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Title: Tessellations
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This activity will introduce, explore, and create tessellations. The students will view samples of art made by tessellating shapes. They will also create their own piece of art by choosing a tessellation.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Mathematics (9  12)
Title: Tessellations
Description: This activity will introduce, explore, and create tessellations. The students will view samples of art made by tessellating shapes. They will also create their own piece of art by choosing a tessellation.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Symmetry: Theory, Reality and Art!
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Students will explore symmetry as defined in geometry, as seen in their community and through the art of EscherEscher Art Website. Technology and art are incorporated in this lesson. The incorporation of art is an important element in developing the ‘whole child’ if a school system has been forced to eliminate a formal arts program. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [AED] VA1 (712) 5: Demonstrate the use of traditional, digital, and multimedia techniques to create works of art. [AED] VA1 (712) 1: Create original works of art from direct observation. [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Arts Education (7  12), or Mathematics (9  12)
Title: Symmetry: Theory, Reality and Art!
Description: Students will explore symmetry as defined in geometry, as seen in their community and through the art of EscherEscher Art Website. Technology and art are incorporated in this lesson. The incorporation of art is an important element in developing the ‘whole child’ if a school system has been forced to eliminate a formal arts program. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Minerals
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The students will gain information on the 5 characteristics of minerals. The information can be related to nonrenewable resources. This lesson should facilitate discussion on the difference in precious gems and semiprecious gems.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [S1] E&S (912) 7: Explain techniques for determining the age and composition of Earth and the universe. [S1] GEL (912) 5: Classify rocks as sedimentary, igneous, and metamorphic. [S1] CHE (912) 1: Differentiate among pure substances, mixtures, elements, and compounds. [S1] E&S (912) 7: Explain techniques for determining the age and composition of Earth and the universe. [S1] GEL (912) 5: Classify rocks as sedimentary, igneous, and metamorphic. [S1] PHS (912) 1: Recognize periodic trends of elements, including the number of valence electrons, atomic size, and reactivity. [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4] [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama) [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4] [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Mathematics (9  12), or Science (9  12)
Title: Minerals
Description: The students will gain information on the 5 characteristics of minerals. The information can be related to nonrenewable resources. This lesson should facilitate discussion on the difference in precious gems and semiprecious gems.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Golden Ratios of the Body, Architecture, and Nature
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Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.
Standard(s): [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama) [MA2013] MI1 (912) 3: Use special numbers, including e, i, π and the golden ratio, to solve applicationbased problems. [MA2013] GEO (912) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [GMG3] [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] (7) 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7SP4] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Subject: Mathematics (6  12), or Technology Education (9  12)
Title: Golden Ratios of the Body, Architecture, and Nature
Description: Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.
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Title: Symmetries II: Conclusions
Description:
In this lesson, one of a multipart unit from Illuminations, students reflect on what they learned in the three previous lessons. Eight thought questions (with a link to the answers) are provided.
Standard(s): [MA2013] GEO (912) 2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [GCO2] [MA2013] GEO (912) 3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. [GCO3] [MA2013] GEO (912) 4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. [GCO4] [MA2013] GEO (912) 5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [GCO5] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Mathematics Title: Symmetries II: Conclusions
Description: In this lesson, one of a multipart unit from Illuminations, students reflect on what they learned in the three previous lessons. Eight thought questions (with a link to the answers) are provided. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Symmetries III
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This lesson, from Illuminations, helps students to understand how translations work and what happens when two or more translations are applied one after the other. Students discover that all band ornaments have translational symmetry and all wallpaper patterns have translational symmetry in at least two directions.
Standard(s): [MA2013] (8) 16: Verify experimentally the properties of rotations, reflections, and translations: [8G1] [MA2013] (8) 17: Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. [8G2] [MA2013] (8) 19: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. [8G4] [MA2013] GEO (912) 2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [GCO2] [MA2013] GEO (912) 3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. [GCO3] [MA2013] GEO (912) 5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [GCO5] [MA2013] GEO (912) 12: Make formal geometric constructions with a variety of tools and methods such as compass and straightedge, string, reflective devices, paper folding, and dynamic geometric software. Constructions include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. [GCO12] [MA2013] GEO (912) 15: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. [GSRT2] [MA2013] GEO (912) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [GMG3] [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Mathematics Title: Symmetries III
Description: This lesson, from Illuminations, helps students to understand how translations work and what happens when two or more translations are applied one after the other. Students discover that all band ornaments have translational symmetry and all wallpaper patterns have translational symmetry in at least two directions. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Art Algorithms
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In this Science Update, from Science NetLinks, you'll hear about new methods of art conservation. Art conservation is traditionally a painstaking and timeconsuming business. But the process of fixing up a damaged da Vinci or a scarred Seurat may become a lot easier, thanks to the work of mathematicians. Science Updates are audio interviews with scientists and are accompanied by a set of questions as well as links to related Science NetLinks lessons and other related resources.
Standard(s): [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] DM1 (912) 7: Solve problems through investigation and application of existence and nonexistence of Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. (Alabama) [MA2013] DM1 (912) 8: Apply algorithms, including Kruskal's and Prim's, relating to minimum weight spanning trees, networks, flows, and Steiner trees. (Alabama) [MA2013] DM1 (912) 9: Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the listprocessing algorithm, and studentcreated algorithms. (Alabama) [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Arts, Mathematics, Science Title: Art Algorithms
Description: In this Science Update, from Science NetLinks, you'll hear about new methods of art conservation. Art conservation is traditionally a painstaking and timeconsuming business. But the process of fixing up a damaged da Vinci or a scarred Seurat may become a lot easier, thanks to the work of mathematicians. Science Updates are audio interviews with scientists and are accompanied by a set of questions as well as links to related Science NetLinks lessons and other related resources. Thinkfinity Partner: Science NetLinks Grade Span: 6,7,8,9,10,11,12
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Title: Golden Ratio
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In this Illuminations lesson, students explore the Fibonacci sequence. They examine how the ratio of two consecutive Fibonacci numbers creates the Golden Ratio and identify reallife examples of the Golden Ratio.
Standard(s): [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] DM1 (912) 2: Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal numbers. (Alabama) [MA2013] MI1 (912) 5: Identify beginnings of algebraic symbolism and structure through the works of European mathematicians. (Alabama) [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Mathematics Title: Golden Ratio
Description: In this Illuminations lesson, students explore the Fibonacci sequence. They examine how the ratio of two consecutive Fibonacci numbers creates the Golden Ratio and identify reallife examples of the Golden Ratio. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Art Algorithms
Description:
In this Science Update, from Science NetLinks, you'll hear about new methods of art conservation. Art conservation is traditionally a painstaking and timeconsuming business. But the process of fixing up a damaged da Vinci or a scarred Seurat may become a lot easier, thanks to the work of mathematicians. Science Updates are audio interviews with scientists and are accompanied by a set of questions as well as links to related Science NetLinks lessons and other related resources.
Standard(s): [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] DM1 (912) 7: Solve problems through investigation and application of existence and nonexistence of Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. (Alabama) [MA2013] DM1 (912) 8: Apply algorithms, including Kruskal's and Prim's, relating to minimum weight spanning trees, networks, flows, and Steiner trees. (Alabama) [MA2013] DM1 (912) 9: Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the listprocessing algorithm, and studentcreated algorithms. (Alabama) [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Arts, Mathematics, Science Title: Art Algorithms
Description: In this Science Update, from Science NetLinks, you'll hear about new methods of art conservation. Art conservation is traditionally a painstaking and timeconsuming business. But the process of fixing up a damaged da Vinci or a scarred Seurat may become a lot easier, thanks to the work of mathematicians. Science Updates are audio interviews with scientists and are accompanied by a set of questions as well as links to related Science NetLinks lessons and other related resources. Thinkfinity Partner: Science NetLinks Grade Span: 6,7,8,9,10,11,12
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Title: Fractal Tool
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This student interactive, from Illuminations, illustrates iteration graphically. Students can view preset iterations of various shapes and/or choose to create their own iterations.
Standard(s): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 19: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. [8G4] [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] GEO (912) 15: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. [GSRT2] [MA2013] GEO (912) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [GSRT5] [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama) [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
Subject: Mathematics Title: Fractal Tool
Description: This student interactive, from Illuminations, illustrates iteration graphically. Students can view preset iterations of various shapes and/or choose to create their own iterations. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12

