**Title:** Figure it out...

**Description:**
This is an Internet-based (online) and group discussion lesson. Students will learn the formulas for surface area and volume of cylinders and cones. Students should have previously learned how to determine the area for a circle; however, this lesson will review that particular process.
**Standard(s): **

[MA2015] GEO (9-12) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)

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

**Title:**Figure it out...

**Description:**This is an Internet-based (online) and group discussion lesson. Students will learn the formulas for surface area and volume of cylinders and cones. Students should have previously learned how to determine the area for a circle; however, this lesson will review that particular process.

**Title:** Surface Area of Pyramids and Cones

**Description:**
In this inquiry-based lesson, students will discover the formulas for the surface area of pyramids and cones.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] GEO (9-12) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)

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

**Title:**Surface Area of Pyramids and Cones

**Description:**In this inquiry-based lesson, students will discover the formulas for the surface area of pyramids and cones. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**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:** Tetrahedral Kites

**Description:**
In this Illuminations lesson, students construct tetrahedrons and describe the linear, area and volume using non-traditional units of measure. They combine four tetrahedra to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed. In addition, there is a link to an assessment activity sheet.
**Standard(s): **

[MA2015] GEO (9-12) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)

**Subject:**Mathematics

**Title:**Tetrahedral Kites

**Description:**In this Illuminations lesson, students construct tetrahedrons and describe the linear, area and volume using non-traditional units of measure. They combine four tetrahedra to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed. In addition, there is a link to an assessment activity sheet.

**Thinkfinity Partner:**Illuminations

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

**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:** Are They Possible? Overhead

**Description:**
This reproducible transparency, from an Illuminations lesson, depicts several isometric drawings of several '' impossible'' figures.
**Standard(s): **

[MA2015] GEO (9-12) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)

**Subject:**Mathematics

**Title:**Are They Possible? Overhead

**Description:**This reproducible transparency, from an Illuminations lesson, depicts several isometric drawings of several '' impossible'' figures.

**Thinkfinity Partner:**Illuminations

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

**Title:** Building Using the Front-Right-Top View

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students explore drawing the front-right-top view when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the front-right-top view.
**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:**Building Using the Front-Right-Top View

**Description:**In this lesson, one of a multi-part unit from Illuminations, students explore drawing the front-right-top view when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the front-right-top view.

**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:** Circle Packing and Curvature

**Description:**
In this lesson, one of a three-part unit from Illuminations, students investigate the curvature of circles. Students apply definitions and theorems regarding curvature to solve circle problems. In addition, there are links to an online activity sheet 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:**Circle Packing and Curvature

**Description:**In this lesson, one of a three-part unit from Illuminations, students investigate the curvature of circles. Students apply definitions and theorems regarding curvature to solve circle problems. In addition, there are links to an online activity sheet and other related resources.

**Thinkfinity Partner:**Illuminations

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

**Title:** Do They Match? Overhead

**Description:**
This reproducible transparency, from an Illuminations lesson, depicts several pairs of isometric drawings of three-dimensional figures. Students determine whether the drawings in each pair represent the same shape as one another.
**Standard(s): **

[MA2015] GEO (9-12) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [G-GMD3]

**Subject:**Mathematics

**Title:**Do They Match? Overhead

**Description:**This reproducible transparency, from an Illuminations lesson, depicts several pairs of isometric drawings of three-dimensional figures. Students determine whether the drawings in each pair represent the same shape as one another.

**Thinkfinity Partner:**Illuminations

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

**Title:** Flowing Through Mathematics

**Description:**
This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.
**Standard(s): **

[MA2015] ALC (9-12) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)

**Subject:**Mathematics

**Title:**Flowing Through Mathematics

**Description:**This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.

**Thinkfinity Partner:**Illuminations

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