**Title:** Human Angles

**Description:**
This lesson is designed to get your students moving! The lesson focuses primarily on transversals and angles. Students will be able to identify and relate some angles to cheer moves.
This is a College- and Career-Ready Standards showcase lesson plan.
**Standard(s): **

[MA2015] GEO (9-12) 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).* [G-MG3]

**Subject:**English Language Arts (10), or Mathematics (9 - 12)

**Title:**Human Angles

**Description:**This lesson is designed to get your students moving! The lesson focuses primarily on transversals and angles. Students will be able to identify and relate some angles to cheer moves. This is a College- and Career-Ready Standards showcase lesson plan.

**Title:** Investigation of Special Segments of Triangles

**Description:**
This lesson will enable students to investigate three special segments of triangles in a very concrete way. The students will fold paper triangles to create the segments. This lesson would be a great way for students to explore the properties of the segments and their intersections.
**Standard(s): **

[MA2015] GEO (9-12) 26: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [G-C3]

**Subject:**Mathematics (9 - 12)

**Title:**Investigation of Special Segments of Triangles

**Description:**This lesson will enable students to investigate three special segments of triangles in a very concrete way. The students will fold paper triangles to create the segments. This lesson would be a great way for students to explore the properties of the segments and their intersections.

**Title:** Swimming Pool Math

**Description:**
Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
**Standard(s): **

[MA2015] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. [8-G9]

**Subject:**Mathematics (6 - 12)

**Title:**Swimming Pool Math

**Description:**Students will use a swimming pool example to practice finding perimeter and area of different rectangles.

**Title:** Soda Cans

**Description:**
This reproducible activity sheet, from an Illuminations lesson, guides students through a simulation in which they try different arrangements to make the most efficient use of space and thus pack the most soda cans into a rectangular packing box.
**Standard(s): **

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

**Subject:**Mathematics

**Title:**Soda Cans

**Description:**This reproducible activity sheet, from an Illuminations lesson, guides students through a simulation in which they try different arrangements to make the most efficient use of space and thus pack the most soda cans into a rectangular packing box.

**Thinkfinity Partner:**Illuminations

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

**Title:** Symmetries II: Conclusions

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

[MA2015] MI1 (9-12) 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 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

**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:** 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:** Inequalities in Triangles

**Description:**
In this Illuminations lesson, students use pasta to create models of triangles and non-triangles in order to investigate the relationship between the longest side of the triangle and the sum of the other two sides of the triangle. In addition, students measure the sides and angles of a scalene triangle and investigate the relationship between the location of the largest angle and largest side in a triangle. There are also links to online activity sheets.
**Standard(s): **

[MA2015] GEO (9-12) 17: Prove theorems about triangles. *Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity.* [G-SRT4]

**Subject:**Mathematics

**Title:**Inequalities in Triangles

**Description:**In this Illuminations lesson, students use pasta to create models of triangles and non-triangles in order to investigate the relationship between the longest side of the triangle and the sum of the other two sides of the triangle. In addition, students measure the sides and angles of a scalene triangle and investigate the relationship between the location of the largest angle and largest side in a triangle. There are also links to online activity sheets.

**Thinkfinity Partner:**Illuminations

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

**Title:** Location, Location, Location

**Description:**
In this Illuminations lesson, students use a dynamic geometry applet to investigate the relationship between the distances from a point inside a regular polygon to each side. In addition, there are links to online activity sheets and other related resources.
**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

**Title:**Location, Location, Location

**Description:**In this Illuminations lesson, students use a dynamic geometry applet to investigate the relationship between the distances from a point inside a regular polygon to each side. In addition, there are links to online activity sheets and other related resources.

**Thinkfinity Partner:**Illuminations

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

**Title:** Reflect on This

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

[MA2015] MI1 (9-12) 11: Describe the development of mathematical tools and their applications. (Alabama)

**Subject:**Mathematics

**Title:**Reflect on This

**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

**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:** Soda Rack

**Description:**
In this lesson, one of a three-part unit from Illuminations, students consider the arrangement of cans placed in a bin with two vertical sides and discover an interesting result. They then prove their conjectures about the interesting results. In addition, there are links to online activity sheets and other related resources.
**Standard(s): **

[MA2015] GEO (9-12) 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).* [G-MG3]

**Subject:**Mathematics

**Title:**Soda Rack

**Description:**In this lesson, one of a three-part unit from Illuminations, students consider the arrangement of cans placed in a bin with two vertical sides and discover an interesting result. They then prove their conjectures about the interesting results. In addition, there are links to online activity sheets and other related resources.

**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:** Triangle Classification

**Description:**
In this Illuminations lesson, based on the Triangle Classification problem, students attempt to classify triangles formed in a plane when a randomly selected point is connected to the endpoints of a given line segment. Students classify triangles according to sides and angles. In addition, there are links to online activity sheets and other related resources.
**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:**Triangle Classification

**Description:**In this Illuminations lesson, based on the Triangle Classification problem, students attempt to classify triangles formed in a plane when a randomly selected point is connected to the endpoints of a given line segment. Students classify triangles according to sides and angles. In addition, there are links to online activity sheets and other related resources.

**Thinkfinity Partner:**Illuminations

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

**Title:** Triangle Classification

**Description:**
This transparency, from an Illuminations lesson, asks students to identify all points that create right, obtuse, isosceles, acute, scalene and equilateral triangles when given an AB segment.
**Standard(s): **

[MA2015] GEO (9-12) 26: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [G-C3]

**Subject:**Mathematics

**Title:**Triangle Classification

**Description:**This transparency, from an Illuminations lesson, asks students to identify all points that create right, obtuse, isosceles, acute, scalene and equilateral triangles when given an AB segment.

**Thinkfinity Partner:**Illuminations

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

**Title:** Triangula Island Overhead

**Description:**
This reproducible transparency, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular polygon such that the sum of the distances to each side is a minimum.
**Standard(s): **

[MA2015] GEO (9-12) 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).* [G-MG3]

**Subject:**Mathematics

**Title:**Triangula Island Overhead

**Description:**This reproducible transparency, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular polygon such that the sum of the distances to each side is a minimum.

**Thinkfinity Partner:**Illuminations

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

**Title:** Triangula Island

**Description:**
This student reproducible, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular triangle such that the sum of the distances to each side is a minimum.
**Standard(s): **

[MA2015] GEO (9-12) 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).* [G-MG3]

**Subject:**Mathematics

**Title:**Triangula Island

**Description:**This student reproducible, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular triangle such that the sum of the distances to each side is a minimum.

**Thinkfinity Partner:**Illuminations

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

**Title:** Using Cubes and Isometric Drawings

**Description:**
In this unit of six lessons, from Illuminations, students explore polyhedra using different representations and perspectives for three dimensional block figures. In addition, students examine area and volume concepts for block figures within this context.
**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:**Using Cubes and Isometric Drawings

**Description:**In this unit of six lessons, from Illuminations, students explore polyhedra using different representations and perspectives for three dimensional block figures. In addition, students examine area and volume concepts for block figures within this context.

**Thinkfinity Partner:**Illuminations

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

**Title:** Dividing a Town into Pizza Delivery Regions

**Description:**
In this Illuminations lesson, students must determine how to divide a town based on which pizzeria is closest to a given location. To solve this problem, students will construct perpendicular bisectors, find circumcenters, calculate area, and use proportions.
**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:**Dividing a Town into Pizza Delivery Regions

**Description:**In this Illuminations lesson, students must determine how to divide a town based on which pizzeria is closest to a given location. To solve this problem, students will construct perpendicular bisectors, find circumcenters, calculate area, and use proportions.

**Thinkfinity Partner:**Illuminations

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

**Title:** Geoboard Paper

**Description:**
This reproducible geoboard grid, from an Illuminations lesson, allows students to complete geoboard activities using pencils and paper.
**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:**Geoboard Paper

**Description:**This reproducible geoboard grid, from an Illuminations lesson, allows students to complete geoboard activities using pencils and paper.

**Thinkfinity Partner:**Illuminations

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

**Title:** Geometric Constructions with Dynamic Geometric Software

**Digital Tool:**
Geogebra **Web Address URL:**
http://www.geogebra.org **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. **Digital Tool Description:** Geogebra is a free downloadable geometry software package that provides for both graphical and algebraic input. It will allow students the opportunity to use interactive software to do constructions.

**Title:**Geometric Constructions with Dynamic Geometric Software

**Digital Tool:**Geogebra

**Digital Tool Description:**Geogebra is a free downloadable geometry software package that provides for both graphical and algebraic input. It will allow students the opportunity to use interactive software to do constructions.

**Title:** Virtual Geometry

**Digital Tool:**
Geometry Pad App (iPad App) **Web Address URL:**
https://itunes.apple.com/us/app/geometry-pad/id517461177?mt=8 **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. **Digital Tool Description:** Geometry Pad is an iPad App that provides students interactive practice in creating geometric shapes and understanding geomteric cocepts. This app helps students learn geometry using an engaging and interactive coordinate plane.

**Title:**Virtual Geometry

**Digital Tool:**Geometry Pad App (iPad App)

**Digital Tool Description:**Geometry Pad is an iPad App that provides students interactive practice in creating geometric shapes and understanding geomteric cocepts. This app helps students learn geometry using an engaging and interactive coordinate plane.

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

**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.
**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: Visualizing Transformations

**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

**Title:** Hexagon Island

**Description:**
This student interactive, from an Illuminations lesson, allows students to explore the distances from an interior point of a hexagon to its sides and determine the sum of these perpendicular distances.
**Standard(s): **

[MA2015] GEO (9-12) 25: Identify and describe *relationships* among inscribed angles, radii, and chords. *Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.* [G-C2]

**Subject:**Mathematics

**Title:**Hexagon Island

**Description:**This student interactive, from an Illuminations lesson, allows students to explore the distances from an interior point of a hexagon to its sides and determine the sum of these perpendicular distances.

**Thinkfinity Partner:**Illuminations

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

**Title:** Hospital Locator

**Description:**
In this student interactive, from an Illuminations lesson, students act as community planners, trying to place a new medical center equidistant from three cities.
**Standard(s): **

[MA2015] MI1 (9-12) 11: Describe the development of mathematical tools and their applications. (Alabama)

**Subject:**Mathematics

**Title:**Hospital Locator

**Description:**In this student interactive, from an Illuminations lesson, students act as community planners, trying to place a new medical center equidistant from three cities.

**Thinkfinity Partner:**Illuminations

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

**Title:** IGD: Angle Bisector

**Description:**
This student interactive, from Illuminations, helps students understand and investigate angle bisectors. Students read a definition and then construct an angle bisector using the interactive tool. Finally, students take a closer look at the properties of angle bisectors by answering a set of questions and then checking their answers.
**Standard(s): **

[MA2015] MI1 (9-12) 11: Describe the development of mathematical tools and their applications. (Alabama)

**Subject:**Mathematics

**Title:**IGD: Angle Bisector

**Description:**This student interactive, from Illuminations, helps students understand and investigate angle bisectors. Students read a definition and then construct an angle bisector using the interactive tool. Finally, students take a closer look at the properties of angle bisectors by answering a set of questions and then checking their answers.

**Thinkfinity Partner:**Illuminations

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

**Title:** IGD: Area of a Triangle

**Description:**
This student interactive, from Illuminations, helps students understand and investigate how to find the area of a triangle by finding a way to make it look like a simpler shap--one whose area formula is known. Students make a copy of the triangle, and then make a parallelogram using the triangle and its copy. Students then determine that the area of the triangle is one-half that of the parallelogram.
**Standard(s): **

[MA2015] GEO (9-12) 17: Prove theorems about triangles. *Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity.* [G-SRT4]

**Subject:**Mathematics

**Title:**IGD: Area of a Triangle

**Description:**This student interactive, from Illuminations, helps students understand and investigate how to find the area of a triangle by finding a way to make it look like a simpler shap--one whose area formula is known. Students make a copy of the triangle, and then make a parallelogram using the triangle and its copy. Students then determine that the area of the triangle is one-half that of the parallelogram.

**Thinkfinity Partner:**Illuminations

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

**Title:** IGD: Euler Line

**Description:**
This student interactive, from Illuminations, helps students understand and investigate Euler lines. Students read a definition and then construct the Euler line of a triangle using the interactive tool. They learn that the Euler line involves three points associated with triangles: the circumcenter, orthocenter, and centroid.
**Standard(s): **

[MA2015] MI1 (9-12) 11: Describe the development of mathematical tools and their applications. (Alabama)

**Subject:**Mathematics

**Title:**IGD: Euler Line

**Description:**This student interactive, from Illuminations, helps students understand and investigate Euler lines. Students read a definition and then construct the Euler line of a triangle using the interactive tool. They learn that the Euler line involves three points associated with triangles: the circumcenter, orthocenter, and centroid.

**Thinkfinity Partner:**Illuminations

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

**Title:** IGD: Median

**Description:**
This student interactive, from Illuminations, helps students understand and investigate the median of a triangle. Students read a definition and then use the interactive tool to manipulate and explore the properties of triangle medians by changing the shape of a triangle.
**Standard(s): **

[MA2015] GEO (9-12) 26: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [G-C3]

**Subject:**Mathematics

**Title:**IGD: Median

**Description:**This student interactive, from Illuminations, helps students understand and investigate the median of a triangle. Students read a definition and then use the interactive tool to manipulate and explore the properties of triangle medians by changing the shape of a triangle.

**Thinkfinity Partner:**Illuminations

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

**Title:** IGD: Perpendicular Bisector

**Description:**
This student interactive, from Illuminations, helps students understand and investigate perpendicular bisectors, which are lines perpendicular to a segment that divide it into two congruent segments. Students read a definition and then construct a perpendicular bisector of a segment using the interactive tool.
**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:**IGD: Perpendicular Bisector

**Description:**This student interactive, from Illuminations, helps students understand and investigate perpendicular bisectors, which are lines perpendicular to a segment that divide it into two congruent segments. Students read a definition and then construct a perpendicular bisector of a segment using the interactive tool.

**Thinkfinity Partner:**Illuminations

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

**Title:** IGD: Perpendicular Lines

**Description:**
This student interactive, from Illuminations, helps students understand and investigate perpendicular lines. Students read a definition, and then use the interactive to explore the properties of two perpendicular 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.

**Subject:**Mathematics

**Title:**IGD: Perpendicular Lines

**Description:**This student interactive, from Illuminations, helps students understand and investigate perpendicular lines. Students read a definition, and then use the interactive to explore the properties of two perpendicular lines.

**Thinkfinity Partner:**Illuminations

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

**Title:** IGD: Simson Line

**Description:**
This student interactive, from Illuminations, helps students understand and investigate a triangle s Simson line, which is the line passing through the feet of the perpendiculars dropped from P to the three sides of a triangle. Students construct the Simson line for a given triangle using the interactive applet.
**Standard(s): **

[MA2015] MI1 (9-12) 11: Describe the development of mathematical tools and their applications. (Alabama)

**Subject:**Mathematics

**Title:**IGD: Simson Line

**Description:**This student interactive, from Illuminations, helps students understand and investigate a triangle s Simson line, which is the line passing through the feet of the perpendiculars dropped from P to the three sides of a triangle. Students construct the Simson line for a given triangle using the interactive applet.

**Thinkfinity Partner:**Illuminations

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

**Title:** Interactive Geometry Dictionary: Lines in Geometry

**Description:**
This student interactive, from Illuminations, explores lines and their importance to geometry. Students can investigate the definitions and properties of perpendicular lines, segments, medians, Euler lines, and more.
**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:**Interactive Geometry Dictionary: Lines in Geometry

**Description:**This student interactive, from Illuminations, explores lines and their importance to geometry. Students can investigate the definitions and properties of perpendicular lines, segments, medians, Euler lines, and more.

**Thinkfinity Partner:**Illuminations

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

**Title:** Interactive Geometry Dictionary: Areas in Geometry

**Description:**
This student interactive, from Illuminations, demonstrates how to find the area of three common shapes. Interactive investigations demonstrate finding the area of a rectangle, parallelogram, and triangle.
**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:**Interactive Geometry Dictionary: Areas in Geometry

**Description:**This student interactive, from Illuminations, demonstrates how to find the area of three common shapes. Interactive investigations demonstrate finding the area of a rectangle, parallelogram, and triangle.

**Thinkfinity Partner:**Illuminations

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

**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:** Isosceles Triangle Investigation

**Description:**
This student interactive, from an Illuminations lesson, allows students to investigate the relationship between the area of the triangle and the length of its base.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Isosceles Triangle Investigation

**Description:**This student interactive, from an Illuminations lesson, allows students to investigate the relationship between the area of the triangle and the length of its base.

**Thinkfinity Partner:**Illuminations

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

**Title:** Octagon Island

**Description:**
This student interactive, from an Illuminations lesson, allows students to explore the distances from an interior point of a octagon to its sides and determine the sum of these distances.
**Standard(s): **

[MA2015] GEO (9-12) 34: Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama)

**Subject:**Mathematics

**Title:**Octagon Island

**Description:**This student interactive, from an Illuminations lesson, allows students to explore the distances from an interior point of a octagon to its sides and determine the sum of these distances.

**Thinkfinity Partner:**Illuminations

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

**Title:** Soccer Problem

**Description:**
This student interactive, from an Illuminations lesson, allows students to investigate a soccer problem by changing the location of a soccer player as well as the distance between the player and the goal posts. The angle changes as the player is moved, and students must therefore determine the player s position so that the angle is maximized.
**Standard(s): **

[MA2015] GEO (9-12) 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).* [G-MG3]

**Subject:**Mathematics

**Title:**Soccer Problem

**Description:**This student interactive, from an Illuminations lesson, allows students to investigate a soccer problem by changing the location of a soccer player as well as the distance between the player and the goal posts. The angle changes as the player is moved, and students must therefore determine the player s position so that the angle is maximized.

**Thinkfinity Partner:**Illuminations

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

**Title:** Square Graphs

**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.
**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:**Square Graphs

**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

**Title:** Triangle Classification

**Description:**
This student interactive, from an Illuminations lesson, allows students to turn a segment into a right triangle, an isosceles triangle, and an obtuse triangle.
**Standard(s): **

[MA2015] GEO (9-12) 17: Prove theorems about triangles. *Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity.* [G-SRT4]

**Subject:**Mathematics

**Title:**Triangle Classification

**Description:**This student interactive, from an Illuminations lesson, allows students to turn a segment into a right triangle, an isosceles triangle, and an obtuse triangle.

**Thinkfinity Partner:**Illuminations

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

**Title:** Triangle Island

**Description:**
This student interactive, from an Illuminations lesson, allows students to explore the distances from an interior point of a polygon to its sides and determine the sum of these distances.
**Standard(s): **

[MA2015] GEO (9-12) 17: Prove theorems about triangles.

**Subject:**Mathematics

**Title:**Triangle Island

**Description:**This student interactive, from an Illuminations lesson, allows students to explore the distances from an interior point of a polygon to its sides and determine the sum of these distances.

**Thinkfinity Partner:**Illuminations

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

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

**Description:**
**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: Identifying Unknown Transformations

**Description:**

**Thinkfinity Partner:**Illuminations

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

**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.

**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