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Title: Human Angles
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This lesson is designed to get your students moving! This lesson focuses primarily on transversals and angles. Students will be able to identify and relate some angles to cheer moves.
This is a College and CareerReady Standards showcase lesson plan.
Standard(s): [ELA2013] (10) 35: Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. [SL.910.5] [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) 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: English Language Arts (10), or Mathematics (9  12)
Title: Human Angles
Description: This lesson is designed to get your students moving! This lesson focuses primarily on transversals and angles. Students will be able to identify and relate some angles to cheer moves.
This is a College and CareerReady Standards showcase lesson plan.
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Title: Card Table Project
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Students will work in groups to design a card table. Students will communicate with each other through a class blog or class discussion page. Students will then work in groups to design a card table. After the design phase, students will try to sell their product to the outside expert.
Standard(s): [MA2013] GEO (912) 23: (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).
[GSRT11] [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 (9  12)
Title: Card Table Project
Description: Students will work in groups to design a card table. Students will communicate with each other through a class blog or class discussion page. Students will then work in groups to design a card table. After the design phase, students will try to sell their product to the outside expert.
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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: Golden Ratios of the Body, Architecture, and Nature
Description:
Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.
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] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama) [MA2013] MI1 (912) 3: Use special numbers, including e, i, π and the golden ratio, to solve applicationbased problems. [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] [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] (7) 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7SP4] [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) 2: Recognize and represent proportional relationships between quantities. [7RP2] [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] (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 (6  12), or Technology Education (9  12)
Title: Golden Ratios of the Body, Architecture, and Nature
Description: Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.
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Title: Swimming Pool Math
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Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
Standard(s): [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] ALC (912) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) [MA2013] ALC (912) 1: Create algebraic models for applicationbased problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. [ACED3] [MA2013] AL1 (912) 12: Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [ACED1] [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] 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] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [MA2013] AL1 (912) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* [FIF4] [MA2013] AL1 (912) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL1 (912) 5: Define appropriate quantities for the purpose of descriptive modeling. [NQ2] [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] [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] (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  12)
Title: Swimming Pool Math
Description: Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
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Title: Soda Cans
Description:
This reproducible activity sheet, from an Illuminations lesson, guides students through a simulation in which they try different arrangements to make the most efficient use of space and thus pack the most soda cans into a rectangular packing box.
Standard(s): [MA2013] GEO (912) 1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [GCO1] [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) 24: Prove that all circles are similar. [GC1] [MA2013] GEO (912) 25: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. [GC2] [MA2013] GEO (912) 27: (+) Construct a tangent line from a point outside a given circle to the circle. [GC4] [MA2013] GEO (912) 28: Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. [GC5] [MA2013] GEO (912) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [GGMD3] [MA2013] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4] [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] [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) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (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)
Subject: Mathematics Title: Soda Cans
Description: This reproducible activity sheet, from an Illuminations lesson, guides students through a simulation in which they try different arrangements to make the most efficient use of space and thus pack the most soda cans into a rectangular packing box. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Playing with Squares
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This reproducible activity sheet, from an Illuminations lesson, prompts students to investigate the meaning of square roots by considering the area of squares and the heights of various stacks of squares.
Standard(s): [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] 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: Playing with Squares
Description: This reproducible activity sheet, from an Illuminations lesson, prompts students to investigate the meaning of square roots by considering the area of squares and the heights of various stacks of squares. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Hospital Problem
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This reproducible transparency, from an Illuminations lesson, describes an activity in which students must plan where to build a new hospital so that it can serve the needs of three cities.
Standard(s): [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] [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)
Subject: Mathematics Title: Hospital Problem
Description: This reproducible transparency, from an Illuminations lesson, describes an activity in which students must plan where to build a new hospital so that it can serve the needs of three cities. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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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.
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: Circle Packing and Curvature
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In this lesson, one of a threepart unit from Illuminations, students investigate the curvature of circles. Students apply definitions and theorems regarding curvature to solve circle problems. In addition, there are links to an online activity sheet and other related resources.
Standard(s): [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) 28: Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. [GC5] [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 and Curvature
Description: In this lesson, one of a threepart unit from Illuminations, students investigate the curvature of circles. Students apply definitions and theorems regarding curvature to solve circle problems. In addition, there are links to an online activity sheet and other related resources. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Cubes Everywhere
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In this Illuminations lesson, students use cubes to develop spatial thinking and review basic geometric principles through reallife applications. Students are given the opportunity to build and take apart structures based on cubes.
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) 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] GEO (912) 38: Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [GGMD4] [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: Cubes Everywhere
Description: In this Illuminations lesson, students use cubes to develop spatial thinking and review basic geometric principles through reallife applications. Students are given the opportunity to build and take apart structures based on cubes. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Hospital Locator
Description:
In this Illuminations lesson, students begin with a problem in a realworld context to motivate the need to construct circumcenters and then incenters of triangles. Students must make sense of these constructions in terms of bisecting sides and angles. There are links to student interactives and other resources.
Standard(s): [MA2013] GEO (912) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180^{o}, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [GCO10] [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: Hospital Locator
Description: In this Illuminations lesson, students begin with a problem in a realworld context to motivate the need to construct circumcenters and then incenters of triangles. Students must make sense of these constructions in terms of bisecting sides and angles. There are links to student interactives and other 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
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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: Symmetries III
Description:
This lesson, from Illuminations, helps students to understand how translations work and what happens when two or more translations are applied one after the other. Students discover that all band ornaments have translational symmetry and all wallpaper patterns have translational symmetry in at least two directions.
Standard(s): [MA2013] (8) 16: Verify experimentally the properties of rotations, reflections, and translations: [8G1] [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] (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] GEO (912) 2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). [GCO2] [MA2013] GEO (912) 3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. [GCO3] [MA2013] GEO (912) 5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [GCO5] [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) 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) 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] [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Mathematics Title: Symmetries III
Description: This lesson, from Illuminations, helps students to understand how translations work and what happens when two or more translations are applied one after the other. Students discover that all band ornaments have translational symmetry and all wallpaper patterns have translational symmetry in at least two directions. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Triangula Island Overhead
Description:
This reproducible transparency, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular polygon such that the sum of the distances to each side is a minimum.
Standard(s): [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] 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: Triangula Island Overhead
Description: This reproducible transparency, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular polygon such that the sum of the distances to each side is a minimum. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Triangula Island
Description:
This student reproducible, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular triangle such that the sum of the distances to each side is a minimum.
Standard(s): [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: Triangula Island
Description: This student reproducible, from an Illuminations lesson, contains an activity that asks students to conjecture the best location of a point inside a regular triangle such that the sum of the distances to each side is a minimum. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Robot Sketcher
Description:
In this student interactive, from Illuminations, students can build compound arms having multiple joints of two types: one that rotates and is typical of rotating motors, and one that slides and is typical of hydraulic lifts. A circle is used to represent a rotating joint, and a rectangle is used to represent a sliding joint.
Standard(s): [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: Robot Sketcher
Description: In this student interactive, from Illuminations, students can build compound arms having multiple joints of two types: one that rotates and is typical of rotating motors, and one that slides and is typical of hydraulic lifts. A circle is used to represent a rotating joint, and a rectangle is used to represent a sliding joint. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Hospital Locator
Description:
In this student interactive, from an Illuminations lesson, students act as community planners, trying to place a new medical center equidistant from three cities.
Standard(s): [MA2013] GEO (912) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180^{o}, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [GCO10] [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) 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] [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics Title: Hospital Locator
Description: In this student interactive, from an Illuminations lesson, students act as community planners, trying to place a new medical center equidistant from three cities. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Soccer Problem
Description:
This student interactive, from an Illuminations lesson, allows students to investigate a soccer problem by changing the location of a soccer player as well as the distance between the player and the goal posts. The angle changes as the player is moved, and students must therefore determine the player s position so that the angle is maximized.
Standard(s): [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) 25: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. [GC2] [MA2013] GEO (912) 28: Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. [GC5] [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: Soccer Problem
Description: This student interactive, from an Illuminations lesson, allows students to investigate a soccer problem by changing the location of a soccer player as well as the distance between the player and the goal posts. The angle changes as the player is moved, and students must therefore determine the player s position so that the angle is maximized. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12

