Illustrative Math Alignment: Grade 8 Unit 9
Putting It All Together
Lesson 2: Regular Tessellations
Use the following Media4Math resources with this Illustrative Math lesson.
| Thumbnail Image | Title | Body | Curriculum Topic |
|---|---|---|---|
|
Math Example--Geometric Transformation--Transformations: Example 35 | Math Example--Geometric Transformation--Transformations: Example 35TopicTransformations DescriptionThis example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows a black L-shaped figure with a red dot on a grid. The "Before" figure is at the top left, and the "After" figure is at the top right. Below, there are three transformations: first, a translation moves the shape, then a rotation turns it around an axis shown by a pushpin, and finally, a reflection flips it across an axis shown by a red dashed line. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 36 | Math Example--Geometric Transformation--Transformations: Example 36TopicTransformations DescriptionThis example demonstrates a simple translation in geometric transformations. The image shows two hexagons on grids. The "Before" figure is at the top left, and the "After" figure is at the top right. Below, there is a single transformation: translation, as indicated by an arrow showing movement from one position to another. This showcases how an object can move position without changing its size or orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 37 | Math Example--Geometric Transformation--Transformations: Example 37TopicTransformations DescriptionThis example illustrates a combination of translation and rotation in geometric transformations. The image shows a hexagon on a grid, with a "Before" and "After" transformation. The pushpin indicates the axis of rotation, and the hexagon is translated and rotated. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 38 | Math Example--Geometric Transformation--Transformations: Example 38TopicTransformations DescriptionThis example demonstrates a combination of reflection and translation in geometric transformations. The image shows a hexagon on a grid, with a "Before" and "After" transformation. A red dashed line shows the axis of reflection, followed by a translation. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 39 | Math Example--Geometric Transformation--Transformations: Example 39TopicTransformations DescriptionThis example demonstrates a single rotation in geometric transformations. The image shows a hexagon on a grid, with a "Before" and "After" transformation. A pushpin indicates the axis of rotation, and only one transformation occurs. This illustrates how an object can change its orientation without altering its size or shape. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 4 | Math Example--Geometric Transformation--Transformations: Example 4TopicTransformations DescriptionThis example demonstrates a single rotation in geometric transformations. Two "T" shapes are shown on a grid, labeled "Before" and "After". The shape undergoes a rotation around a point indicated by a pushpin, which serves as the axis of rotation. This illustrates how an object can change its orientation without altering its size or position relative to the rotation point. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 40 | Math Example--Geometric Transformation--Transformations: Example 40TopicTransformations DescriptionThis example illustrates a combination of rotation and reflection in geometric transformations. The image shows a hexagon on a grid, with a "Before" and "After" transformation. A pushpin indicates the axis of rotation, and a red dashed line shows the axis of reflection. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in orientation and position. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 41 | Math Example--Geometric Transformation--Transformations: Example 41TopicTransformations DescriptionThis example demonstrates a single reflection in geometric transformations. The image shows two hexagons on a grid, labeled "Before" and "After." The hexagon is reflected over a vertical axis, with a red dashed line indicating the reflection axis. This illustrates how an object can be flipped over a line while maintaining its size and shape but changing its orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 42 | Math Example--Geometric Transformation--Transformations: Example 42TopicTransformations DescriptionThis example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows two hexagons on a grid, labeled "Before" and "After." There are three transformations: first, a translation moves the shape, then a rotation turns it (indicated by a pushpin showing the axis of rotation), and finally, a reflection flips it across a red dashed line representing the axis of reflection. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 43 | Math Example--Geometric Transformation--Transformations: Example 43TopicTransformations DescriptionThis example demonstrates a simple translation in geometric transformations. The image shows two house icons on a grid, labeled "Before" and "After." The house is translated horizontally to the right, with an arrow indicating the movement direction. This showcases how an object can move position without changing its size or orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 44 | Math Example--Geometric Transformation--Transformations: Example 44TopicTransformations DescriptionThis example illustrates a combination of translation and rotation in geometric transformations. The image shows two house icons on a grid, labeled "Before" and "After." Two transformations occur: translation (shown by an arrow) and rotation (shown by a pushpin). This demonstrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 45 | Math Example--Geometric Transformation--Transformations: Example 45TopicTransformations DescriptionThis example demonstrates a combination of reflection and translation in geometric transformations. The image shows two figures labeled as "Before" and "After." The left figure illustrates a shape on a grid, while the right figure shows the same shape after a transformation involving reflection and translation, marked with a dashed red line. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 46 | Math Example--Geometric Transformation--Transformations: Example 46TopicTransformations DescriptionThis example demonstrates a single rotation in geometric transformations. The image presents two figures labeled "Before" and "After." The left figure shows a shape on a grid, while the right one displays the same shape after a rotation around a specified point marked with a pushpin. This illustrates how an object can change its orientation without altering its size or shape. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 47 | Math Example--Geometric Transformation--Transformations: Example 47TopicTransformations DescriptionThis example illustrates a combination of rotation and reflection in geometric transformations. Two figures are presented, labeled "Before" and "After." The left figure shows the original shape on a grid, while the right figure depicts the shape after undergoing a combination of transformations: first, a rotation around a point indicated by a pushpin, followed by a reflection across a dashed red line. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 48 | Math Example--Geometric Transformation--Transformations: Example 48TopicTransformations DescriptionThis example demonstrates a single reflection in geometric transformations. The image shows two figures labeled as "Before" and "After." The left figure includes a shape positioned within a grid, and the right figure illustrates the transformed shape after reflecting across a dashed red line. This showcases how an object can be flipped over a line while maintaining its size and shape but changing its orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 49 | Math Example--Geometric Transformation--Transformations: Example 49TopicTransformations DescriptionThis example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows two house-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right. The transformation involves three steps: first, a translation moves the shape, then a rotation turns it around an axis marked by a pushpin, and finally, a reflection flips it across a dashed red line representing the axis of reflection. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 5 | Math Example--Geometric Transformation--Transformations: Example 5TopicTransformations DescriptionThis example illustrates a combination of rotation and reflection in geometric transformations. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The shape first undergoes a rotation, indicated by a pushpin showing the axis of rotation, and then a reflection, shown by a red dashed line representing the axis of reflection. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in orientation and position. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 50 | Math Example--Geometric Transformation--Transformations: Example 50TopicTransformations DescriptionThis example demonstrates a simple translation in geometric transformations. The image shows two star-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right. The transformation consists of a simple translation from left to right, showcasing how an object can move position without changing its size or orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 51 | Math Example--Geometric Transformation--Transformations: Example 51TopicTransformations DescriptionThis example illustrates a combination of translation and rotation in geometric transformations. The image shows two star-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right. There are two transformations: first, a translation moves the shape, then a rotation turns it around an axis marked by a pushpin. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 52 | Math Example--Geometric Transformation--Transformations: Example 52TopicTransformations DescriptionThis example demonstrates a combination of reflection and translation in geometric transformations. The image shows two star-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right, located lower and to the right. There are two transformations: first, a reflection across an axis shown by a red dashed line, followed by a translation to move the shape to its final position. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 53 | Math Example--Geometric Transformation--Transformations: Example 53TopicTransformations DescriptionThis example demonstrates a single rotation in geometric transformations. The image shows a star on a grid labeled "Before" and "After." The star has been rotated to a new position on the grid, as indicated by a pushpin that marks the axis of rotation. This illustrates how an object can change its orientation without altering its size or shape. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 54 | Math Example--Geometric Transformation--Transformations: Example 54TopicTransformations DescriptionThis example illustrates a combination of rotation and reflection in geometric transformations. The image displays a star on a grid with "Before" and "After" labels. The transformation involves two steps: first, a rotation around an axis marked by a pushpin, and second, a reflection across a vertical axis shown by a red dashed line. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in orientation and position. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 55 | Math Example--Geometric Transformation--Transformations: Example 55TopicTransformations DescriptionThis example demonstrates a single reflection in geometric transformations. In this image, a star is shown before and after undergoing a reflection. The red dashed line represents the axis of reflection, which is horizontal in this case. This showcases how an object can be flipped over a line while maintaining its size and shape but changing its orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 56 | Math Example--Geometric Transformation--Transformations: Example 56TopicTransformations DescriptionThis example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows three transformations applied to the star: first, a translation moves the star to another position, then a rotation turns it around an axis indicated by a pushpin, and finally a reflection flips it across a vertical axis shown by a red dashed line. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 6 | Math Example--Geometric Transformation--Transformations: Example 6TopicTransformations DescriptionThis example demonstrates a single reflection in geometric transformations. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The solution diagram below illustrates a reflection of the shape across a red dashed line, which represents the axis of reflection. This transformation showcases how an object can be flipped over a line while maintaining its size and shape. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 7 | Math Example--Geometric Transformation--Transformations: Example 7TopicTransformations DescriptionThis example illustrates a complex combination of transformations: translation, rotation, and reflection. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The solution diagram below demonstrates three sequential transformations: first, a translation moves the shape, then a rotation turns it (indicated by a pushpin showing the axis of rotation), and finally, a reflection flips it across a red dashed line representing the axis of reflection. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 8 | Math Example--Geometric Transformation--Transformations: Example 8TopicTransformations DescriptionThis example demonstrates a simple translation in geometric transformations. Two grids labeled "Before" and "After" show an "O" shape slightly shifted between the grids. The solution diagram below illustrates a translation of the shape from one position to another, showcasing how an object can move position without changing its size or orientation. |
Definition of Transformations |
|
Math Example--Geometric Transformation--Transformations: Example 9 | Math Example--Geometric Transformation--Transformations: Example 9TopicTransformations DescriptionThis example illustrates a combination of transformations: translation and rotation. Two circular "O" shapes are shown on a grid, one labeled "Before" and the other "After". The solution involves a translation (movement) and a rotation, with a pushpin indicating the axis of rotation. This demonstrates how multiple transformations can be applied sequentially to a shape. |
Definition of Transformations |
|
MATH EXAMPLES--Teacher's Guide: Circular Area and Circumference | MATH EXAMPLES--Teacher's Guide: Circular Area and Circumference
This set of tutorials provides 23 examples of solving for the area and circumferences of circles and sections of circles. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Area and Circumference |
|
|
MATH EXAMPLES--Teacher's Guide: Transformations | MATH EXAMPLES--Teacher's Guide: Transformations
This set of tutorials provides 56 examples of transformations of geometric figures on a graph. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Transformations and Definition of Transformations |
|
MATH EXAMPLES--Transformations | MATH EXAMPLES--Transformations
This set of tutorials provides 56 examples of transformations of geometric figures on a graph. NOTE: The download is a PPT file. |
Applications of Transformations and Definition of Transformations |
|
Promethean Flipchart: Geometry Applications: Transformations 1 | Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Transformations, Segment 1: Translations and Rotations]: https://www.media4math.com/library/geometry-applications-transformations-segment-1-translations-and-rotations This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-1-translations-and-rotations |
Applications of Transformations |
|
Promethean Flipchart: Geometry Applications: Transformations 2 | Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Transformations, Segment 2: 3D Translations]: https://www.media4math.com/library/geometry-applications-transformations-segment-2-3d-translations This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-2-3d-translations |
Applications of Transformations |
|
Promethean Flipchart: Geometry Applications: Transformations 3 | The Gemini telescope in Hawaii is an example of architecture that moves. All observatories rotate in order to follow objects in the sky. This also provides an opportunity to explore rotations, reflections, and symmetry. Note: The download for this resources is the Promethean Flipchart. The full video [Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry] can be found here: https://media4math.com/library/geometry-applications-transformations-segment-3-rotations-reflections-and-symmetry |
Applications of Transformations |
|
Video Transcript: Geometry Applications: Circles | Video Transcript: Geometry Applications: Circles
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. |
Applications of Circles |
|
|
Video Transcript: Geometry Applications: Circles, Segment 1: The Basics of Circles | Video Transcript: Geometry Applications: Circles, Segment 1: The Basics of Circles
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. This is part of a collection of video transcript from the Geometry Applications video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
Applications of Circles |
|
|
Video Transcript: Geometry Applications: Circles, Segment 2: Circles and Arcs | Video Transcript: Geometry Applications: Circles, Segment 2: Circles and Arcs
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. |
Applications of Circles |
|
|
Video Transcript: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles | Video Transcript: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles
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. |
Applications of Circles |
|
|
Video Transcript: Geometry Applications: Transformations | Video Transcript: Geometry Applications: Transformations
This is the transcript for the video of same title. Video contents: In this program we look at applications of transformations. We do this in the context of three real-world applications. In the first, we look at translations and rotations in the context of roller coaster rides. In the second example we look at translations in three-dimensional space in the context of cargo ships. In the third example, we look at the design of observatories to look at rotations, reflections, and symmetry. |
Applications of Transformations |
|
|
Video Transcript: Geometry Applications: Transformations, Segment 1: Translations and Rotations | Video Transcript: Geometry Applications: Transformations, Segment 1: Translations and Rotations
This is the transcript for the video of same title. Video contents: Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced. This is part of a collection of video transcript from the Geometry Applications video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
Applications of Transformations |
|
|
Video Transcript: Geometry Applications: Transformations, Segment 2: 3D Translations | Video Transcript: Geometry Applications: Transformations, Segment 2: 3D Translations
This is the transcript for the video of same title. Video contents: Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations. |
Applications of Transformations |
|
|
Video Transcript: Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry | Video Transcript: Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry
This is the transcript for the video of same title. Video contents: The Gemini telescope in Hawaii is an example of architecture that moves. All observatories rotate in order to follow objects in the sky. This also provides an opportunity to explore rotations, reflections, and symmetry. |
Applications of Transformations |
|
VIDEO: Geometry Applications: Area and Volume, 2 | VIDEO: Geometry Applications: Area and Volume, 2
TopicArea and Volume DescriptionThis 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. |
Applications of Surface Area and Volume, Surface Area and Volume |
|
VIDEO: Geometry Applications: Transformations | VIDEO: Geometry Applications: Transformations
TopicTransformations |
Applications of Transformations and Definition of Transformations |
|
VIDEO: Geometry Applications: Transformations, 1 | VIDEO: Geometry Applications: Transformations, 1
TopicTransformations DescriptionExplores translations and rotations in motion, using roller coasters as an example. Key concepts include displacement vectors, magnitude, and direction, modeled geometrically and computationally for practical applications in physics and engineering. |
Applications of Transformations and Definition of Transformations |
|
VIDEO: Geometry Applications: Transformations, 2 | VIDEO: Geometry Applications: Transformations, 2
TopicTransformations DescriptionThis segment applies 3D translations to logistics, focusing on container arrangement in shipping. Using coordinate systems, it demonstrates efficiency in loading/unloading cargo, leveraging geometric organization and data sorting methods for real-world impact. |
Applications of Transformations and Definition of Transformations |
|
VIDEO: Geometry Applications: Transformations, 3 | VIDEO: Geometry Applications: Transformations, 3
TopicTransformations DescriptionAnalyzes observatory designs and their use of rotational and reflective symmetry for astronomical viewing. The segment models celestial movements and applies rotational geometry concepts to optimize the structure’s functionality. |
Applications of Transformations and Definition of Transformations |
|
Worksheet: Crossword Puzzle--Circles | Worksheet: Crossword Puzzle--Circles
This is part of a collection of math worksheets that are crossword puzzles of math vocabulary. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Worksheet LibraryTo see the complete collection of Worksheets, click on this link. |
Definition of a Circle |
