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Title: How Far Can You Leap?
Description:
This lesson will allow students to become familiar with the concept of unit rate. Through an open investigation students will develop methods to find unit rate with a table, equivalent ratios, or an equation. This is a lesson to be used as part of a unit with "Painter Problems" and "How Big Should It Be?"
This is a College and CareerReady Standards showcase lesson plan.
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) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1]
Subject: Mathematics (6  7)
Title: How Far Can You Leap?
Description: This lesson will allow students to become familiar with the concept of unit rate. Through an open investigation students will develop methods to find unit rate with a table, equivalent ratios, or an equation. This is a lesson to be used as part of a unit with "Painter Problems" and "How Big Should It Be?"
This is a College and CareerReady Standards showcase lesson plan.
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Title: It IS Easy Being "Green": Part II of III Creating Your Own Cleaning Supplies
Description:
In this second part of a threepart lesson, students will collaborate in ability groups to complete a Jigsaw activity on allpurpose cleaners. Next, students will research, create, and evaluate homemade cleaning supplies and determine the effectiveness compared to conventional (storebought) cleaners. Students will present their findings for both the jigsaw and their product in a flipchart on the Interactive WhiteBoard.
Standard(s): [EDT] ED02 (7) 2: Describe the process of decisionmaking, problemsolving, and goalsetting. [EDT] ED02 (7) 18: Determine procedures for basic household maintenance and safety. [EDT] ED03 (8) 17: Demonstrate methods to maintain a clean home. [TC2] (68) 12: Use digital tools to communicate and collaborate at all levels from interpersonal to global. [S1] (8) 6: Define solution in terms of solute and solvent. [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]
Subject: Education and Training (7  8), or Mathematics (6), or Science (8), or Technology Education (6  8)
Title: It IS Easy Being "Green": Part II of III Creating Your Own Cleaning Supplies
Description: In this second part of a threepart lesson, students will collaborate in ability groups to complete a Jigsaw activity on allpurpose cleaners. Next, students will research, create, and evaluate homemade cleaning supplies and determine the effectiveness compared to conventional (storebought) cleaners. Students will present their findings for both the jigsaw and their product in a flipchart on the Interactive WhiteBoard.
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Title: Thirsty for Ratios
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In this lesson the students will learn what a ratio is and how it can be used in comparison. In this lesson, students will also determine how to combine a sports drink in powder form and water to make enough for a whole football team. Students will be encouraged to use different strategies such as ratios and proportions. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] (6) 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] (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]
Subject: Mathematics (6)
Title: Thirsty for Ratios
Description: In this lesson the students will learn what a ratio is and how it can be used in comparison. In this lesson, students will also determine how to combine a sports drink in powder form and water to make enough for a whole football team. Students will be encouraged to use different strategies such as ratios and proportions. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Thinkfinity Lesson Plans
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Title: Ratios
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This reproducible transparency, from an Illuminations lesson, features equations for finding the ratios for surface area and volume when comparing a model to a fullsize object.
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]
Subject: Mathematics Title: Ratios
Description: This reproducible transparency, from an Illuminations lesson, features equations for finding the ratios for surface area and volume when comparing a model to a fullsize object. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: The Ratio of Circumference to Diameter
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In this lesson, one of a multipart unit from Illuminations, students measure the circumference and diameter of circular objects. They calculate the ratio of circumference to diameter for each object in an attempt to identify the value of pi and the circumference formula.
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] (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]
Subject: Mathematics Title: The Ratio of Circumference to Diameter
Description: In this lesson, one of a multipart unit from Illuminations, students measure the circumference and diameter of circular objects. They calculate the ratio of circumference to diameter for each object in an attempt to identify the value of pi and the circumference formula. 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: Paper Pool: Analyzing Numeric and Geometric Patterns
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This page provides an overview of a fourlesson Illuminations unit plan titled '' Analyzing Numeric and Geometric Patterns of Paper Pool.'' The interactive paper pool game in this unit plan provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. This investigation includes student resources for the Paper Pool project, preparation notes, answers, and a holisticbycategory scoring rubric with guidelines for how it can be used to assess the project. Samples of two students' work and comments from a teacher accompany the suggested rubric. This resource references the Illuminations lessons titled '' Paper Pool Game,'' '' Explore More Tables,'' '' Look for Patterns,'' and '' Go the Distance.''
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]
Subject: Mathematics Title: Paper Pool: Analyzing Numeric and Geometric Patterns
Description: This page provides an overview of a fourlesson Illuminations unit plan titled '' Analyzing Numeric and Geometric Patterns of Paper Pool.'' The interactive paper pool game in this unit plan provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. This investigation includes student resources for the Paper Pool project, preparation notes, answers, and a holisticbycategory scoring rubric with guidelines for how it can be used to assess the project. Samples of two students' work and comments from a teacher accompany the suggested rubric. This resource references the Illuminations lessons titled '' Paper Pool Game,'' '' Explore More Tables,'' '' Look for Patterns,'' and '' Go the Distance.'' Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Constant Dimensions
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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: Linking Length, Perimeter, Area, and Volume
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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: Can It Be?
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In this lesson, one of a multipart unit from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. They listen to the story The Phantom Tollbooth, by Norton Juster, and then explore and interpret the concept of averages.
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) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [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] (7) 19: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. [7SP3] [ELA2013] (6) 1: Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. [RL.6.1] [ELA2013] (6) 2: Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments. [RL.6.2] [ELA2013] (6) 3: Describe how a particular story's or drama's plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution. [RL.6.3] [ELA2013] (6) 4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of a specific word choice on meaning and tone. [RL.6.4] [ELA2013] (6) 5: Analyze how a particular sentence, chapter, scene, or stanza fits into the overall structure of a text and contributes to the development of the theme, setting, or plot. [RL.6.5] [ELA2013] (6) 6: Explain how an author develops the point of view of the narrator or speaker in a text. [RL.6.6] [ELA2013] (6) 10: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RL.6.10] [ELA2013] (7) 1: Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. [RL.7.1] [ELA2013] (7) 2: Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text. [RL.7.2] [ELA2013] (7) 3: Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot). [RL.7.3] [ELA2013] (7) 4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of rhymes and other repetitions of sounds (e.g., alliteration) on a specific verse or stanza of a poem or section of a story or drama. [RL.7.4] [ELA2013] (7) 5: Analyze how a drama's or poem's form or structure (e.g., soliloquy, sonnet) contributes to its meaning. [RL.7.5] [ELA2013] (7) 6: Analyze how an author develops and contrasts the points of view of different characters or narrators in a text. [RL.7.6] [ELA2013] (7) 9: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RL.7.10] [ELA2013] (8) 1: Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. [RL.8.1] [ELA2013] (8) 2: Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text. [RL.8.2] [ELA2013] (8) 3: Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision. [RL.8.3] [ELA2013] (8) 4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. [RL.8.4] [ELA2013] (8) 5: Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style. [RL.8.5] [ELA2013] (8) 6: Analyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor. [RL.8.6] [ELA2013] (8) 9: By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of Grades 68 text complexity band independently and proficiently. [RL.8.10]
Subject: Language Arts,Mathematics Title: Can It Be?
Description: In this lesson, one of a multipart unit from Illuminations, students participate in activities in which they focus on connections between mathematics and children s literature. They listen to the story The Phantom Tollbooth, by Norton Juster, and then explore and interpret the concept of averages. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Inclined Plane
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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: How Much is a Million?
Description:
This lesson focuses students on the concept of 1,000,000. It allows students to see firsthand the sheer size of a million while at the same time providing students with an introduction to sampling and its use in mathematics. Students will use grains of rice and a balance to figure out the approximate volume and mass of 1,000,000 grains of rice.
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) 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] (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: Language Arts,Mathematics Title: How Much is a Million?
Description: This lesson focuses students on the concept of 1,000,000. It allows students to see firsthand the sheer size of a million while at the same time providing students with an introduction to sampling and its use in mathematics. Students will use grains of rice and a balance to figure out the approximate volume and mass of 1,000,000 grains of rice. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: A Swath of Red
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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: First Class First? Using Data to Explore the Tragedy of the Titanic
Description:
In this Science NetLinks lesson, students analyze and interpret data related to the crew and passengers of the Titanic. They draw conclusions to better understand the people who were lost or saved as a result of the disaster, and whether or not social status affected the outcome.
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) 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) 26: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [6SP2] [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) 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] (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] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1] [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]
Subject: Mathematics, Social Studies Title: First Class First? Using Data to Explore the Tragedy of the Titanic
Description: In this Science NetLinks lesson, students analyze and interpret data related to the crew and passengers of the Titanic. They draw conclusions to better understand the people who were lost or saved as a result of the disaster, and whether or not social status affected the outcome. Thinkfinity Partner: Science NetLinks Grade Span: 9,10,11,12
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Title: Capture  Recapture
Description:
In this lesson, students experience an application of proportion that scientists actually use to solve reallife problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of tagged items to the number of items in a sample is the same as the ratio of tagged items to the total population.
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) 3: Use proportional relationships to solve multistep ratio and percent problems. [7RP3] [MA2013] AL2 (912) 14: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.* [ASSE4]
Subject: Mathematics Title: Capture  Recapture
Description: In this lesson, students experience an application of proportion that scientists actually use to solve reallife problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of tagged items to the number of items in a sample is the same as the ratio of tagged items to the total population. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Bean Counting
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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
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Title: How Can Math Help You Cook?
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You might think the best part of making brownies is enjoying the end result, but gathering and mixing the ingredients can be just as fun. Grab a spoon and let's find out what ice cream can teach us about math. Yummy!
Standard(s): [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [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) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3]
Subject: CrossDisciplinary  Informal Education , Health  Nutrition , Mathematics  Applied Mathematics , Mathematics  Arithmetic , Mathematics  Measurement , Science  Biological and Life Sciences , Science  Biology , Science  Chemistry , Science  General Science , Adult & Family Literacy  Lifeskills , Informal Education  Health/Wellness/Nutrition/Cooking Title: How Can Math Help You Cook?
Description: You might think the best part of making brownies is enjoying the end result, but gathering and mixing the ingredients can be just as fun. Grab a spoon and let's find out what ice cream can teach us about math. Yummy! Thinkfinity Partner: Wonderopolis Grade Span: K,PreK,1,2,3,4,5
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Title: Thinking Blocks Ratios
Description:
Thinking Blocks is an interactive video that models word problems that involve ratios and provides practice problems.
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]
Thinking Blocks Ratios
http://www.mathplayg...
Thinking Blocks is an interactive video that models word problems that involve ratios and provides practice problems.
Thinkfinity Learning Activities
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Title: How Can Math Help You Cook?
Description:
You might think the best part of making brownies is enjoying the end result, but gathering and mixing the ingredients can be just as fun. Grab a spoon and let's find out what ice cream can teach us about math. Yummy!
Standard(s): [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [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) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3]
Subject: CrossDisciplinary  Informal Education , Health  Nutrition , Mathematics  Applied Mathematics , Mathematics  Arithmetic , Mathematics  Measurement , Science  Biological and Life Sciences , Science  Biology , Science  Chemistry , Science  General Science , Adult & Family Literacy  Lifeskills , Informal Education  Health/Wellness/Nutrition/Cooking Title: How Can Math Help You Cook?
Description: You might think the best part of making brownies is enjoying the end result, but gathering and mixing the ingredients can be just as fun. Grab a spoon and let's find out what ice cream can teach us about math. Yummy! Thinkfinity Partner: Wonderopolis Grade Span: K,PreK,1,2,3,4,5
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Title: Calculation Nation
Description:
Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement.
Standard(s): [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] [MA2013] (3) 13: Understand a fraction ^{1}/_{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction ^{a}/_{b} as the quantity formed by a parts and size ^{1}/_{b}. [3NF1] [MA2013] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3] [MA2013] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4NF1] [MA2013] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4NF2] [MA2013] (4) 28: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. [4G3] [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) 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) 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) 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) 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] (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] (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) 18: Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. [8G3] [MA2013] DM1 (912) 1: Analyze topics from elementary number theory, including perfect numbers and prime numbers, to determine properties of integers. (Alabama)
Subject: Mathematics Title: Calculation Nation
Description: Become a citizen of Calculation Nation! Play online math strategy games to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area! Calculation Nation uses the power of the Web to let students challenge themselves and opponents from anywhere in the world. The element of competition adds an extra layer of excitement. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9

