**Title:** Falling Down a Rabbit Hole Can Lead to a King Sized Experience - Exploring Similar Figures Using Proportions

**Description:**
In this lesson, students will explore the concept of similarity. Students will first simplify ratios, solve proportions using the cross product property, and use properties of proportions to solve real-world problems. Similar polygons will then be introduced and their properties used to solve real-world problems.
**Standard(s): **

[MA2015] (7) 2: Recognize and represent proportional relationships between quantities. [7-RP2]

**Subject:**Mathematics (7 - 12)

**Title:**Falling Down a Rabbit Hole Can Lead to a King Sized Experience - Exploring Similar Figures Using Proportions

**Description:**In this lesson, students will explore the concept of similarity. Students will first simplify ratios, solve proportions using the cross product property, and use properties of proportions to solve real-world problems. Similar polygons will then be introduced and their properties used to solve real-world problems.

**Title:** I Can Determine The Height Of A Rocket!

**Description:**
The lesson is intended to give students a fun real-world experience in applying their math skills. They will use trigonometric ratios to calculate heights of tall structures. They will also use the Internet to convert their calculations from standard to metric units and visa versa.
**Standard(s): **

[MA2015] GEO (9-12) 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).* [G-MG1]

**Subject:**Mathematics (9 - 12), or Technology Education (9 - 12)

**Title:**I Can Determine The Height Of A Rocket!

**Description:**The lesson is intended to give students a fun real-world experience in applying their math skills. They will use trigonometric ratios to calculate heights of tall structures. They will also use the Internet to convert their calculations from standard to metric units and visa versa.

**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:** 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:** 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:** 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:** 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