ALEX Lesson Plans
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Title: How Big Should it Be?
Description:
This lesson will allow students to become familiar with the concept of equivalent ratios and similar objects. Through an open investigation students will develop methods to find equivalent ratios. This is a lesson to be used as part of a unit with Painter Problems and How Far Can You Leap found in ALEX.
This is a College and CareerReady Standards showcase lesson plan.
Standard(s): [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) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6RP1] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [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]
Subject: Mathematics (6  7)
Title: How Big Should it Be?
Description: This lesson will allow students to become familiar with the concept of equivalent ratios and similar objects. Through an open investigation students will develop methods to find equivalent ratios. This is a lesson to be used as part of a unit with Painter Problems and How Far Can You Leap found in ALEX.
This is a College and CareerReady Standards showcase lesson plan.
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Title: Is it Really that BIG?
Description:
Just how tall is that object? In this lesson, students will participate in an outdoor group activity using shadows to extend their knowledge of proportions to solve problems dealing with similarity. The cooperative learning groups will measure the heights and shadows of familiar objects (like themselves!) and use indirect measurement to find the heights of things that are much bigger in size, such as a tree, a school building, or a flagpole.
Standard(s): [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] [TC2] (68) 2: Publish digital products that communicate curriculum concepts.
Subject: Mathematics (7), or Technology Education (6  8)
Title: Is it Really that BIG?
Description: Just how tall is that object? In this lesson, students will participate in an outdoor group activity using shadows to extend their knowledge of proportions to solve problems dealing with similarity. The cooperative learning groups will measure the heights and shadows of familiar objects (like themselves!) and use indirect measurement to find the heights of things that are much bigger in size, such as a tree, a school building, or a flagpole.
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Title: To Scale or not to Scale? That is the Factor.
Description:
Students will learn to solve proportions and find missing sides of similar figures using the scale factor. This lesson is best taught before the concept of cross multiplication is developed. Not only will the student learn the process of using a scale factor to find a missing value from a proportion, but they will also practice these skills in a timed game online. They will realize that the scale factor is sometimes not an integer, and some proportions are more difficult to solve. This lesson is a great precursor to the means and extremes property of proportions also known as cross multiplication.
Standard(s): [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]
Subject: Mathematics (7)
Title: To Scale or not to Scale? That is the Factor.
Description: Students will learn to solve proportions and find missing sides of similar figures using the scale factor. This lesson is best taught before the concept of cross multiplication is developed. Not only will the student learn the process of using a scale factor to find a missing value from a proportion, but they will also practice these skills in a timed game online. They will realize that the scale factor is sometimes not an integer, and some proportions are more difficult to solve. This lesson is a great precursor to the means and extremes property of proportions also known as cross multiplication.
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Title: Falling Down a Rabbit Hole Can Lead to a King Sized Experience  Exploring Similar Figures Using Proportions
Description:
In this lesson, students will explore the concept of similarity. Students will first simplify ratios, solve proportions using the cross product property, and use properties of proportions to solve realworld problems. Similar polygons will then be introduced and their properties used to solve realworld problems.
Standard(s): [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] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2]
Subject: Mathematics (7  12)
Title: Falling Down a Rabbit Hole Can Lead to a King Sized Experience  Exploring Similar Figures Using Proportions
Description: In this lesson, students will explore the concept of similarity. Students will first simplify ratios, solve proportions using the cross product property, and use properties of proportions to solve realworld problems. Similar polygons will then be introduced and their properties used to solve realworld problems.
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Title: Find that Height!
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The students are to find the height of several objects around the school. They will set up proportions in order to find the height of tall objects not easily measured. Students will use a digital camera to record the objects they are measuring.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) 2: Publish digital products that communicate curriculum concepts. [TC2] (68) 5: Use basic features of word processing, spreadsheets, databases, and presentation software. [TC2] (68) 9: Practice responsible and legal use of technology systems and digital content. [TC2] (68) 14: Use digital tools to generate new ideas, products, or processes. [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2]
Subject: Mathematics (7), or Technology Education (6  8)
Title: Find that Height!
Description: The students are to find the height of several objects around the school. They will set up proportions in order to find the height of tall objects not easily measured. Students will use a digital camera to record the objects they are measuring.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: Comparing Fuel Economy (adapted from CMP "Comparing and Scaling" Investigation 4.1)
Description:
In this lesson students will explore rates. They will use the concept of rates to compute and compare fuel economy.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) 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] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3]
Subject: Mathematics (4  7)
Title: Comparing Fuel Economy (adapted from CMP "Comparing and Scaling" Investigation 4.1)
Description: In this lesson students will explore rates. They will use the concept of rates to compute and compare fuel economy.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: Cool KoolAid Experiment
Description:
Seventh grade students have had wideranging experiences with fractions and operations on fractions, but ratios and rates may be new concepts for them. This activity introduces students to the idea of rates via a familiar and tangible product: KoolAid. Students will add varying amounts of KoolAid powder to a set amount of water, thereby producing a sensory experience of rates. The KoolAid example also provides a base experience upon which other examples can build.
Standard(s): [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]
Subject: Mathematics (7)
Title: Cool KoolAid Experiment
Description: Seventh grade students have had wideranging experiences with fractions and operations on fractions, but ratios and rates may be new concepts for them. This activity introduces students to the idea of rates via a familiar and tangible product: KoolAid. Students will add varying amounts of KoolAid powder to a set amount of water, thereby producing a sensory experience of rates. The KoolAid example also provides a base experience upon which other examples can build.
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Title: Where Did You Get Those "Jeans"?
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This lesson can be interdisciplinary involving science, mathematics, and language arts. The primary nature of the lesson is inquiry, project, and technologybased. In science this project is a culminating activity in the heredity unit.
Standard(s): [S1] (7) 8: Describe the function of chromosomes. [TC2] (68) 2: Publish digital products that communicate curriculum concepts. [TC2] (68) 5: Use basic features of word processing, spreadsheets, databases, and presentation software. [TC2] (68) 6: Select specific digital tools for completing curriculumrelated tasks. [TC2] (68) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information. [TC2] (68) 13: Use digital tools to formulate solutions to authentic problems. [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]
Subject: Mathematics (7), or Science (7), or Technology Education (6  8)
Title: Where Did You Get Those "Jeans"?
Description: This lesson can be interdisciplinary involving science, mathematics, and language arts. The primary nature of the lesson is inquiry, project, and technologybased. In science this project is a culminating activity in the heredity unit.
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Title: Golden Ratios of the Body, Architecture, and Nature
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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: Trading and Tracking Stock Portfolios Online
Description:
Student teams will trade stocks and track the progress of their Alabama Stock Market Simulation portfolio by using spreadsheet software and the Internet. They will relate the information to a previous social studies unit on economics and will be utilizing math concepts they have learned. The Internet will be used to research stock trends.
Standard(s): [T1] ECN (12) 5: Explain the competitive nature of the market system. [TC2] (68) 5: Use basic features of word processing, spreadsheets, databases, and presentation software. [TC2] (68) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information. [TC2] (68) 13: Use digital tools to formulate solutions to authentic problems. [MA2013] (6) 9: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. [6NS6] [MA2013] (6) 11: Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. [6NS8] [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) 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]
Subject: Mathematics (6  7), or Social Studies (12), or Technology Education (6  8)
Title: Trading and Tracking Stock Portfolios Online
Description: Student teams will trade stocks and track the progress of their Alabama Stock Market Simulation portfolio by using spreadsheet software and the Internet. They will relate the information to a previous social studies unit on economics and will be utilizing math concepts they have learned. The Internet will be used to research stock trends.
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Title: How Much Money Can I Make?
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This lesson is a technologybased activity in which students will research two careers they are possibly interested in pursuing. They will convert the average yearly salary of each career into an hourly wage and record their findings in a spreadsheet. They will calculate their weekly gross and net pay for each career choice.
Standard(s): [TC2] (68) 5: Use basic features of word processing, spreadsheets, databases, and presentation software. [TC2] (68) 6: Select specific digital tools for completing curriculumrelated tasks. [TC2] (68) 7: Demonstrate correct keyboarding techniques. [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. [TC2] (68) 13: Use digital tools to formulate solutions to authentic problems. [MA2013] (6) 5: Fluently divide multidigit numbers using the standard algorithm. [6NS2] [MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3] [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) 4: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. [7NS1] [MA2013] (7) 6: Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) [7NS3]
Subject: Mathematics (6  7), or Technology Education (6  8)
Title: How Much Money Can I Make?
Description: This lesson is a technologybased activity in which students will research two careers they are possibly interested in pursuing. They will convert the average yearly salary of each career into an hourly wage and record their findings in a spreadsheet. They will calculate their weekly gross and net pay for each career choice.
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Title: Fly Away With Averages
Description:
This is a handson lesson that allows students to gather their own data before finding the mean. This activity is the culminating activity of a mean, median and mode unit.
Standard(s): [TC2] (35) 8: Collect information from a variety of digital sources. [TC2] (35) 9: Use technology tools to organize, interpret, and display data. [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2]
Subject: Mathematics (6  7), or Technology Education (3  5)
Title: Fly Away With Averages
Description: This is a handson lesson that allows students to gather their own data before finding the mean. This activity is the culminating activity of a mean, median and mode unit.
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Title: Bagel Algebra
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In this Illuminations lesson, a real life exampletaken from a bagel shopis used to get students to think about solving a problem symbolically. Students must decipher a series of equations and interpret results to understand the point that the bagel shop s owner is trying to make about the price of his bagels compared to that of his competitor.
Standard(s): [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] (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] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5]
Subject: Mathematics Title: Bagel Algebra
Description: In this Illuminations lesson, a real life exampletaken from a bagel shopis used to get students to think about solving a problem symbolically. Students must decipher a series of equations and interpret results to understand the point that the bagel shop s owner is trying to make about the price of his bagels compared to that of his competitor. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Blue Squares and Beyond
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In this lesson, one of a multipart unit from Illuminations, students manipulate two rectangles to create examples of similarity and to study the effects on area ratios. Students sketch similar figures, verify proportionality, and apply these concepts to structures in their world.
Standard(s): [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [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 Title: Blue Squares and Beyond
Description: In this lesson, one of a multipart unit from Illuminations, students manipulate two rectangles to create examples of similarity and to study the effects on area ratios. Students sketch similar figures, verify proportionality, and apply these concepts to structures in their world. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Big Math and Fries
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This Illuminations lesson is designed to enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein. The calculations are made to determine if a person can follow the Zone Diet with only McDonald's food items.
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) 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) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3] [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]
Subject: Health,Mathematics,Informal Education Title: Big Math and Fries
Description: This Illuminations lesson is designed to enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein. The calculations are made to determine if a person can follow the Zone Diet with only McDonald's food items. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Bagel Comparison
Description:
This reproducible transparency, from an Illuminations lesson, presents information from a sign displayed by a real bagel retailer, comparing the price of their bagels to that of their competitor.
Standard(s): [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] (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] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5]
Subject: Mathematics Title: Bagel Comparison
Description: This reproducible transparency, from an Illuminations lesson, presents information from a sign displayed by a real bagel retailer, comparing the price of their bagels to that of their competitor. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: The Next Billion
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In this lesson, from Illuminations, students predict when the world's population will reach 7 billion. To do so, they use an online counter that simulates the changing world population. They time the counter to find how long it takes for the population to increase by 50 or 100 people. They use that measurement to predict how long it would take for the population to increase by 1 billion. Students discuss the reliability of their predictions, compare them to past trends, and discuss social factors that can affect population growth.
Standard(s): [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] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5]
Subject: Mathematics Title: The Next Billion
Description: In this lesson, from Illuminations, students predict when the world's population will reach 7 billion. To do so, they use an online counter that simulates the changing world population. They time the counter to find how long it takes for the population to increase by 50 or 100 people. They use that measurement to predict how long it would take for the population to increase by 1 billion. Students discuss the reliability of their predictions, compare them to past trends, and discuss social factors that can affect population growth. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Purple Prisms
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In this lesson, one of a multipart unit from Illuminations, students investigate rectangular prisms using an online, interactive applet. They manipulate the scale factor that links two threedimensional rectangular prisms to learn about edge lengths and surface area relationships.
Standard(s): [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) 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) 2: Recognize and represent proportional relationships between quantities. [7RP2] [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]
Subject: Mathematics Title: Purple Prisms
Description: In this lesson, one of a multipart unit from Illuminations, students investigate rectangular prisms using an online, interactive applet. They manipulate the scale factor that links two threedimensional rectangular prisms to learn about edge lengths and surface area relationships. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Constant Dimensions
Description:
In this Illuminations lesson, students measure the length and width of a rectangle using both standard and nonstandard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. For many middle school students, this discovery is surprising.
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] (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) 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]
Subject: Mathematics Title: Constant Dimensions
Description: In this Illuminations lesson, students measure the length and width of a rectangle using both standard and nonstandard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. For many middle school students, this discovery is surprising. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Real Estate Tycoon
Description:
This yearlong project, from Illuminations, is divided into three parts and reinforces skills that lay a foundation for algebra, such as measurement, fractions, decimals, percents, and proportions. Students design, build, and sell a house and then simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, solve simple equations, and learn valuable lessons about how money really works.
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) 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) 4: Interpret and compute quotients of fractions, and solve word problems involving division of fractions, e.g., by using visual fraction models and equations to represent the problem. [6NS1] [MA2013] (6) 13: Write, read, and evaluate expressions in which letters stand for numbers. [6EE2] [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) 6: Solve realworld and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) [7NS3] [MA2013] (8) 9: Solve linear equations in one variable. [8EE7]
Subject: Arts,Mathematics,Social Studies Title: Real Estate Tycoon
Description: This yearlong project, from Illuminations, is divided into three parts and reinforces skills that lay a foundation for algebra, such as measurement, fractions, decimals, percents, and proportions. Students design, build, and sell a house and then simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, solve simple equations, and learn valuable lessons about how money really works. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Making Your First Million
Description:
In this lesson, one of a multipart unit from Illuminations, students attempt to identify the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition until a million is reached. Additionally, they use critical thinking to analyze situations and to identify mathematical patterns that enable them to develop the concept of very large numbers.
Standard(s): [MA2013] (3) 3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 2.) [3OA3] [MA2013] (3) 9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3OA9] [MA2013] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4OA2] [MA2013] (5) 5: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. [5NBT2] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [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] (8) 6: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. [8EE4]
Subject: Mathematics Title: Making Your First Million
Description: In this lesson, one of a multipart unit from Illuminations, students attempt to identify the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition until a million is reached. Additionally, they use critical thinking to analyze situations and to identify mathematical patterns that enable them to develop the concept of very large numbers. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Linking Length, Perimeter, Area, and Volume
Description:
In this fourlesson unit, from Illuminations, students explore ratio, proportion, scale factor and similarity using perimeter, area, volume and surface area of various rectangular shapes. Students use an online interactive applet to explore how the perimeters, areas, and side lengths of similar rectangles are related.
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) 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) 2: Recognize and represent proportional relationships between quantities. [7RP2]
Subject: Mathematics Title: Linking Length, Perimeter, Area, and Volume
Description: In this fourlesson unit, from Illuminations, students explore ratio, proportion, scale factor and similarity using perimeter, area, volume and surface area of various rectangular shapes. Students use an online interactive applet to explore how the perimeters, areas, and side lengths of similar rectangles are related. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Inclined Plane
Description:
In this multipleday activity, from Illuminations, students time balls rolling down inclines of varying lengths and heights. They then try to make inferences about the relationships among the variables involved.
Standard(s): [S1] (8) 8: Identify Newton's three laws of motion. [S1] (8) 10: Differentiate between potential and kinetic energy. [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) 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] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5] [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) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [SID7]
Subject: Mathematics,Science Title: Inclined Plane
Description: In this multipleday activity, from Illuminations, students time balls rolling down inclines of varying lengths and heights. They then try to make inferences about the relationships among the variables involved. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Getting into the Electoral College
Description:
In this unit of 3 lessons from Illuminations, students are engaged in activities involving percentages, ratios, and area, with a focus throughout on building problemsolving and reasoning skills. They are designed to be used individually to fit within curriculum being covered at the time of an election. Additionally, the lesson extensions include many ideas for interdisciplinary activities and some possible schoolwide activities.
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) 27: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [6SP3] [MA2013] (6) 28: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [6SP4] [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) 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] 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] AL1 (912) 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [SID2] [MA2013] AL1 (912) 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [SID3] [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama)
Subject: Mathematics Title: Getting into the Electoral College
Description: In this unit of 3 lessons from Illuminations, students are engaged in activities involving percentages, ratios, and area, with a focus throughout on building problemsolving and reasoning skills. They are designed to be used individually to fit within curriculum being covered at the time of an election. Additionally, the lesson extensions include many ideas for interdisciplinary activities and some possible schoolwide activities. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Go with Green Rectangles
Description:
In this lesson, one of a multipart unit from Illuminations, students manipulate 2dimensional rectangles using an online interactive applet. They focus on the relationship between the scale factor and ratio of perimeters of similar rectangles, and on the relationship between scale factor and ratio of areas of similar rectangles.
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] (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]
Subject: Mathematics Title: Go with Green Rectangles
Description: In this lesson, one of a multipart unit from Illuminations, students manipulate 2dimensional rectangles using an online interactive applet. They focus on the relationship between the scale factor and ratio of perimeters of similar rectangles, and on the relationship between scale factor and ratio of areas of similar rectangles. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Look for Patterns
Description:
In this lesson, one of a multipart unit from Illuminations, students further develop their understanding of ratio, proportion, and least common multiple.
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) 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) 7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. [6NS4] [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]
Subject: Mathematics Title: Look for Patterns
Description: In this lesson, one of a multipart unit from Illuminations, students further develop their understanding of ratio, proportion, and least common multiple. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Explore More Tables
Description:
In this lesson, one of a multipart unit from Illuminations, students further develop their understanding of ratio, proportion, and least common multiple.
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) 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) 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] (8) 28: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. [8SP4]
Subject: Mathematics Title: Explore More Tables
Description: In this lesson, one of a multipart unit from Illuminations, students further develop their understanding of ratio, proportion, and least common multiple. 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: Graph Chart
Description:
This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.
Standard(s): [MA2013] (6) 20: Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. [6EE9] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5] [MA2013] (8) 11: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) [8F1] [MA2013] (8) 12: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8F2] [MA2013] (8) 13: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8F3] [MA2013] (8) 14: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8F4] [MA2013] (8) 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [8SP2] [MA2013] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8SP3] [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) 22: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [AREI10] [MA2013] AL1 (912) 25: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [FIF1] [MA2013] AL1 (912) 26: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [FIF2] [MA2013] AL1 (912) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [FIF5] [MA2013] AL1 (912) 30: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] AL1 (912) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] AL1 (912) 32: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [FIF8] [MA2013] AL1 (912) 34: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL1 (912) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [FLE1] [MA2013] AL1 (912) 38: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). [FLE2] [MA2013] AL1 (912) 40: Interpret the parameters in a linear or exponential function in terms of a context. [FLE5] [MA2013] AL1 (912) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [SID6] [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] AL2 (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] AL2 (912) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [ACED2] [MA2013] AL2 (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 12: Interpret expressions that represent a quantity in terms of its context.* [ASSE1] [MA2013] PRE (912) 16: 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. Determine odd, even, neither.)* [FIF4] (Alabama) [MA2013] PRE (912) 17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [FIF6] [MA2013] ALT (912) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [FIF7] [MA2013] ALT (912) 33: Write a function that describes a relationship between two quantities.* [FBF1]
Subject: Mathematics Title: Graph Chart
Description: This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Bean Counting
Description:
By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions. The numbersense of recognizing equivalent fractions is useful when students study slope and proportions.
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] (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] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5] [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)
Subject: Mathematics Title: Bean Counting
Description: By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions. The numbersense of recognizing equivalent fractions is useful when students study slope and proportions. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
ALEX Podcasts
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Title: Percents 3: Percent Equations
Overview:
This podcast is part of a series on operations with percents. Designed with the middle school student in mind, it is a refresher on the basics of solving percent equations. The lesson also covers amount, base, and percent using the translation method. The podcast can be used as a lesson or as a supplement to a lesson. A suggestion would be to stop the lesson as it goes along and allow the students to work problems out themselves. Standard(s):
[MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3] [MA2013] (6) 9: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. [6NS6] [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) 4: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. [7NS1] [MA2013] (7) 5: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. [7NS2] [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]
Percents 3: Percent Equations Overview: This podcast is part of a series on operations with percents. Designed with the middle school student in mind, it is a refresher on the basics of solving percent equations. The lesson also covers amount, base, and percent using the translation method. The podcast can be used as a lesson or as a supplement to a lesson. A suggestion would be to stop the lesson as it goes along and allow the students to work problems out themselves.
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Title: Lip Balm Science
Overview:
This podcast is associated with the lesson plan, Lip Balm Science. The podcast shows the students creating lip balms, collecting data to test the lip balms and shows the results of the data collection. Standard(s):
[S1] (5) 1: Identify evidence of chemical changes through color, gas formation, solid formation, and temperature change. [MA2013] (6) 28: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [6SP4] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6]
Lip Balm Science Overview:
This podcast is associated with the lesson plan, Lip Balm Science. The podcast shows the students creating lip balms, collecting data to test the lip balms and shows the results of the data collection.
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Title: Writing & Solving Proportions
Description:
This animated video from BrainPOP explores writing & solving proportions. The high production value makes for an engaging video; there are also links to a related activity, game, and quiz.
Standard(s): [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2]
Writing & Solving Proportions
http://www.brainpop....
This animated video from BrainPOP explores writing & solving proportions. The high production value makes for an engaging video; there are also links to a related activity, game, and quiz.
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Title: Over Ruled! (Proportions)
Description:
A short video that describes ratios and proportions. Two besotted rulers must embrace proportional units in order to complete a bridge to unite their lands. It takes mathematical reasoning to deduce the problem, and solution, when engineers from Queentopia and Kingopolis try to build a bridge that meets in the middle of the river.
Standard(s): [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2]
Over Ruled! (Proportions)
http://www.mathsnack...
A short video that describes ratios and proportions. Two besotted rulers must embrace proportional units in order to complete a bridge to unite their lands. It takes mathematical reasoning to deduce the problem, and solution, when engineers from Queentopia and Kingopolis try to build a bridge that meets in the middle of the river.
Interactives/Games
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Title: Lure of the Labyrinth: Proportion Game
Description:
"Hungry monsters come to feed here. Your mission: Figure out what they want to eat using ratios, multiplication, division, and factoring!"
Free interactive online game from BrainPOP. Students must compare the food these hungry monsters are eating and provide them with foods of equal proportion.
Standard(s): [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] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2]
Lure of the Labyrinth: Proportion Game
http://www.brainpop....
"Hungry monsters come to feed here. Your mission: Figure out what they want to eat using ratios, multiplication, division, and factoring!"
Free interactive online game from BrainPOP. Students must compare the food these hungry monsters are eating and provide them with foods of equal proportion.
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Title: Graphing Lines
Description:
Students explore the world of lines by investigating the relationships between linear equations, slope, and graphs of lines. This interactive tool requires Javascript.
Standard(s): [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8EE8] [MA2013] AL1 (912) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [AREI3] [MA2013] GEO (912) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [GGPE5]
Graphing Lines
http://phet.colorado...
Students explore the world of lines by investigating the relationships between linear equations, slope, and graphs of lines. This interactive tool requires Javascript.
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Title: Pan Balance  Numbers
Description:
This student interactive, from Illuminations, can be used to find numerical expressions that are equivalent to one another. If equivalent expressions are placed in the blue and red pans on the virtual scale, it will balance.
Standard(s): [MA2013] (6) 16: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. [6EE5] [MA2013] (6) 18: Solve realworld and mathematical problems by writing and solving equations of the form
x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. [6EE7] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [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) 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] (8) 9: Solve linear equations in one variable. [8EE7]
Subject: Mathematics Title: Pan Balance  Numbers
Description: This student interactive, from Illuminations, can be used to find numerical expressions that are equivalent to one another. If equivalent expressions are placed in the blue and red pans on the virtual scale, it will balance. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Canada Data Map
Description:
Investigate data for the Canadian provinces and territories with this interactive tool. Students can examine data sets contained within the interactive, or they can enter their own data.
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) 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) 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) 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) 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] [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 Title: Canada Data Map
Description: Investigate data for the Canadian provinces and territories with this interactive tool. Students can examine data sets contained within the interactive, or they can enter their own data. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12

