ALEX Lesson Plans
Subject: Mathematics (8  12) Title: Geometric Quilts
Description: Students will use a square to investigate other polygonal shapes that can be formed. Students will work with these polygons to make designs that will later constitute cooperatively designed quilts. The quilts will be made by translating, rotating, or reflecting a thirtysix patch design. The completed quilts will then be used for a discussion of area and perimeter. Students will blog about what they have learned while doing the lesson and will include pictures of their finished product in our class blog.
Subject: Mathematics (9  12) Title: Transformations on the Graphing Calculator
Description: Investigate transformations through use of a graphing calculator and then using graph paper.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Thinkfinity Lesson Plans
Subject: Mathematics Title: Frieze Patterns
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Description: Students can experiment with the seven classes of Frieze patterns with this activity. They can explore the transformations that constitute each of the seven categories. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
Subject: Mathematics Title: Shape Cutter
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Description: This student interactive, from Illuminations, allows students to explore how they can decompose shapes and recompose them to make other shapes. Students draw and cut shapes, and also use slides, turns, and flips to move the cut pieces around. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5,6,7,8,9,10,11,12
Subject: Mathematics Title: Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Identifying Unknown Transformations
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Description: Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Subject: Mathematics Title: Exploring the Isometric Drawing Tool
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Description: In this lesson, one of a multipart unit from Illuminations, students explore using an isometric drawing tool and gain practice and experience in manipulating drawings. They explore polyhedra using different representations and perspectives. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Subject: Mathematics Title: Symmetries II: Conclusions
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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
Subject: Mathematics Title: Describing Rotations
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Description: In this lesson, one of a multipart unit from Illuminations, students learn how to describe rotations of a figure. They then use an interactive Java applet to investigate the effect of rotations through different angles and on different shapes. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Covering the Plane with RepTiles
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Description: In this lesson, from Illuminations, students discover and explore a special kind of tiling of the plane. Reptiles are geometric figures such that n copies can fit together to form a larger, similar figure. Students experiment with various shapes and values of n. Spatial sense is encouraged by the need to visualize and perform transformations with the shapes involved. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
Subject: Mathematics Title: Transformations and Frieze Patterns
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Description: In two lessons, this unit will introduce students to the world of symmetry and rotation in figures and patterns. Students learn to recognize and classify symmetry in decorative figures and frieze patterns, and will also get the chance to create and classify their own figures and patterns using JavaSketchpad applets. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Visualizing Transformations
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Description: The interactive figures in this fourpart example from Illuminations allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Subject: Mathematics Title: Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Transformations
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Description: This is part four of a fourpart eexample from Illuminations that features interactive figures that allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. In this part, Composing Transformations, the users are challenged to compose equivalent transformations in two different ways. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath Investigations. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Subject: Mathematics Title: Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Reflections
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Description: This is part three of a fourpart eexample from Illuminations that features interactive figures that allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. In this part, Composing Reflections, users can examine the result of reflecting a shape successively through two different lines. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards for School Mathematics (PSSM). Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath Investigations. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Subject: Mathematics Title: Symmetries I
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Description: In this unit of four lessons, from Illuminations, investigate rotational symmetry. They learn about the mathematical properties of rotations and have an opportunity to make their own designs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Reflections Across Two Mirror Lines
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Description: In this lesson, one of a multipart unit from Illuminations, students learn what happens when a design is reflected twice across two different mirror lines. They use interactive Java applets to explore reflections across parallel and intersecting mirror lines. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Dihedral Figures
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Description: Students will recognize dihedral symmetry and reflections in figures and examining various symmetries. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
Subject: Arts,Mathematics Title: Recognizing Transformations
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Description: This lesson introduces students to the world of symmetry and rotation in figures and patterns. Students learn how to recognize and classify symmetry in decorative figures and frieze patterns, and get the chance to create and classify their own figures and patterns using JavaSketchpad applets. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Cyclic Figures
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Description: Students will recognize rotation symmetry in figures and examining various rotation symmetries. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Subject: Mathematics Title: Finding What Doesn't Change
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Description: In this lesson, one of a multipart unit from Illuminations, students predict the effect of a rotation through a given angle. They also learn to predict the effect of two or more rotations performed one after the other, and they find angles that leave a figure unchanged. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Reflect on This
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Description: In this lesson, from Illuminations, students investigate reflections in a plane using mirrors (or other reflective materials) and a geometry utility. They apply their findings to examination of interior angles of regular polygons. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Arts,Mathematics Title: Classifying Transformations
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Description: Students will identify and classify reflections and symmetries in figures and patterns. They will also have the opportunity to create frieze patterns from each of the seven classes using the supplemental online activities. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Square Graphs
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Description: This student interactive, from an Illuminations lesson, allows students to view six different graphs. Each graph plots one characteristic of the square along the horizontal axis and another along the vertical axis. Students then determine which two characteristics are used to make each graph. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Symmetries III
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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
Subject: Mathematics Title: Describing Reflections
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Description: In this lesson, one of a multipart unit from Illuminations, students learn how reflections work and what happens when two or more reflections are applied one after the other. They use interactive Java applets to examine the reflection of a point and how to describe reflections. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Symmetries II
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Description: In this unit of four lessons, from Illuminations, students use Java applets to investigate reflection, mirror, or bilateral symmetry. They learn about the mathematical properties of mirror symmetry and have a chance to create designs with mirror symmetry. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Subject: Mathematics Title: Symmetries IV
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Description: This lesson, from Illuminations, helps students to understand and identify glide reflections. With the help of a Java applet, students construct glide reflections using a translation and a reflection. Students then identify glide reflections from groups of band ornaments and wallpaper patterns. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

