**Title:** The Golden Face

**Description:**
The following lesson serves as a review surface area activity. Specifically, the students will explore the surface area of a three-dimensional Styrofoam cube using lima beans. To accommodate at-risk or diverse learners, cooperative learning groups will be utilized. This activity was created for a module entitled Exploring the Surface Area with the Mad Scientist (TU Math & Science Partnership Project).
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics (7)

**Title:**The Golden Face

**Description:**The following lesson serves as a review surface area activity. Specifically, the students will explore the surface area of a three-dimensional Styrofoam cube using lima beans. To accommodate at-risk or diverse learners, cooperative learning groups will be utilized. This activity was created for a module entitled Exploring the Surface Area with the Mad Scientist (TU Math & Science Partnership Project).

**Title:** Have Your Math and Eat It, Too!

**Description:**
In this two-day lesson, students will collaborate to create a healthy pizza using only geometric items that have been precisely measured. Students must identify the items as triangle, quadrilateral (parallelogram), or cube. Next, students will measure the items that they place on their pizza. Finally, students will bake their pizza; therefore, having their math and eating it, too!
**Standard(s): **

[MA2015] (6) 21: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. [6-G1]

**Subject:**Human Services (7), or Mathematics (4 - 7)

**Title:**Have Your Math and Eat It, Too!

**Description:**In this two-day lesson, students will collaborate to create a healthy pizza using only geometric items that have been precisely measured. Students must identify the items as triangle, quadrilateral (parallelogram), or cube. Next, students will measure the items that they place on their pizza. Finally, students will bake their pizza; therefore, having their math and eating it, too!

**Title:** 2020 - Year of the Cool School!

**Description:**
Hey! Are you tired of your old lame school? Are the halls too narrow? Do you like walking outside to get to the cafeteria? Are the classrooms too small? Is the design too simple - just too wacky for a middle school? Well, now is the biggest break of your lives - You and your peers will design the school of the future and make history! Your biggest challenge is to create a section of a dream school that oozes and awes your peers. Each team will design a section (cafeteria, library, performing arts room, or recreational room) of the school, research different floor coverings for the section, research different loans to cover the cost of the floor coverings, and design a model of each section. Grab your math knowledge and as many construction tools as you can because you are about to construct a building for the world to remember. But wait, THE CATCH - your team will be competing against other groups. So put your thinking caps on and let the building begin!
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

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

**Title:**2020 - Year of the Cool School!

**Description:**Hey! Are you tired of your old lame school? Are the halls too narrow? Do you like walking outside to get to the cafeteria? Are the classrooms too small? Is the design too simple - just too wacky for a middle school? Well, now is the biggest break of your lives - You and your peers will design the school of the future and make history! Your biggest challenge is to create a section of a dream school that oozes and awes your peers. Each team will design a section (cafeteria, library, performing arts room, or recreational room) of the school, research different floor coverings for the section, research different loans to cover the cost of the floor coverings, and design a model of each section. Grab your math knowledge and as many construction tools as you can because you are about to construct a building for the world to remember. But wait, THE CATCH - your team will be competing against other groups. So put your thinking caps on and let the building begin!

**Title:** Painting the Pyramids

**Description:**
The students will find the area of each two dimensional figure on a net of a square pyramid. In groups, students will cut out the net and create a square pyramid. Groups will then discuss how to find the lateral area and the total surface area of the solid.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics (6 - 7)

**Title:**Painting the Pyramids

**Description:**The students will find the area of each two dimensional figure on a net of a square pyramid. In groups, students will cut out the net and create a square pyramid. Groups will then discuss how to find the lateral area and the total surface area of the solid. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Popcorn - Bucket or Box?

**Description:**
In this exploration, students will apply their knowledge of finding volume and surface area of cylinders and rectangular prisms. Students will make recommendations to the local movie theater after determining which package is cost effective. Students will support their decision through a presentation.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**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 - 8)

**Title:**Popcorn - Bucket or Box?

**Description:**In this exploration, students will apply their knowledge of finding volume and surface area of cylinders and rectangular prisms. Students will make recommendations to the local movie theater after determining which package is cost effective. Students will support their decision through a presentation. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Cutting the CHEESE

**Description:**
The students will find the area of each two dimensional figure on a net of a triangular prism. In groups, students will cut out the net and create a triangular prism. Groups will then discuss how to find the lateral area and the total surface area of the solid.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics (6 - 7)

**Title:**Cutting the CHEESE

**Description:**The students will find the area of each two dimensional figure on a net of a triangular prism. In groups, students will cut out the net and create a triangular prism. Groups will then discuss how to find the lateral area and the total surface area of the solid. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Nifty Nets

**Description:**
During this activity, students will create nets for prisms. They will find the volume and surface area of the shapes. They will also use interactive activities to review three-dimensional shapes.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.
**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 - 8)

**Title:**Nifty Nets

**Description:**During this activity, students will create nets for prisms. They will find the volume and surface area of the shapes. They will also use interactive activities to review three-dimensional shapes.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.

**Title:** Pump Up the Volume

**Description:**
In this lesson, students will be required to generate a formula for volume of a rectangular prism. Students working in cooperative groups will use prior knowledge for finding area of a rectangle to determine the "amount of area in a rectangular prism" they have created with a stack of cards.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics (6 - 7)

**Title:**Pump Up the Volume

**Description:**In this lesson, students will be required to generate a formula for volume of a rectangular prism. Students working in cooperative groups will use prior knowledge for finding area of a rectangle to determine the "amount of area in a rectangular prism" they have created with a stack of cards. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Thinking outside the "BOX"

**Description:**
The students will find the area of each two dimensional figure on a net of a rectangular prism. In groups, students will cut out the net and create a rectangular prism. Groups will then discuss how to find the lateral area and the total surface area of the solid.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics (6 - 7)

**Title:**Thinking outside the "BOX"

**Description:**The students will find the area of each two dimensional figure on a net of a rectangular prism. In groups, students will cut out the net and create a rectangular prism. Groups will then discuss how to find the lateral area and the total surface area of the solid. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Ping Pong Madness

**Description:**
In this lesson, students will use their knowledge of 3D shapes to create packages for ping pong balls. They must create small, medium and large packages that are cost effective and stack easily. They will make nets of the their packages and find the volume and surface area of each. Students will present the information using a multi-media presentation and a spreadsheet software. This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.
**Standard(s): **

[MA2015] (6) 24: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. [6-G4]

**Subject:**Mathematics (5 - 7), or Technology Education (6 - 8)

**Title:**Ping Pong Madness

**Description:**In this lesson, students will use their knowledge of 3D shapes to create packages for ping pong balls. They must create small, medium and large packages that are cost effective and stack easily. They will make nets of the their packages and find the volume and surface area of each. Students will present the information using a multi-media presentation and a spreadsheet software. This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.

**Title:** Applications of Area Abound

**Description:**
The teacher will first provide direction instruction on area formulas and provide students an opportunity to practice using those formulas. Students will then apply their knowledge of area to real-life situations. They will write a short story to go along with the area problem, then record themselves "acting" it out, and finally add clip art images to illustrate their story. They will then turn all of this into a podcast using Photo Story 3, which can be uploaded to the Internet.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics (6 - 7), or Technology Education (9 - 12)

**Title:**Applications of Area Abound

**Description:**The teacher will first provide direction instruction on area formulas and provide students an opportunity to practice using those formulas. Students will then apply their knowledge of area to real-life situations. They will write a short story to go along with the area problem, then record themselves "acting" it out, and finally add clip art images to illustrate their story. They will then turn all of this into a podcast using Photo Story 3, which can be uploaded to the Internet.

**Title:** Water Tank Creations Part I

**Description:**
In this lesson students will study the surface area and volume of three-dimensional shapes by creating a water tank comprised of these shapes. Students will work in groups of 4-5 to research water tanks, develop scale drawings and build a scale model. Teacher will evaluate the project using a rubric and students will assess one anothers cooperative skills using a rubric.
**Standard(s): **

[MA2015] GEO (9-12) 40: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).* [G-MG2]

**Subject:**Mathematics (7 - 12), or Technology Education (9 - 12)

**Title:**Water Tank Creations Part I

**Description:**In this lesson students will study the surface area and volume of three-dimensional shapes by creating a water tank comprised of these shapes. Students will work in groups of 4-5 to research water tanks, develop scale drawings and build a scale model. Teacher will evaluate the project using a rubric and students will assess one anothers cooperative skills using a rubric.

**Title:** Creating a Water Tank - Part II "Selling the Tank"

**Description:**
Working in groups of 4-5 students will take the information,pictures and 3-D model of the water tank they assembled in Part I of Creating a Water Tank and develop a web page and a video presentation. The web page will be a tool to advertise their water tank construction company and must include hyperlinks and digital pictures. The video presentation will be a "sales pitch" to a city council. The web page and video will be scored using a rubric. The web page and video must include the surface area, volume and cost of construction.
**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 (7 - 12), or Technology Education (9 - 12)

**Title:**Creating a Water Tank - Part II "Selling the Tank"

**Description:**Working in groups of 4-5 students will take the information,pictures and 3-D model of the water tank they assembled in Part I of Creating a Water Tank and develop a web page and a video presentation. The web page will be a tool to advertise their water tank construction company and must include hyperlinks and digital pictures. The video presentation will be a "sales pitch" to a city council. The web page and video will be scored using a rubric. The web page and video must include the surface area, volume and cost of construction.

**Title:** Let’s Tessellate

**Description:**
This lesson is a hands-on, technology-based project that will take place in the classroom and computer lab. Students will discover which regular polygons tessellate the plane by constructing polygonal tessellations. Students will also use a spreadsheet to calculate the area and perimeter of the polygons.
**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 (7 - 12), or Technology Education (9 - 12)

**Title:**Let’s Tessellate

**Description:**This lesson is a hands-on, technology-based project that will take place in the classroom and computer lab. Students will discover which regular polygons tessellate the plane by constructing polygonal tessellations. Students will also use a spreadsheet to calculate the area and perimeter of the polygons.

**Title:** A Swath of Red

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students estimate the area of the country that voted for the Republican candidate and the area that voted for the Democratic candidate in the 2000 presidential election using a grid overlay. Students then compare the areas to the electoral and popular vote election results. Ratios of electoral votes to area are used to make generalizations about the population distribution of the United States.
**Standard(s): **

[MA2015] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7-SP2]

**Subject:**Mathematics

**Title:**A Swath of Red

**Description:**In this lesson, one of a multi-part unit from Illuminations, students estimate the area of the country that voted for the Republican candidate and the area that voted for the Democratic candidate in the 2000 presidential election using a grid overlay. Students then compare the areas to the electoral and popular vote election results. Ratios of electoral votes to area are used to make generalizations about the population distribution of the United States.

**Thinkfinity Partner:**Illuminations

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

**Title:** Circle Packing

**Description:**
In this unit of three Illuminations lessons, students explore circles. In the first lesson students apply the concepts of area and circumference to explore arrangements for soda cans that lead to a more efficient package. In the second lesson they then experiment with three-dimensional arrangements to discover the effect of gravity on the arrangement of soda cans. The final lesson allows students to examine the more advanced mathematical concept of curvature. There are also links to online interactives that are used in the lessons.
**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:**Circle Packing

**Description:**In this unit of three Illuminations lessons, students explore circles. In the first lesson students apply the concepts of area and circumference to explore arrangements for soda cans that lead to a more efficient package. In the second lesson they then experiment with three-dimensional arrangements to discover the effect of gravity on the arrangement of soda cans. The final lesson allows students to examine the more advanced mathematical concept of curvature. There are also links to online interactives that are used in the lessons.

**Thinkfinity Partner:**Illuminations

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

**Title:** Do They Match?

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use three dimensional figures they have constructed to determine when two isometric drawings can represent the same shape. They also determine what possible shapes might have the same isometric drawing and explain their reasoning.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Do They Match?

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use three dimensional figures they have constructed to determine when two isometric drawings can represent the same shape. They also determine what possible shapes might have the same isometric drawing and explain their reasoning.

**Thinkfinity Partner:**Illuminations

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

**Title:** Front-right-top Views

**Description:**
This reproducible transparency, from an Illuminations lesson, depicts an isometric drawing of a three-dimensional figure, along with its front, right, and top views.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Front-right-top Views

**Description:**This reproducible transparency, from an Illuminations lesson, depicts an isometric drawing of a three-dimensional figure, along with its front, right, and top views.

**Thinkfinity Partner:**Illuminations

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

**Title:** Soda Cans

**Description:**
In this lesson, one of a three-part unit from Illuminations, students investigate various designs for packaging soda cans and use geometry to analyze their designs. Students work to create more efficient arrangements that require less packaging material than the traditional rectangular arrays. 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 Cans

**Description:**In this lesson, one of a three-part unit from Illuminations, students investigate various designs for packaging soda cans and use geometry to analyze their designs. Students work to create more efficient arrangements that require less packaging material than the traditional rectangular arrays. In addition, there are links to online activity sheets and other related resources.

**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:** 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:** Area Contractor

**Description:**
In this Illuminations lesson, students are given the opportunity to explore surface area in the same way that a contractor might when providing an estimate to a potential customer. Once the customer accepts the estimate, a more detailed measurement is taken and a quote prepared.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Area Contractor

**Description:**In this Illuminations lesson, students are given the opportunity to explore surface area in the same way that a contractor might when providing an estimate to a potential customer. Once the customer accepts the estimate, a more detailed measurement is taken and a quote prepared.

**Thinkfinity Partner:**Illuminations

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

**Title:** Scaling Away

**Description:**
In this Illuminations lesson, students measure the dimensions of a common object, multiply each dimension by a scale factor, and examine a model using the multiplied dimensions. Students then compare the surface area and volume of the original object with those of the enlarged model.
**Standard(s): **

[MA2015] GEO (9-12) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [G-SRT5]

**Subject:**Mathematics

**Title:**Scaling Away

**Description:**In this Illuminations lesson, students measure the dimensions of a common object, multiply each dimension by a scale factor, and examine a model using the multiplied dimensions. Students then compare the surface area and volume of the original object with those of the enlarged model.

**Thinkfinity Partner:**Illuminations

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

**Title:** History on Stage Pop-Up Lesson

**Description:**
This lesson plan, developed in support of the exhibition Paper Engineering: Fold, Pull, Pop, and Turn , introduces students to the variety of mechanisms included in movable books and encourages them to build their own pop-up in support of a social studies lesson. Making pop-ups subtly reinforces student's understanding of mechanical movement and helps budding architects, designers, and engineers begin to envision objects three-dimensionally.
**Standard(s): **

[MA2015] (8) 16: Verify experimentally the properties of rotations, reflections, and translations: [8-G1]

**Subject:**Arts,Mathematics,Social Studies, Language arts

**Title:**History on Stage Pop-Up Lesson

**Description:**This lesson plan, developed in support of the exhibition Paper Engineering: Fold, Pull, Pop, and Turn , introduces students to the variety of mechanisms included in movable books and encourages them to build their own pop-up in support of a social studies lesson. Making pop-ups subtly reinforces student's understanding of mechanical movement and helps budding architects, designers, and engineers begin to envision objects three-dimensionally.

**Thinkfinity Partner:**Smithsonian

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

**Title:** Mathematics and Children's Literature

**Description:**
In this five-lesson unit, from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. Five pieces of literature are applied to teaching a wide range of topics in the mathematics curriculum, from sorting and classifying to the meaning of averages.
**Standard(s): **

[ELA2015] (8) 9: By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of Grades 6-8 text complexity band independently and proficiently. [RL.8.10]

**Subject:**Language Arts,Mathematics

**Title:**Mathematics and Children's Literature

**Description:**In this five-lesson unit, from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. Five pieces of literature are applied to teaching a wide range of topics in the mathematics curriculum, from sorting and classifying to the meaning of averages.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,PreK,1,2,3,4,5,6,7,8

**Title:** Area Formulas

**Description:**
In this unit of four lessons, from Illuminations, students use the area formula for a rectangle to discover the area formulas for triangles, parallelograms and trapezoids. Students also consider irregular figures whose areas can be determined by estimation or decomposition.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Area Formulas

**Description:**In this unit of four lessons, from Illuminations, students use the area formula for a rectangle to discover the area formulas for triangles, parallelograms and trapezoids. Students also consider irregular figures whose areas can be determined by estimation or decomposition.

**Thinkfinity Partner:**Illuminations

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

**Title:** Discovering the Area Formula for Triangles

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students learn the area formula for a triangle. Students find the areas of rectangles and squares and compare them to the areas of triangles derived from the original shape.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Discovering the Area Formula for Triangles

**Description:**In this lesson, one of a multi-part unit from Illuminations, students learn the area formula for a triangle. Students find the areas of rectangles and squares and compare them to the areas of triangles derived from the original shape.

**Thinkfinity Partner:**Illuminations

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

**Title:** Finding the Area of Trapezoids

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students discover the area formula for trapezoids and explore alternative methods for calculating the area of a trapezoid.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Finding the Area of Trapezoids

**Description:**In this lesson, one of a multi-part unit from Illuminations, students discover the area formula for trapezoids and explore alternative methods for calculating the area of a trapezoid.

**Thinkfinity Partner:**Illuminations

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

**Title:** Finding the Area of Irregular Figures

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students estimate the areas of highly irregular shapes and use a process of decomposition to calculate the areas of irregular polygons.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Finding the Area of Irregular Figures

**Description:**In this lesson, one of a multi-part unit from Illuminations, students estimate the areas of highly irregular shapes and use a process of decomposition to calculate the areas of irregular polygons.

**Thinkfinity Partner:**Illuminations

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

**Title:** Trapezoid

**Description:**
This reproducible activity sheet, from an Illuminations lesson, features several drawings of trapezoids of different sizes. Students first estimate then measure the area of the trapezoids.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Trapezoid

**Description:**This reproducible activity sheet, from an Illuminations lesson, features several drawings of trapezoids of different sizes. Students first estimate then measure the area of the trapezoids.

**Thinkfinity Partner:**Illuminations

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

**Title:** Finding the Area of Parallelograms

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use their knowledge of rectangles to discover the area formula for parallelograms.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Finding the Area of Parallelograms

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use their knowledge of rectangles to discover the area formula for parallelograms.

**Thinkfinity Partner:**Illuminations

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

**Title:** Creating A Firewise Defensible Space

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students learn about creating defensible space around a home using a series of fire protection zones. Students then draw the zones that surround a house and estimate the area of each zone.
**Standard(s): **

[MA2015] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Creating A Firewise Defensible Space

**Description:**In this lesson, one of a multi-part unit from Illuminations, students learn about creating defensible space around a home using a series of fire protection zones. Students then draw the zones that surround a house and estimate the area of each zone.

**Thinkfinity Partner:**Illuminations

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

**Title:** Patterns and Function

**Description:**
In this lesson, from Illuminations, students investigate properties of perimeter, area, and volume related to various geometric two- and three-dimensional shapes.
**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

**Title:**Patterns and Function

**Description:**In this lesson, from Illuminations, students investigate properties of perimeter, area, and volume related to various geometric two- and three-dimensional shapes.

**Thinkfinity Partner:**Illuminations

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

**Title:** Learning about Multiplication Using Dynamic Sketches of an Area Model

**Description:**
Students can learn to visualize the effects of multiplying a fixed positive number by positive numbers greater than 1 and less than 1 with this tool. Using interactive figures, students can investigate how changing the height of a rectangle with a fixed width changes its area. 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] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Learning about Multiplication Using Dynamic Sketches of an Area Model

**Description:**Students can learn to visualize the effects of multiplying a fixed positive number by positive numbers greater than 1 and less than 1 with this tool. Using interactive figures, students can investigate how changing the height of a rectangle with a fixed width changes its area. 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:** Pan Balance -- Expressions

**Description:**
This interactive pan balance, from Illuminations, allows students to enter and compare numeric or algebraic expressions. They can '' weigh'' the expressions they want to compare by entering them on either side of the balance, allowing them to practice arithmetic and algebraic skills, as well as to investigate the concept of equivalence.
**Standard(s): **

[MA2015] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8-F2]

**Subject:**Mathematics

**Title:**Pan Balance -- Expressions

**Description:**This interactive pan balance, from Illuminations, allows students to enter and compare numeric or algebraic expressions. They can '' weigh'' the expressions they want to compare by entering them on either side of the balance, allowing them to practice arithmetic and algebraic skills, as well as to investigate the concept of equivalence.

**Thinkfinity Partner:**Illuminations

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

**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

**Title:** Learning about Length, Perimeter, Area, and Volume of Similar Objects by Using Interactive Figures: Side Length, Volume, and Surface Area of Similar Solids

**Description:**
This is part two of a two-part e-example from Illuminations that illustrates how students can learn about the length, perimeter, area, and volume of similar objects using dynamic figures. In this part, Side Length, Volume, and Surface Area of Similar Solids, the user can manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes. 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] (7) 16: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7-G6]

**Subject:**Mathematics

**Title:**Learning about Length, Perimeter, Area, and Volume of Similar Objects by Using Interactive Figures: Side Length, Volume, and Surface Area of Similar Solids

**Description:**This is part two of a two-part e-example from Illuminations that illustrates how students can learn about the length, perimeter, area, and volume of similar objects using dynamic figures. In this part, Side Length, Volume, and Surface Area of Similar Solids, the user can manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes. 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