**Title:** How Tall Is Hagrid?

**Description:**
This activity uses data collection method for students to mathematically compute the height and shoulder width of the character Hagrid from Harry Potter. Students will measure their own heights and shoulder widths to come up with a class average. They will use this average to find an approximation of the size of Hagrid.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.
**Standard(s): **

[MA2015] (8) 19: Understand that a two-dimensional 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 two-dimensional figures, describe a sequence that exhibits the similarity between them. [8-G4]

**Subject:**Mathematics (6 - 8)

**Title:**How Tall Is Hagrid?

**Description:**This activity uses data collection method for students to mathematically compute the height and shoulder width of the character Hagrid from Harry Potter. Students will measure their own heights and shoulder widths to come up with a class average. They will use this average to find an approximation of the size of Hagrid.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.

**Title:** What Shape Are You?

**Description:**
In this lesson, students will read "The Greedy Triangle" by Marilyn Burns, participate in class activities to classify two- and three-dimensional shapes, produce a powerpoint describing a chosen shape, and make a picture of themselves as one of the shapes.
**Standard(s): **

[MA2015] (8) 19: Understand that a two-dimensional 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 two-dimensional figures, describe a sequence that exhibits the similarity between them. [8-G4]

**Subject:**Mathematics (7 - 8), or Technology Education (6 - 8)

**Title:**What Shape Are You?

**Description:**In this lesson, students will read "The Greedy Triangle" by Marilyn Burns, participate in class activities to classify two- and three-dimensional shapes, produce a powerpoint describing a chosen shape, and make a picture of themselves as one of the shapes.

**Title:** Scale Drawings

**Description:**
During this lesson students practice measuring and converting to scaled measurements. Students measure various places on campus, such as a classroom or the gym. They place their findings on a spreadsheet. After converting these measurements to a scaled version, students draw a scaled model.
**Standard(s): **

[MA2015] ALC (9-12) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama)

**Subject:**Mathematics (8 - 12)

**Title:**Scale Drawings

**Description:**During this lesson students practice measuring and converting to scaled measurements. Students measure various places on campus, such as a classroom or the gym. They place their findings on a spreadsheet. After converting these measurements to a scaled version, students draw a scaled model.

**Title:** Covering the Plane with Rep-Tiles

**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.
**Standard(s): **

[MA2015] GEO (9-12) 16: Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar. [G-SRT3]

**Subject:**Mathematics

**Title:**Covering the Plane with Rep-Tiles

**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

**Title:** Describing Reflections

**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.
**Standard(s): **

[MA2015] GEO (9-12) 6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. [G-CO6]

**Subject:**Mathematics

**Title:**Describing Reflections

**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

**Title:** Exploring the Isometric Drawing Tool

**Description:**
In this lesson, one of a multi-part 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.
**Standard(s): **

[MA2015] GEO (9-12) 38: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. [G-GMD4]

**Subject:**Mathematics

**Title:**Exploring the Isometric Drawing Tool

**Description:**In this lesson, one of a multi-part 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

**Title:** Reflections Across Two Mirror Lines

**Description:**
In this lesson, one of a multi-part 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.
**Standard(s): **

[MA2015] GEO (9-12) 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.* [G-CO12]

**Subject:**Mathematics

**Title:**Reflections Across Two Mirror Lines

**Description:**In this lesson, one of a multi-part 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

**Title:** Relating Rotations to Symmetry

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students investigate the relationship between rotations and the symmetry in a figure or a design. They use an interactive Java applet to illustrate rotational symmetry and investigate cyclic designs and point symmetry.
**Standard(s): **

[MA2015] GEO (9-12) 16: Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar. [G-SRT3]

**Subject:**Mathematics

**Title:**Relating Rotations to Symmetry

**Description:**In this lesson, one of a multi-part unit from Illuminations, students investigate the relationship between rotations and the symmetry in a figure or a design. They use an interactive Java applet to illustrate rotational symmetry and investigate cyclic designs and point symmetry.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Relationships Between Reflections and Symmetry

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students learn the properties of designs that have bilateral symmetry. They also make their own designs and investigate dihedral symmetry.
**Standard(s): **

[MA2015] (8) 19: Understand that a two-dimensional 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 two-dimensional figures, describe a sequence that exhibits the similarity between them. [8-G4]

**Subject:**Mathematics

**Title:**Relationships Between Reflections and Symmetry

**Description:**In this lesson, one of a multi-part unit from Illuminations, students learn the properties of designs that have bilateral symmetry. They also make their own designs and investigate dihedral symmetry.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Symmetries I

**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.
**Standard(s): **

[MA2015] GEO (9-12) 14: Verify experimentally the properties of dilations given by a center and a scale factor. [G-SRT1]

**Subject:**Mathematics

**Title:**Symmetries I

**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

**Title:** Symmetries II

**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.
**Standard(s): **

[MA2015] GEO (9-12) 16: Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar. [G-SRT3]

**Subject:**Mathematics

**Title:**Symmetries II

**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

**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.
**Standard(s): **

[MA2015] MI1 (9-12) 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

**Title:** Symmetries IV

**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.
**Standard(s): **

[MA2015] GEO (9-12) 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.* [G-CO12]

**Subject:**Mathematics

**Title:**Symmetries IV

**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

**Title:** Blue Squares and Beyond

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students manipulate two rectangles to create examples of similarity and to study the effects on area ratios. Students sketch similar figures, verify proportionality, and apply these concepts to structures in their world.
**Standard(s): **

[MA2015] (8) 19: Understand that a two-dimensional 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 two-dimensional figures, describe a sequence that exhibits the similarity between them. [8-G4]

**Subject:**Mathematics

**Title:**Blue Squares and Beyond

**Description:**In this lesson, one of a multi-part unit from Illuminations, students manipulate two rectangles to create examples of similarity and to study the effects on area ratios. Students sketch similar figures, verify proportionality, and apply these concepts to structures in their world.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Archimedes' Puzzle

**Description:**
In this lesson, students learn about the history of the Stomachion, an ancient tangram-type puzzle. Students use the puzzle pieces to create other figures, learn about symmetry and transformations and investigate the areas of the pieces.
**Standard(s): **

[MA2015] (8) 19: Understand that a two-dimensional 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 two-dimensional figures, describe a sequence that exhibits the similarity between them. [8-G4]

**Subject:**Mathematics

**Title:**Archimedes' Puzzle

**Description:**In this lesson, students learn about the history of the Stomachion, an ancient tangram-type puzzle. Students use the puzzle pieces to create other figures, learn about symmetry and transformations and investigate the areas of the pieces.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8

**Title:** Cyclic Figures

**Description:**
Students will recognize rotation symmetry in figures and examining various rotation symmetries.
**Standard(s): **

[MA2015] GEO (9-12) 6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. [G-CO6]

**Subject:**Mathematics

**Title:**Cyclic Figures

**Description:**Students will recognize rotation symmetry in figures and examining various rotation symmetries.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Dihedral Figures

**Description:**
Students will recognize dihedral symmetry and reflections in figures and examining various symmetries.
**Standard(s): **

[MA2015] GEO (9-12) 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. [G-SRT2]

**Subject:**Mathematics

**Title:**Dihedral Figures

**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

**Title:** Isometric Drawing Tool

**Description:**
Create dynamic drawings on isometric dot paper with this interactive tool. Draw 2-D and 3-D figures using edges, faces, or cubes that you can shift, rotate, color, or decompose.
**Standard(s): **

[MA2015] GEO (9-12) 38: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. [G-GMD4]

**Subject:**Mathematics

**Title:**Isometric Drawing Tool

**Description:**Create dynamic drawings on isometric dot paper with this interactive tool. Draw 2-D and 3-D figures using edges, faces, or cubes that you can shift, rotate, color, or decompose.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8,9,10,11,12

**Title:** Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Reflections

**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.
**Standard(s): **

[MA2015] GEO (9-12) 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.* [G-CO12]

**Subject:**Mathematics

**Title:**Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Reflections

**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

**Title:** Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Transformations

**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.
**Standard(s): **

[MA2015] GEO (9-12) 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.

**Subject:**Mathematics

**Title:**Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures: Composing Transformations

**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

**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.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**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