ALEX Lesson Plans
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Title: Mad Scientist Jam Too!
Description:
This activity will serve as an interactive culminating activity for surface area. Specifically, the students will get an opportunity to create a rap, song, or chant utilizing information they have learned and discussed about surface area. Students may use notes or other information approved by the teacher on surface area. Teachers may allow students to incorporate instrumental music to enhance the activity. All performances will be videotaped. This activity was created for a module entitled Exploring the Surface Area with the Mad Scientist (TU Math & Science Partnership Project).
Standard(s): [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [S1] (8) 7: Describe states of matter based on kinetic energy of particles in matter. [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [S1] (8) 7: Describe states of matter based on kinetic energy of particles in matter.
Subject: Mathematics (7), or Science (8)
Title: Mad Scientist Jam Too!
Description: This activity will serve as an interactive culminating activity for surface area. Specifically, the students will get an opportunity to create a rap, song, or chant utilizing information they have learned and discussed about surface area. Students may use notes or other information approved by the teacher on surface area. Teachers may allow students to incorporate instrumental music to enhance the activity. All performances will be videotaped. This activity was created for a module entitled Exploring the Surface Area with the Mad Scientist (TU Math & Science Partnership Project).
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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 threedimensional Styrofoam cube using lima beans. To accommodate atrisk 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): [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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 threedimensional Styrofoam cube using lima beans. To accommodate atrisk 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)
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Title: WHAT ABOUT WOODENRUBIK!
Description:
This activity will serve as a review surface area activity. Specifically, the students will explore what happens to the surface area of a threedimensional wooden rubik cube if it is broken down into smaller pieces or smaller cubes. Cooperative learning groups and handson wooden cubes will be used to accommodate the various learning styles. This activity was created for a module entitled Exploring the Surface Area with the Mad Scientist (TU Math & Science Partnership Project).
Standard(s): [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics (7)
Title: WHAT ABOUT WOODENRUBIK!
Description: This activity will serve as a review surface area activity. Specifically, the students will explore what happens to the surface area of a threedimensional wooden rubik cube if it is broken down into smaller pieces or smaller cubes. Cooperative learning groups and handson wooden cubes will be used to accommodate the various learning styles. This activity was created for a module entitled Exploring the Surface Area with the Mad Scientist (TU Math & Science Partnership Project).
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Title: Have Your Math and Eat It, Too!
Description:
In this twoday 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): [EDT] ED02 (7) 8: Prepare nutritious snacks. [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4] [MA2013] (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 realworld and mathematical problems. [6G1]
Subject: Education and Training (7), or Mathematics (4  7)
Title: Have Your Math and Eat It, Too!
Description: In this twoday 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!
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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): [TC2] (68) 2: Publish digital products that communicate curriculum concepts. [TC2] (68) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information. [MA2013] (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. [7G1] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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!
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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): [MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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.
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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): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
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.
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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): [MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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.
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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 threedimensional shapes.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
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 threedimensional shapes.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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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): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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.
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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): [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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.
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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 multimedia presentation and a spreadsheet software. This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [TC2] (68) 2: Publish digital products that communicate curriculum concepts. [MA2013] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5MD3] [MA2013] (5) 21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5MD4] [MA2013] (5) 22: Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume. [5MD5] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4]
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 multimedia presentation and a spreadsheet software. This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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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 reallife 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): [TC2] CA2 (912) 12: Use digital tools to publish curriculumrelated content. [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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 reallife 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.
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Title: Build a City on Geometry
Description:
The students will be split into small, cooperative groups and build a city following specific guidelines. The students will learn how a city is constructed with angles, intersections, parallel, intersecting, and transversal streets. They will understand that buildings are located at particular points which are considered alternate interior or exterior angles, corresponding angles, etc. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] (7) 15: Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. [7G5] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 20: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. [8G5]
Subject: Mathematics (7  8)
Title: Build a City on Geometry
Description: The students will be split into small, cooperative groups and build a city following specific guidelines. The students will learn how a city is constructed with angles, intersections, parallel, intersecting, and transversal streets. They will understand that buildings are located at particular points which are considered alternate interior or exterior angles, corresponding angles, etc. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Polygons  Changing Area versus Changing Perimeter
Description:
Students will investigate what happens to the perimeter of a polygon when the area stays the same. Students will investigate what happens to the area when the perimeter stays the same.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [CE] (012) 18: Cheerfulness [CE] (012) 9: Selfrespect [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Character Education (K  12), or Mathematics (6  7)
Title: Polygons  Changing Area versus Changing Perimeter
Description: Students will investigate what happens to the perimeter of a polygon when the area stays the same. Students will investigate what happens to the area when the perimeter stays the same.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Geometry City
Description:
In this lesson, students will review coordinate plane concepts, practice map skills, review shapes, transform geometric figures, and calculate the area and perimeter of figures.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [TC2] (68) 9: Practice responsible and legal use of technology systems and digital content. [TC2] (68) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information. [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (6) 23: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems. [6G3] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 18: Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. [8G3] [MA2013] (8) 19: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. [8G4]
Subject: Mathematics (6  8), or Technology Education (6  8)
Title: Geometry City
Description: In this lesson, students will review coordinate plane concepts, practice map skills, review shapes, transform geometric figures, and calculate the area and perimeter of figures.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Volume: Moving Dirt
Description:
This technology enriched lesson is designed to assist students in understanding how to calculate complex volume and how those concepts translate to use in the real world. Learning styles addressed include visual, auditory, and tactile/kinesthetic.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project, funded by the Malone Family Foundation.
Standard(s): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
Subject: Mathematics (6  8)
Title: Volume: Moving Dirt
Description: This technology enriched lesson is designed to assist students in understanding how to calculate complex volume and how those concepts translate to use in the real world. Learning styles addressed include visual, auditory, and tactile/kinesthetic.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project, funded by the Malone Family Foundation.
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Title: Dog Gone Again!
Description:
In this lesson, the students' dogs have escaped once again from the backyard because there is not a fence to contain the dog when it goes out to use the bathroom. The student is to design a rectangular fence that will keep the dog from escaping the yard again. Students will find the perimeter and area of their fence. The students' products will be a Microsoft Word drawing.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project, funded by the Malone Family Foundation.
Standard(s): [TC2] (35) 2: Use various technology applications, including word processing and multimedia software. [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (3) 23: Solve realworld and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. [3MD8] [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3]
Subject: Mathematics (3  7), or Technology Education (3  5)
Title: Dog Gone Again!
Description: In this lesson, the students' dogs have escaped once again from the backyard because there is not a fence to contain the dog when it goes out to use the bathroom. The student is to design a rectangular fence that will keep the dog from escaping the yard again. Students will find the perimeter and area of their fence. The students' products will be a Microsoft Word drawing.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project, funded by the Malone Family Foundation.
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Title: Water Tank Creations Part I
Description:
In this lesson students will study the surface area and volume of threedimensional shapes by creating a water tank comprised of these shapes. Students will work in groups of 45 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): [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. [TC2] CA2 (912) 4: Utilize advanced features of word processing software, including outlining, tracking changes,
hyperlinking, and mail merging. [MA2013] (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. [7G1] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9] [MA2013] AL1 (912) 4: Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. [NQ1] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [MA2013] AL1 (912) 6: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. [NQ3] [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3] [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama) [MA2013] GEO (912) 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).* [GMG1] [MA2013] GEO (912) 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).* [GMG2]
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 threedimensional shapes by creating a water tank comprised of these shapes. Students will work in groups of 45 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.
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Title: Creating a Water Tank  Part II "Selling the Tank"
Description:
Working in groups of 45 students will take the information,pictures and 3D 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): [TC2] CA2 (912) 12: Use digital tools to publish curriculumrelated content. [TC2] CA2 (912) 9: Practice ethical and legal use of technology systems and digital content. [MA2013] (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. [7G1] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] ALC (912) 7: Use analytical, numerical, and graphical methods to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. (Alabama) [MA2013] ALC (912) 10: Critique measurements in terms of precision, accuracy, and approximate error. (Alabama) [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3] [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama) [MA2013] GEO (912) 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).* [GMG1] [MA2013] GEO (912) 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).* [GMG3]
Subject: Mathematics (7  12), or Technology Education (9  12)
Title: Creating a Water Tank  Part II "Selling the Tank"
Description: Working in groups of 45 students will take the information,pictures and 3D 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.
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Title: Let’s Tessellate
Description:
This lesson is a handson, technologybased 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): [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 17: Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. [8G2] [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] GEO (912) 34: Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama) [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] GEO (912) 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 handson, technologybased 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.
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Title: How Big Can a Bee Be?
Description:
Students will study the relationship between surface area and volume. Math, science, and technology components are included.
Standard(s): [S1] (8) 1: Identify steps within the scientific process. [S1] (7) 1: Describe characteristics common to living things, including growth and development, reproduction, cellular organization, use of energy, exchange of gases, and response to the environment. [S1] BIO (912) 2: Describe cell processes necessary for achieving homeostasis, including active and passive transport, osmosis, diffusion, exocytosis, and endocytosis. [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. [TC2] CA2 (912) 14: Use digital tools to defend solutions to authentic problems. [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics (7), or Science (7  12), or Technology Education (9  12)
Title: How Big Can a Bee Be?
Description: Students will study the relationship between surface area and volume. Math, science, and technology components are included.
Thinkfinity Lesson Plans
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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): [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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
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Title: Finding the Area of Irregular Figures
Description:
In this lesson, one of a multipart 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): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics Title: Finding the Area of Irregular Figures
Description: In this lesson, one of a multipart 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
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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): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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
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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): [MA2013] (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. [7G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9] [MA2013] GEO (912) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [GSRT5]
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
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Title: Discovering the Area Formula for Triangles
Description:
In this lesson, one of a multipart 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): [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics Title: Discovering the Area Formula for Triangles
Description: In this lesson, one of a multipart 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
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Title: Creating A Firewise Defensible Space
Description:
In this lesson, one of a multipart 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): [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics Title: Creating A Firewise Defensible Space
Description: In this lesson, one of a multipart 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
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Title: Mathematics and Children's Literature
Description:
In this fivelesson 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): [MA2013] (3) 17: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^{3} and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of "times as much").) (See Appendix A, Table 2.) [3MD2] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 23: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems. [6G3] [MA2013] (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. [7G1] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9] [ELA2013] (3) 29: Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories. [W.3.8] [ELA2013] (5) 1: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. [RL.5.1] [ELA2013] (5) 10: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. [RI.5.1] [ELA2013] (5) 13: Determine the meaning of general academic and domainspecific words and phrases in a text relevant to a Grade 5 topic or subject area. [RI.5.4] [ELA2013] (5) 18: Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably. [RI.5.9] [ELA2013] (6) 7: Compare and contrast the experience of reading a story, drama, or poem to listening to or viewing an audio, video, or live version of the text, including contrasting what they "see" and "hear" when reading the text to what they perceive when they listen or watch. [RL.6.7] [ELA2013] (6) 8: Differentiate among odes, ballads, epic poetry, and science fiction. (Alabama) [ELA2013] (6) 9: Compare and contrast texts in different forms or genres (e.g., stories and poems; historical novels and fantasy stories) in terms of their approaches to similar themes and topics. [RL.6.9] [ELA2013] (6) 10: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RL.6.10] [ELA2013] (7) 7: Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film). [RL.7.7] [ELA2013] (7) 8: Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history. [RL.7.9] [ELA2013] (7) 9: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RL.7.10] [ELA2013] (8) 7: Analyze the extent to which a filmed or live production of a story or drama stays faithful to or departs from the text or script, evaluating the choices made by the director or actors. [RL.8.7] [ELA2013] (8) 8: Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new. [RL.8.9] [ELA2013] (8) 9: By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of Grades 68 text complexity band independently and proficiently. [RL.8.10]
Subject: Language Arts,Mathematics Title: Mathematics and Children's Literature
Description: In this fivelesson 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
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Title: Finding the Area of Parallelograms
Description:
In this lesson, one of a multipart unit from Illuminations, students use their knowledge of rectangles to discover the area formula for parallelograms.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics Title: Finding the Area of Parallelograms
Description: In this lesson, one of a multipart unit from Illuminations, students use their knowledge of rectangles to discover the area formula for parallelograms. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Finding the Area of Trapezoids
Description:
In this lesson, one of a multipart unit from Illuminations, students discover the area formula for trapezoids and explore alternative methods for calculating the area of a trapezoid.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics Title: Finding the Area of Trapezoids
Description: In this lesson, one of a multipart 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
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Title: History on Stage PopUp 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 popup in support of a social studies lesson. Making popups subtly reinforces student's understanding of mechanical movement and helps budding architects, designers, and engineers begin to envision objects threedimensionally.
Standard(s): [MA2013] (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. [7G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 16: Verify experimentally the properties of rotations, reflections, and translations: [8G1]
Subject: Arts,Mathematics,Social Studies, Language arts Title: History on Stage PopUp 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 popup in support of a social studies lesson. Making popups subtly reinforces student's understanding of mechanical movement and helps budding architects, designers, and engineers begin to envision objects threedimensionally. Thinkfinity Partner: Smithsonian Grade Span: 5,6,7,8
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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): [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (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. [7G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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
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Title: Do They Match?
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In this lesson, one of a multipart 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): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics Title: Do They Match?
Description: In this lesson, one of a multipart 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
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Title: Frontrighttop Views
Description:
This reproducible transparency, from an Illuminations lesson, depicts an isometric drawing of a threedimensional figure, along with its front, right, and top views.
Standard(s): [MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Subject: Mathematics Title: Frontrighttop Views
Description: This reproducible transparency, from an Illuminations lesson, depicts an isometric drawing of a threedimensional figure, along with its front, right, and top views. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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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): [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] GEO (912) 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. [GCO12] [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama) [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4]
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
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Title: Patterns and Function
Description:
In this lesson, from Illuminations, students investigate properties of perimeter, area, and volume related to various geometric two and threedimensional shapes.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9]
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 threedimensional shapes. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: A Swath of Red
Description:
In this lesson, one of a multipart 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): [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6RP1] [MA2013] (6) 2: Understand the concept of a unit rate ^{a}/_{b} associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. [6RP2] [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 3: Use proportional relationships to solve multistep ratio and percent problems. [7RP3] [MA2013] (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. [7G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (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. [7SP2]
Subject: Mathematics Title: A Swath of Red
Description: In this lesson, one of a multipart 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
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Title: Circle Packing
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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 threedimensional 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): [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3] [MA2013] GEO (912) 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).* [GMG1] [MA2013] GEO (912) 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).* [GMG3]
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 threedimensional 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
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Title: Soda Rack
Description:
In this lesson, one of a threepart 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): [MA2013] (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. [7G1] [MA2013] (7) 13: Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [7G3] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] GEO (912) 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. [GCO12] [MA2013] GEO (912) 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).* [GMG1] [MA2013] GEO (912) 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).* [GMG3]
Subject: Mathematics Title: Soda Rack
Description: In this lesson, one of a threepart 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
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Title: Soda Cans
Description:
In this lesson, one of a threepart 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): [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve realworld and mathematical problems. [8G9] [MA2013] GEO (912) 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).* [GMG1] [MA2013] GEO (912) 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).* [GMG3]
Subject: Mathematics Title: Soda Cans
Description: In this lesson, one of a threepart 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
ALEX Podcasts
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Title: Archimedes and Density
Overview:
This podcast is an introduction to using displacement to determine the density of an object. Because density is an intrinsic property, it can be used to identify a substance. A followup lab should be used so students can apply the ideas introduced. Standard(s):
[S1] CHE (912) 1: Differentiate among pure substances, mixtures, elements, and compounds. [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Archimedes and Density Overview: This podcast is an introduction to using displacement to determine the density of an object. Because density is an intrinsic property, it can be used to identify a substance. A followup lab should be used so students can apply the ideas introduced.
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Title: Pi  The Mathematical Dessert
Overview:
Watch this podcast and discover the mathematical number pi! Discussion includes the history of pi, mathematical concept of pi, and modern notation of the ∏ symbol used today. Interesting trivia, jokes, pi reciting contests, and pi day celebrations are included. This podcast is a must to add to your mathematics classroom and especially any pi day celebration. Standard(s):
[MA2013] (6) 24: Represent threedimensional 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 realworld and mathematical problems. [6G4] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3]
Pi  The Mathematical Dessert Overview: Watch this podcast and discover the mathematical number pi! Discussion includes the history of pi, mathematical concept of pi, and modern notation of the ∏ symbol used today. Interesting trivia, jokes, pi reciting contests, and pi day celebrations are included. This podcast is a must to add to your mathematics classroom and especially any pi day celebration.
Web Resources
Assessments
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Title: Alcumus Online Learning System
Description:
Alcumus offers students a customized learning experience, adjusting to student performance to deliver appropriate problems and lessons. Alcumus is specifically designed to provide highperforming students with a challenging curriculum appropriate to their abilities.
Standard(s): [MA2013] (7) 3: Use proportional relationships to solve multistep ratio and percent problems. [7RP3] [MA2013] (7) 9: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3] [MA2013] (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. [7G1] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Alcumus Online Learning System
http://www.artofprob...
Alcumus offers students a customized learning experience, adjusting to student performance to deliver appropriate problems and lessons. Alcumus is specifically designed to provide highperforming students with a challenging curriculum appropriate to their abilities.
Interactives/Games
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Title: Alcumus Online Learning System
Description:
Alcumus offers students a customized learning experience, adjusting to student performance to deliver appropriate problems and lessons. Alcumus is specifically designed to provide highperforming students with a challenging curriculum appropriate to their abilities.
Standard(s): [MA2013] (7) 3: Use proportional relationships to solve multistep ratio and percent problems. [7RP3] [MA2013] (7) 9: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3] [MA2013] (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. [7G1] [MA2013] (7) 14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
Alcumus Online Learning System
http://www.artofprob...
Alcumus offers students a customized learning experience, adjusting to student performance to deliver appropriate problems and lessons. Alcumus is specifically designed to provide highperforming students with a challenging curriculum appropriate to their abilities.
Thinkfinity Interactive Games
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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. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations.
Standard(s): [MA2013] (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 realworld and mathematical problems. [6G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Thinkfinity Learning Activities
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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 twopart eexample 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 threedimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes. eMath Investigations are selected eexamples 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 eexamples are natural companions to the iMath Investigations.
Standard(s): [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 22: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. [6G2] [MA2013] (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. [7G1] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6]
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 twopart eexample 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 threedimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes. eMath Investigations are selected eexamples 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 eexamples are natural companions to the iMath Investigations. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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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): [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (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. [7G1] [MA2013] (7) 12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. [7G2] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 19: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. [8G4] [MA2013] AL1 (912) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [FIF3] [MA2013] GEO (912) 15: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. [GSRT2] [MA2013] GEO (912) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [GSRT5] [MA2013] GEO (912) 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).* [GMG1] [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama) [MA2013] AL1 (912) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [FBF2]
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
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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): [MA2013] (6) 12: Write and evaluate numerical expressions involving wholenumber exponents. [6EE1] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [MA2013] (6) 14: Apply the properties of operations to generate equivalent expressions. [6EE3] [MA2013] (6) 15: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). [6EE4] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (7) 16: Solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [7G6] [MA2013] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8F2]
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

