**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:** 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:** Are They Possible?

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students examine some isometric drawings that seem to be impossible. They investigate one method that Dutch artist M.C. Escher used to create such impossible figures.
**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

**Title:**Are They Possible?

**Description:**In this lesson, one of a multi-part unit from Illuminations, students examine some isometric drawings that seem to be impossible. They investigate one method that Dutch artist M.C. Escher used to create such impossible figures.

**Thinkfinity Partner:**Illuminations

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

**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:** 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:** 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:** Finding Surface Area and Volume

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use an isometric drawing tool to build three-dimensional figures. They then find the surface area and volume of each figure.
**Standard(s): **

[MA2015] GEO (9-12) 35: Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. *Use dissection arguments, Cavalieri's principle, and informal limit arguments.* [G-GMD1]

**Subject:**Mathematics

**Title:**Finding Surface Area and Volume

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use an isometric drawing tool to build three-dimensional figures. They then find the surface area and volume of each figure.

**Thinkfinity Partner:**Illuminations

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

**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:** Purple Prisms

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students investigate rectangular prisms using an online, interactive applet. They manipulate the scale factor that links two three-dimensional rectangular prisms to learn about edge lengths and surface area relationships.
**Standard(s): **

[MA2015] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7-G1]

**Subject:**Mathematics

**Title:**Purple Prisms

**Description:**In this lesson, one of a multi-part unit from Illuminations, students investigate rectangular prisms using an online, interactive applet. They manipulate the scale factor that links two three-dimensional rectangular prisms to learn about edge lengths and surface area relationships.

**Thinkfinity Partner:**Illuminations

**Grade Span:**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:** 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:** 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:** 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