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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: Sweethearts and Data Analysis
Description:
This activity uses boxes of Sweethearts for students to gather data. They will perform computations and use their data to create a circle graph, frequency table, histogram, and line plot.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] AL1 (912) 41: Represent data with plots on the real number line (dot plots, histograms, and box plots). [SID1] [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] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8SP1]
Subject: Mathematics (6  12)
Title: Sweethearts and Data Analysis
Description: This activity uses boxes of Sweethearts for students to gather data. They will perform computations and use their data to create a circle graph, frequency table, histogram, and line plot.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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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"?
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.
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
Description:
Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.
Standard(s): [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. [MA2013] MI1 (912) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama) [MA2013] MI1 (912) 3: Use special numbers, including e, i, π and the golden ratio, to solve applicationbased problems. [MA2013] GEO (912) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [GMG3] [MA2013] ALC (912) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) [MA2013] ALC (912) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2013] (7) 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7SP4] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1] [MA2013] (6) 24: Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [6G4]
Subject: Mathematics (6  12), or Technology Education (9  12)
Title: Golden Ratios of the Body, Architecture, and Nature
Description: Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos.
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Title: 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): [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 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?
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.
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: 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: 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: 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: Playing Games
Description:
In this unit of five lessons, from Illuminations, students participate in activities in which they focus on the uses of numbers. The activities use the theme of games to develop concepts of measurement and statistics. Students are asked to measure distances using standard and nonstandard units and to record their measurement in various tables. Then they are asked to use descriptive statistics to report the results. These lessons include an individual activity for four different levels plus one for parents to complete with their child at home.
Standard(s): [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [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) 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) 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) 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]
Subject: Mathematics Title: Playing Games
Description: In this unit of five lessons, from Illuminations, students participate in activities in which they focus on the uses of numbers. The activities use the theme of games to develop concepts of measurement and statistics. Students are asked to measure distances using standard and nonstandard units and to record their measurement in various tables. Then they are asked to use descriptive statistics to report the results. These lessons include an individual activity for four different levels plus one for parents to complete with their child at home. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2
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Title: Explore More Tables
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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: Look for Patterns
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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: Go with Green Rectangles
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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: Fill'r Up
Description:
In this lesson, one of a multipart unit from Illuminations, students can manipulate the scale factor that links two threedimensional rectangular prisms and learn about the relationships between edge lengths and volumes. Students use an online interactive applet to change the size of a set of rectangular prisms and observe the change in the ratio of the volumes.
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]
Subject: Mathematics Title: Fill'r Up
Description: In this lesson, one of a multipart unit from Illuminations, students can manipulate the scale factor that links two threedimensional rectangular prisms and learn about the relationships between edge lengths and volumes. Students use an online interactive applet to change the size of a set of rectangular prisms and observe the change in the ratio of the volumes. 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: Numbers and Language
Description:
In this fivelesson unit, from Illuminations, students participate in activities in which they focus on the role of numbers and language in realworld situations. Students discuss, describe, read, and write about numbers they find in familiar realworld situations. An emphasis on using components of language helps students build a broader vocabulary of numbers than the traditional symbolic representation of numbers.
Standard(s): [MA2013] (4) 17: Use decimal notation for fractions with denominators 10 or 100. [4NF6] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [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) 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) 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] [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] [ELA2013] (3) 28: Conduct short research projects that build knowledge about a topic. [W.3.7] [ELA2013] (4) 28: Conduct short research projects that build knowledge through investigation of different aspects of a topic. [W.4.7] [ELA2013] (5) 28: Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic. [W.5.7] [ELA2013] (6) 14: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings. [RI.6.4] [ELA2013] (6) 17: Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue. [RI.6.7] [ELA2013] (6) 18: Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not. [RI.6.8] [ELA2013] (6) 20: By the end of the year, read and comprehend literary nonfiction in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RI.6.10] [ELA2013] (7) 13: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone. [RI.7.4] [ELA2013] (7) 19: By the end of the year, read and comprehend literary nonfiction in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RI.7.10] [ELA2013] (8) 10: Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. [RI.8.1] [ELA2013] (8) 19: By the end of the year, read and comprehend literary nonfiction at the high end of the
Grades 68 text complexity band independently and proficiently. [RI.8.10]
Subject: Language Arts,Mathematics Title: Numbers and Language
Description: In this fivelesson unit, from Illuminations, students participate in activities in which they focus on the role of numbers and language in realworld situations. Students discuss, describe, read, and write about numbers they find in familiar realworld situations. An emphasis on using components of language helps students build a broader vocabulary of numbers than the traditional symbolic representation of numbers. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5,6,7,8
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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: Unique Unit Rates
Digital Tool:
Lamar explains Unit Rates Web Address URL:
http://goanimate.com/videos/03fCSBUi8aj0 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] Digital Tool Description: The GoAnimate video, Lamar Explains Unit Rate, will serve as an introduction/review for students.
Title: Unique Unit Rates Digital Tool: Lamar explains Unit Rates Digital Tool Description: The GoAnimate video, Lamar Explains Unit Rate, will serve as an introduction/review for students.
Web Resources
Assessments
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Title: Online Assessments
Description:
This site is a group of online assessments for math, science, vocabulary, and geography. This is a free service for teachers who want to replace paper tests with online testing. Teachers must create a free account to utilize this site. Account includes an online grade book providing fast analysis of class and individual student progress, an exchange for teachers to share the resources they create, a skills site for students, especially useful for math practice and testing.
Standard(s): [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] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [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] (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]
Online Assessments
http://www.thatquiz....
This site is a group of online assessments for math, science, vocabulary, and geography. This is a free service for teachers who want to replace paper tests with online testing. Teachers must create a free account to utilize this site. Account includes an online grade book providing fast analysis of class and individual student progress, an exchange for teachers to share the resources they create, a skills site for students, especially useful for math practice and testing.
Learning Activities
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Title: Online Assessments
Description:
This site is a group of online assessments for math, science, vocabulary, and geography. This is a free service for teachers who want to replace paper tests with online testing. Teachers must create a free account to utilize this site. Account includes an online grade book providing fast analysis of class and individual student progress, an exchange for teachers to share the resources they create, a skills site for students, especially useful for math practice and testing.
Standard(s): [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] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [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] (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]
Online Assessments
http://www.thatquiz....
This site is a group of online assessments for math, science, vocabulary, and geography. This is a free service for teachers who want to replace paper tests with online testing. Teachers must create a free account to utilize this site. Account includes an online grade book providing fast analysis of class and individual student progress, an exchange for teachers to share the resources they create, a skills site for students, especially useful for math practice and testing.
Thinkfinity Learning Activities
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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

