Costa Concordia sank.

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April 2012. In this issue of Math in the News we analyze the sinking of the Titanic. It has been a hundred years, yet the story of the sinkin g of the Titanic still fascinates.

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May 2012. In this issue of Math in the News we look at the architecture of the Freedom Tower, now that it has become the tallest building in NYC.

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August 2013. In this issue we look at the geometry of funnel cakes. You'll like the sweet results.

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5/9/11. In this issue we look at tornado season. In particular we study why the swirling winds of a tornado are so damaging.

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5/16/11. In this issue we look at the flooding along the Mississippi. In particular we analyze the flooding along Memphis, Tennessee. We develop a model for predicting the amount of flooding.

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This Grade 7 geometry lesson focuses on identifying and solving problems involving angle relationships. Students learn to classify acute, right, obtuse, and straight angles, measure angles using a protractor, and explore relationships among supplementary, complementary, vertical, and adjacent angles. A major focus is understanding angle relationships formed when parallel lines are cut by a transversal. Real-world applications include studying city street grids, with a special emphasis on the geometry of Broadway’s diagonal intersections. The lesson aligns with Common Core Standard CCSS.MATH.CONTENT.7.G.B.5. Multimedia resources from Media4Math.com, including animated clip art, vocabulary definitions, and Google Earth Voyager Stories, support visual learning.

This Grade 7 geometry lesson focuses on calculating the area and circumference of circles using the formulas $A = \pi r^2$ and $C = 2\pi r$. Students explore the relationship between radius, diameter, and circumference, while reinforcing their understanding through coordinate geometry and real-world examples. The lesson is aligned to Common Core Standard CCSS.MATH.CONTENT.7.G.B.4 and emphasizes both conceptual understanding and procedural fluency. Students analyze circle diagrams, scale drawings, and apply formulas in problems involving circular structures such as the U.S. Capitol Rotunda and Pueblo Bonito kivas. Multimedia resources from Media4Math.com include clip art collections, instructional videos, and vocabulary definitions that support key concepts.

This Grade 7 geometry lesson introduces students to the formulas and conceptual understanding behind the volume and surface area of cylinders and cones. Aligned to CCSS.MATH.CONTENT.7.G.B.6 and supported by elements of Grade 8 expectations, the lesson includes direct instruction on identifying the radius, height, and slant height of three-dimensional figures. Students review vocabulary using interactive clip art and video definitions from Media4Math.com. Real-world examples feature applications such as soup cans, ice cream cones, party hats, and architectural landmarks like the Leaning Tower of Pisa and the Stamford Cone. Students use visual models, such as nets, to understand surface area and are encouraged to estimate volume through hands-on activities.

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

This is part of a collection of self-scoring interactive math quizzes on a variety of topics.

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This is the transcript for the video entitled, Desmos Geometry Exploration: Types of Angles I. In this video tutorial different types of angles are defined, including acute, right, supplementary, and straight angles. Students are shown how to construct these types of angles using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry.

This is the transcript for the video entitled, Desmos Geometry Exploration: Types of Angles II. In this video tutorial different types of angles are defined, including adjacent angles, complementary angles, supplementary angles, and vertical angles. Students are shown how to construct these types of angles using the Desmos geometry tools. The Desmos geometry tools can be found at www.desmos.com/geometry.

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.

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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 circles. We do this in the context of two real-world applications. In the first, we look at the design of the Roman Coliseum and explore how circular shapes could have been used to design this elliptical structure. In the second application we look at the Roman Pantheon, specifically its spherical dome, to see how the properties of chords and secants help clarify its unique design.

This is the transcript for the video of same title. Video contents: We visit Chaco Canyon in New Mexico to explore the circular kivas and in the process discover how circular buildings have been used to study the heavens.

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This is the transcript for the video of same title. Video contents: The Roman Coliseum is a large elliptical structure. Yet, the Romans likely used circular arcs to build it. This segment explores the properties of circles and shows how arcs can be used to create elliptical shapes.

This is the transcript for the video of same title. Video contents: The Roman Pantheon is a domed structure that shows a keen awareness of the position of the sun throughout the year. The source of light from the top of the dome allows for the exploration of chords, inscribed angles, central angles, and intercepted arcs.

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.

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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.

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Topic

Geometry

Description

This video explains angles and their properties using Desmos geometry tools. It defines angles as formed by two rays meeting at a vertex and measured in degrees or radians. Viewers learn to construct and measure angles, including 0°, 180°, and 360°. Key terms include vertex, rays, and sweep. Applications involve dynamic angle measurement using Desmos tools.

Topic

Geometry

Description

This lesson defines angle types: acute, right, obtuse, and straight, using Desmos tools to measure and create examples. Key terms include angle measure, rays, and straight angle. Applications involve understanding angle properties and classifications for dynamic constructions.

Topic

Geometry

Description

Adjacent angles, complementary angles, and vertical angles are explored. Desmos tools help construct and measure these angles, illustrating concepts like angle addition and congruence. Key terms include supplementary, vertical, and adjacent angles. Applications include analyzing intersecting lines and their angle relationships.