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Subject: Mathematics
Title: Shape Cutter      Add Bookmark
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      Add Bookmark
Description:
Thinkfinity Partner: Illuminations
Grade Span: 6,7,8



Subject: Mathematics
Title: Symmetries II: Conclusions       Add Bookmark
Description: In this lesson, one of a multi-part 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      Add Bookmark
Description: In this lesson, one of a multi-part 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 Rep-Tiles      Add Bookmark
Description: In this lesson, from Illuminations, students discover and explore a special kind of tiling of the plane. Rep-tiles 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: Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Visualizing Transformations      Add Bookmark
Description: The interactive figures in this four-part example from Illuminations allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.
Thinkfinity Partner: Illuminations
Grade Span: 6,7,8



Subject: Mathematics
Title: Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Transformations      Add Bookmark
Description: This is part four of a four-part e-example 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. e-Math Investigations are selected e-examples 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 e-examples are natural companions to the i-Math Investigations.
Thinkfinity Partner: Illuminations
Grade Span: 6,7,8



Subject: Mathematics
Title: Pinwheel      Add Bookmark
Description: In this Illuminations lesson, students create parallelograms from square sheets of paper and connect them to form an octagon. During the construction, students consider angle measures, segment lengths, and areas in terms of the original square. At the end of the lesson, the octagon is transformed into a pinwheel, and students discover a surprising result. There is also a link to a related activity sheet.
Thinkfinity Partner: Illuminations
Grade Span: 6,7,8,9,10,11,12



Subject: Mathematics
Title: Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Reflections      Add Bookmark
Description: This is part three of a four-part e-example 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. e-Math Investigations are selected e-examples 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 e-examples are natural companions to the i-Math Investigations.
Thinkfinity Partner: Illuminations
Grade Span: 6,7,8



Subject: Mathematics
Title: Symmetries I      Add Bookmark
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: Dihedral Figures      Add Bookmark
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: Mathematics
Title: Polygons      Add Bookmark
Description: This reproducible activity sheet, from an Illuminations lesson, features line drawings of several polygons including squares, triangles, rectangles, parallelograms, and trapezoids.
Thinkfinity Partner: Illuminations
Grade Span: 6,7,8



Subject: Arts,Mathematics
Title: Recognizing Transformations      Add Bookmark
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      Add Bookmark
Description: Students will recognize rotation symmetry in figures and examining various rotation symmetries.
Thinkfinity Partner: Illuminations
Grade Span: 6,7,8



Subject: Arts,Mathematics
Title: Classifying Transformations      Add Bookmark
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 on-line activities.
Thinkfinity Partner: Illuminations
Grade Span: 9,10,11,12



Subject: Mathematics
Title: Square Graphs      Add Bookmark
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      Add Bookmark
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      Add Bookmark
Description: In this lesson, one of a multi-part 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      Add Bookmark
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      Add Bookmark
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



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