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Title: SpongeBob RoundPants? What's the Chance?
Description:
What are the chances of SpongeBob having kids with round pants? Working in cooperative learning groups, students explore the concept of probability. Using interactive websites, students explore the possibilities of an organism having a particular trait by completing a virtual lab using Punnett squares. Students will apply their knowledge to predict possible outcomes of the offspring of the residents of Bikini Bottom.
Standard(s): [S1] (7) 11: Identify Mendel's laws of genetics. [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 (7), or Science (7)
Title: SpongeBob RoundPants? What's the Chance?
Description: What are the chances of SpongeBob having kids with round pants? Working in cooperative learning groups, students explore the concept of probability. Using interactive websites, students explore the possibilities of an organism having a particular trait by completing a virtual lab using Punnett squares. Students will apply their knowledge to predict possible outcomes of the offspring of the residents of Bikini Bottom.
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Title: How Tall Is Hagrid?
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This activity uses data collection method for students to mathematically compute the height and shoulder width of the character Hagrid from Harry Potter. Students will measure their own heights and shoulder widths to come up with a class average. They will use this average to find an approximation of the size of Hagrid.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [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] (8) 19: Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. [8G4]
Subject: Mathematics (6  8)
Title: How Tall Is Hagrid?
Description: This activity uses data collection method for students to mathematically compute the height and shoulder width of the character Hagrid from Harry Potter. Students will measure their own heights and shoulder widths to come up with a class average. They will use this average to find an approximation of the size of Hagrid.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Wheel of Fortune and Probability
Description:
This activity will lead students to discover a real life application of probability. This activity utilizes various skills, such as data organization, data analysis, and probability computations. Students will work in cooperative groups to complete the lesson.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5]
Subject: Mathematics (7)
Title: Wheel of Fortune and Probability
Description: This activity will lead students to discover a real life application of probability. This activity utilizes various skills, such as data organization, data analysis, and probability computations. Students will work in cooperative groups to complete the lesson.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Questioning NASA
Description:
In this lesson students will work collaboratively to explore the "Big Question" that led up to this lesson was "Why are there two solid rocket boosters used to launch the space shuttle instead of one with the same amount of fuel?"
This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [S1] (5) 6: Compare effects of gravitational force on Earth, on the moon, and within space. [TC2] (68) 5: Use basic features of word processing, spreadsheets, databases, and presentation software. [MA2013] (4) 8: Use place value understanding to round multidigit whole numbers to any place. [4NBT3] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (6) 10: Understand ordering and absolute value of rational numbers. [6NS7] [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 (4  7), or Science (5), or Technology Education (6  8)
Title: Questioning NASA
Description: In this lesson students will work collaboratively to explore the "Big Question" that led up to this lesson was "Why are there two solid rocket boosters used to launch the space shuttle instead of one with the same amount of fuel?"
This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: Transverse Waves
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Students will classify waves as mechanical or electromagnetic. Students will describe longitudinal and transverse waves. Students will show a transverse wave using a slinky.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): [S1] (8) 1: Identify steps within the scientific process. [S1] (8) 12: Classify waves as mechanical or electromagnetic. [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) 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] [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 (7  8), or Science (8)
Title: Transverse Waves
Description: Students will classify waves as mechanical or electromagnetic. Students will describe longitudinal and transverse waves. Students will show a transverse wave using a slinky.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: Dice Roll Project
Description:
This project is a fun way for students to observe the integration of a probability lesson with spreadsheet software. Students will record 36 rolls of a pair of dice. After they record their data, students will manually calculate the mean, median, mode and range. Students will then observe how quickly a computer can do those same calculations and many more things with that same data. Students will also compare experimental outcomes to the theoretical outcome.
Standard(s): [TC2] CA2 (912) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. [MA2013] (7) 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] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [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] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama) [MA2013] AL2 (912) 43: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. [SCP6]
Subject: Mathematics (7  12), or Technology Education (9  12)
Title: Dice Roll Project
Description: This project is a fun way for students to observe the integration of a probability lesson with spreadsheet software. Students will record 36 rolls of a pair of dice. After they record their data, students will manually calculate the mean, median, mode and range. Students will then observe how quickly a computer can do those same calculations and many more things with that same data. Students will also compare experimental outcomes to the theoretical outcome.
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Title: Count on Math
Description:
In this unit of two lessons, from Illuminations, students develop number sense through activities involving collection, representation, and analysis of data. In addition, students practice reading and writing large numbers and use estimation to arrive at appropriate answers.
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) 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] (8) 5: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. [8EE3] [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] [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) 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 Title: Count on Math
Description: In this unit of two lessons, from Illuminations, students develop number sense through activities involving collection, representation, and analysis of data. In addition, students practice reading and writing large numbers and use estimation to arrive at appropriate answers. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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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: The Beat of Your Heart
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This unit of five lessons, from Illuminations, gives students the opportunity to explore applications involving their own heart. The lessons, which span grades PreK8, focus on measuring and data collection.
Standard(s): [S1] (7) 3: Relate major tissues and organs of the skeletal, circulatory, reproductive, muscular, respiratory, nervous, and digestive systems to their functions. [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) 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,Science Title: The Beat of Your Heart
Description: This unit of five lessons, from Illuminations, gives students the opportunity to explore applications involving their own heart. The lessons, which span grades PreK8, focus on measuring and data collection. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5,6,7,8
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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: Spinning Tops
Description:
In this lesson, one of a multipart unit from Illuminations, students participate in games and activities that develop concepts of measurement and statistics. Students are asked to measure distances using standard and nonstandard units and to record their measurements in various tables. Then they are asked to use descriptive statistics to report the results.
Standard(s): [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) 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]
Subject: Mathematics Title: Spinning Tops
Description: In this lesson, one of a multipart unit from Illuminations, students participate in games and activities that develop concepts of measurement and statistics. Students are asked to measure distances using standard and nonstandard units and to record their measurements in various tables. Then they are asked to use descriptive statistics to report the results. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Building Height
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In this Illuminations lesson, students use a clinometer (a measuring device built from a protractor) and isosceles right triangles to find the height of a building. The class compares measurements, talks about the variation in their results, and selects the best measure of central tendency to report the most accurate height.
Standard(s): [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [MA2013] (7) 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] GEO (912) 18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. [GSRT5] [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1]
Subject: Mathematics Title: Building Height
Description: In this Illuminations lesson, students use a clinometer (a measuring device built from a protractor) and isosceles right triangles to find the height of a building. The class compares measurements, talks about the variation in their results, and selects the best measure of central tendency to report the most accurate height. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Finding the Balance
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In this lesson for grades 7 and 8, one of a multipart unit from Illuminations, students participate in activities in which they focus on patterns and relations that can be developed from the exploration of balance, mass, length of the mass arm, and the position of the fulcrum.
Standard(s): [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) 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: Finding the Balance
Description: In this lesson for grades 7 and 8, one of a multipart unit from Illuminations, students participate in activities in which they focus on patterns and relations that can be developed from the exploration of balance, mass, length of the mass arm, and the position of the fulcrum. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Birthdays and the Binary System: Exploring Binary Numbers in a RealWorld Application
Description:
This lesson, from Illuminations, revolves around patterns and place value in the binary system. Students are drawn into mathematics by the magical ability to guess an unknown number and by the use of birthdays.
Standard(s): [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 9: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3] [MA2013] (7) 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: Birthdays and the Binary System: Exploring Binary Numbers in a RealWorld Application
Description: This lesson, from Illuminations, revolves around patterns and place value in the binary system. Students are drawn into mathematics by the magical ability to guess an unknown number and by the use of birthdays. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Travel in the Solar System: Lesson 2
Description:
In this lesson, one of a multipart unit from Illuminations, students consider the amount of time that space travelers need to travel to the four terrestrial planets. Students also think about what kinds of events might occur on Earth while the space travelers are on their journey.
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) 20: Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. [6EE9] [MA2013] (7) 9: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3] [MA2013] (7) 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] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8EE5]
Subject: Mathematics,Science Title: Travel in the Solar System: Lesson 2
Description: In this lesson, one of a multipart unit from Illuminations, students consider the amount of time that space travelers need to travel to the four terrestrial planets. Students also think about what kinds of events might occur on Earth while the space travelers are on their journey. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Shopping Mall Math
Description:
In this twolesson unit, from Illuminations, students participate in activities in which they develop number sense in and around the shopping mall. Two gradelevel activities deal with size and space, estimation, measurement and applications involving percent.
Standard(s): [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [MA2013] (7) 9: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [MA2013] (7) 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: Shopping Mall Math
Description: In this twolesson unit, from Illuminations, students participate in activities in which they develop number sense in and around the shopping mall. Two gradelevel activities deal with size and space, estimation, measurement and applications involving percent. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Measuring Shadows
Description:
In this Science NetLinks lesson, students determine the pattern (length and direction) of shadows cast by sunlight during a several month period. They develop an interpretation of the daily and seasonal patterns and variations observed.
Standard(s): [S1] (6) 1: Identify global patterns of atmospheric movement, including El Niño, the Gulf Stream, the jet stream, the Coriolis effect, and global winds that influence local weather. [S1] (6) 8: Describe how Earth's rotation, Earth's axial tilt, and distance from the equator cause variations in the heating and cooling of various locations on Earth. [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) 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] 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] [MA2013] AL1 (912) 44: Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. [SID5] [MA2013] MI1 (912) 1: Critique ancient numeration systems and applications, including astronomy and the development and use of money and calendars. (Alabama) [MA2013] MI1 (912) 11: Describe the development of mathematical tools and their applications. (Alabama)
Subject: Mathematics Title: Measuring Shadows
Description: In this Science NetLinks lesson, students determine the pattern (length and direction) of shadows cast by sunlight during a several month period. They develop an interpretation of the daily and seasonal patterns and variations observed. Thinkfinity Partner: Science NetLinks Grade Span: 6,7,8
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Title: State Names
Description:
In this Illuminations lesson, students use multiple representations to analyze the frequency of letters that occur in the names of all 50 states. In the process, they learn how various representations, including steamandleaf plots, boxandwhisker plots, and histograms, can be used to organize the data.
Standard(s): [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [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) 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) 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] [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: State Names
Description: In this Illuminations lesson, students use multiple representations to analyze the frequency of letters that occur in the names of all 50 states. In the process, they learn how various representations, including steamandleaf plots, boxandwhisker plots, and histograms, can be used to organize the data. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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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: Combinations
Description:
This unit of two lessons, from Illuminations, focuses on combinations, a subject related to the probabilityandstatistics strand of mathematics. Students are encouraged to discover all the combinations for a given situation using problemsolving skills (including elimination and collection of organized data) and drawing conclusions. The use of higherlevel thinking skills (synthesis, analysis, and evaluations) is the overall goal.
Standard(s): [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) 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) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL1 (912) 47: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [SCP2] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama)
Subject: Mathematics Title: Combinations
Description: This unit of two lessons, from Illuminations, focuses on combinations, a subject related to the probabilityandstatistics strand of mathematics. Students are encouraged to discover all the combinations for a given situation using problemsolving skills (including elimination and collection of organized data) and drawing conclusions. The use of higherlevel thinking skills (synthesis, analysis, and evaluations) is the overall goal. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Boxing Up
Description:
In this lesson, from Illuminations, students explore the relationship between theoretical and experimental probabilities. They use an interactive box model that allows them to simulate standard probability experiments such as flipping a coin or rolling a die.
Standard(s): [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) 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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL2 (912) 40: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. [SCP3] [MA2013] AL2 (912) 41: Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. [SCP4] [MA2013] AL2 (912) 42: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [SCP5] [MA2013] AL2 (912) 43: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. [SCP6] [MA2013] AL2 (912) 44: Apply the Addition Rule, P(A or B) = P(A) + P(B)  P(A and B), and interpret the answer in terms of the model. [SCP7] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6]
Subject: Mathematics Title: Boxing Up
Description: In this lesson, from Illuminations, students explore the relationship between theoretical and experimental probabilities. They use an interactive box model that allows them to simulate standard probability experiments such as flipping a coin or rolling a die. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Birthday Paradox
Description:
This Illuminations lesson demonstrates the birthday paradox, using it as a springboard into a unit on probability. Students use the TI83 graphing calculator to run a Monte Carlo simulation with the birthday paradox and engage in a graphical analysis of the birthdayproblem function.
Standard(s): [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) 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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama) [MA2013] PRE (912) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [SMD1] [MA2013] PRE (912) 51: (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. [SMD2]
Subject: Mathematics Title: Birthday Paradox
Description: This Illuminations lesson demonstrates the birthday paradox, using it as a springboard into a unit on probability. Students use the TI83 graphing calculator to run a Monte Carlo simulation with the birthday paradox and engage in a graphical analysis of the birthdayproblem function. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Explorations with Chance
Description:
In this lesson, from Illuminations, students analyze the fairness of certain games by examining the probabilities of the outcomes. The explorations provide opportunities for the learning phases of predicting results, playing the games, and calculating probability ratios.
Standard(s): [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] (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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL1 (912) 47: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [SCP2] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] PRE (912) 48: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [SIC5] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6]
Subject: Mathematics Title: Explorations with Chance
Description: In this lesson, from Illuminations, students analyze the fairness of certain games by examining the probabilities of the outcomes. The explorations provide opportunities for the learning phases of predicting results, playing the games, and calculating probability ratios. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Stick or Switch?
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This lesson, from Illuminations, presents a version of a classic gameshow scenario. You pick one of three doors in hopes of winning the prize. The host opens one of the two remaining doors, which reveals no prize, and then asks if you wish to stick or switch. Which choice gives you the best chance to win? Students explore different approaches to this problem including guesses, experiments, computer simulations, and theoretical models.
Standard(s): [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] (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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL1 (912) 47: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [SCP2] [MA2013] AL2 (912) 40: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. [SCP3] [MA2013] AL2 (912) 41: Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. [SCP4] [MA2013] AL2 (912) 42: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [SCP5] [MA2013] AL2 (912) 43: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. [SCP6] [MA2013] AL2 (912) 44: Apply the Addition Rule, P(A or B) = P(A) + P(B)  P(A and B), and interpret the answer in terms of the model. [SCP7] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] PRE (912) 48: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [SIC5] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama) [MA2013] PRE (912) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [SMD1]
Subject: Mathematics Title: Stick or Switch?
Description: This lesson, from Illuminations, presents a version of a classic gameshow scenario. You pick one of three doors in hopes of winning the prize. The host opens one of the two remaining doors, which reveals no prize, and then asks if you wish to stick or switch. Which choice gives you the best chance to win? Students explore different approaches to this problem including guesses, experiments, computer simulations, and theoretical models. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Sticks and Stones Demo
Description:
This student interactive, from an Illuminations lesson, allows students to generate random throws for the game '' Sticks and Stones.'' In the game, three sticks are tossed and a player moves his or her marker according to how the sticks land.
Standard(s): [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] (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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL1 (912) 47: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [SCP2] [MA2013] AL2 (912) 40: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. [SCP3] [MA2013] AL2 (912) 41: Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. [SCP4] [MA2013] AL2 (912) 43: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. [SCP6] [MA2013] AL2 (912) 44: Apply the Addition Rule, P(A or B) = P(A) + P(B)  P(A and B), and interpret the answer in terms of the model. [SCP7] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama) [MA2013] PRE (912) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [SMD1]
Subject: Mathematics Title: Sticks and Stones Demo
Description: This student interactive, from an Illuminations lesson, allows students to generate random throws for the game '' Sticks and Stones.'' In the game, three sticks are tossed and a player moves his or her marker according to how the sticks land. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Sticks and Stones
Description:
In this Illuminations lesson, students play Sticks and Stones, a game based on the Apache game Throw Sticks, which was played at multination celebrations. Students collect data, investigate the likelihood of various moves, and use basic ideas of expected value to determine the average number of turns needed to win a game.
Standard(s): [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [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) 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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [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] AL1 (912) 47: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [SCP2] [MA2013] AL2 (912) 40: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. [SCP3] [MA2013] AL2 (912) 42: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [SCP5] [MA2013] AL2 (912) 43: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. [SCP6] [MA2013] AL2 (912) 44: Apply the Addition Rule, P(A or B) = P(A) + P(B)  P(A and B), and interpret the answer in terms of the model. [SCP7] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [SMD1]
Subject: Mathematics Title: Sticks and Stones
Description: In this Illuminations lesson, students play Sticks and Stones, a game based on the Apache game Throw Sticks, which was played at multination celebrations. Students collect data, investigate the likelihood of various moves, and use basic ideas of expected value to determine the average number of turns needed to win a game. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: The Game of SKUNK
Description:
In this lesson, from Illuminations, students practice decisionmaking skills while playing a dice game called Skunk. This allows them to develop a better understanding of mathematical probability and of the concept of choice versus chance.
Standard(s): [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) 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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Mathematics Title: The Game of SKUNK
Description: In this lesson, from Illuminations, students practice decisionmaking skills while playing a dice game called Skunk. This allows them to develop a better understanding of mathematical probability and of the concept of choice versus chance. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Information Represented Graphically
Description:
In this threelesson unit, from Illuminations, students participate in activities in which they analyze information represented graphically. Students are asked to discuss, describe, read, and write about the graphs and the information they contain.
Standard(s): [MA2013] (1) 18: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. [1MD4] [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [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) 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: Information Represented Graphically
Description: In this threelesson unit, from Illuminations, students participate in activities in which they analyze information represented graphically. Students are asked to discuss, describe, read, and write about the graphs and the information they contain. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5,6,7,8
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Title: Africa's Struggle With AIDS
Description:
In this Xpeditions lesson, students come to understand the enormity of the impact of AIDS on the population of Africa by comparing its effect there with its effect on the population of the world in general, and especially on that of the United States. After locating Africa on a world map, and individual subSaharan nations on a map of Africa, students examine charts and graphs to find and compare data about AIDS in Africa, the world, and the United States.
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) 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) 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) 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] (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: Health  Disease  Mathematics  Applied Mathematics  Science  Biology  Social Studies  Geography Title: Africa's Struggle With AIDS
Description: In this Xpeditions lesson, students come to understand the enormity of the impact of AIDS on the population of Africa by comparing its effect there with its effect on the population of the world in general, and especially on that of the United States. After locating Africa on a world map, and individual subSaharan nations on a map of Africa, students examine charts and graphs to find and compare data about AIDS in Africa, the world, and the United States. Thinkfinity Partner: National Geographic Education Grade Span: 6,7,8
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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.
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: Marble Mania Facilitator Page
Description:
This Science NetLinks Afterschool activity introduces kids to probability and chance with a fun interactive. By flipping coins and pulling marbles out of a virtual bag, afterschool facilitators will help students begin to develop a basic understanding of probabilities, how they are determined, and how the outcome of an experiment can be affected by the number of times it is conducted.
Standard(s): [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [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) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7]
Subject: Mathematics Title: Marble Mania Facilitator Page
Description: This Science NetLinks Afterschool activity introduces kids to probability and chance with a fun interactive. By flipping coins and pulling marbles out of a virtual bag, afterschool facilitators will help students begin to develop a basic understanding of probabilities, how they are determined, and how the outcome of an experiment can be affected by the number of times it is conducted. Thinkfinity Partner: Science NetLinks Grade Span: 3,4,5,6,7,8
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Title: Marble Mania Student Page
Description:
This Science NetLinks Afterschool activity introduces kids to probability and chance with a fun interactive. By pulling marbles out of a virtual bag, students begin to develop a basic understanding of probabilities, how they are determined, and how the outcome of an experiment can be affected by the number of times it is conducted.
Standard(s): [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) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7]
Subject: Mathematics Title: Marble Mania Student Page
Description: This Science NetLinks Afterschool activity introduces kids to probability and chance with a fun interactive. By pulling marbles out of a virtual bag, students begin to develop a basic understanding of probabilities, how they are determined, and how the outcome of an experiment can be affected by the number of times it is conducted. Thinkfinity Partner: Science NetLinks Grade Span: 3,4,5,6,7,8
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Title: Tower of Hanoi
Description:
This student interactive, from Illuminations, presents a tower of from three to 20 disks, initially stacked in increasing size on one of three pegs. The goal is to move all the discs from the left peg to the right one using the smallest number of moves possible.
Standard(s): [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] DM1 (912) 8: Apply algorithms, including Kruskal's and Prim's, relating to minimum weight spanning trees, networks, flows, and Steiner trees. (Alabama) [MA2013] DM1 (912) 9: Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the listprocessing algorithm, and studentcreated algorithms. (Alabama) [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama)
Subject: Mathematics Title: Tower of Hanoi
Description: This student interactive, from Illuminations, presents a tower of from three to 20 disks, initially stacked in increasing size on one of three pegs. The goal is to move all the discs from the left peg to the right one using the smallest number of moves possible. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Random Drawing Tool
Description:
This student interactive, from Illuminations, allows students to explore the relationship between theoretical and experimental probabilities. Students use this '' box model'' as a statistical device to simulate standard probability experiments such as flipping a coin or rolling a die.
Standard(s): [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] (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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7]
Subject: Mathematics Title: Random Drawing Tool
Description: This student interactive, from Illuminations, allows students to explore the relationship between theoretical and experimental probabilities. Students use this '' box model'' as a statistical device to simulate standard probability experiments such as flipping a coin or rolling a die. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12
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Title: Adjustable Spinner
Description:
This student interactive, from Illuminations, allows students to create their own spinners and examine the outcomes given a specified number of spins. Students learn that experimental probabilities differ according to the characteristics of the model.
Standard(s): [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) 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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6]
Subject: Mathematics Title: Adjustable Spinner
Description: This student interactive, from Illuminations, allows students to create their own spinners and examine the outcomes given a specified number of spins. Students learn that experimental probabilities differ according to the characteristics of the model. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5,6,7,8,9,10,11,12
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Title: Fire
Description:
In this student interactive, from Illuminations, students can see the results of a fire if a forest is densely planted in a rectangular grid. Students are able to choose a starting place for the fire and enter the probability that a given tree will burn.
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) 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) 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) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] AL1 (912) 47: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [SCP2] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6]
Subject: Mathematics Title: Fire
Description: In this student interactive, from Illuminations, students can see the results of a fire if a forest is densely planted in a rectangular grid. Students are able to choose a starting place for the fire and enter the probability that a given tree will burn. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12
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Title: Canada Data Map
Description:
Investigate data for the Canadian provinces and territories with this interactive tool. Students can examine data sets contained within the interactive, or they can enter their own data.
Standard(s): [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6RP1] [MA2013] (6) 3: Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6RP3] [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7RP2] [MA2013] (7) 3: Use proportional relationships to solve multistep ratio and percent problems. [7RP3] [MA2013] (7) 11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7G1] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1] [MA2013] GEO (912) 40: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).* [GMG2]
Subject: Mathematics Title: Canada Data Map
Description: Investigate data for the Canadian provinces and territories with this interactive tool. Students can examine data sets contained within the interactive, or they can enter their own data. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8,9,10,11,12

