# DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability

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1 DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability

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3 RIT Score Range: Below 171 Below 171 Data Analysis and Statistics Solves simple problems based on data from tables* Compares data from simple graphs (e.g., largest, smallest, most often, least often) Probability New Vocabulary: dollar, fewest, longest, shortest New Signs and Symbols: \$ dollar sign, = is equal to Data Analysis and Statistics Interprets simple graphs or tables Interprets data using tally charts Reads and interprets data from a pictograph* Solves simple problems based on data from pictographs Displays data appropriately - bar graph - scale is 1 to 1* Solves simple problems based on data from bar graphs Compares data from simple graphs (e.g., largest, smallest, most often, least often) Probability using a table* New Vocabulary: fewer, less, quart, taller New Signs and Symbols: cm centimeter/centimetre, in. inch, tally mark

4 RIT Score Range: Below Data Analysis and Statistics Data Analysis and Statistics Data Analysis and Statistics Solves simple problems based on data from tables* Compares data from simple graphs (e.g., largest, smallest, most often, least often) Interprets simple graphs or tables Interprets data using tally charts Reads and interprets data from a pictograph* Solves simple problems based on data from pictographs Displays data appropriately - bar graph - scale is 1 to 1* Solves simple problems based on data from bar graphs Compares data from simple graphs (e.g., largest, smallest, most often, least often) Probability Probability Probability using a table* Interprets simple graphs or tables Solves simple problems based on data from tally charts* Solves simple problems based on data from pictographs Reads and interprets data from a bar graph Solves simple problems based on data from bar graphs using a spinner with objects hidden in containers* New Vocabulary: dollar, fewest, longest, shortest New Vocabulary: fewer, less, quart, taller New Vocabulary: average, consecutive, lowest, most likely, New Signs and Symbols: \$ dollar sign, = is equal to New Signs and Symbols: cm centimeter/centimetre, in. inch, tally mark most often, spinner New Signs and Symbols: none

5 RIT Score Range: Data Analysis and Statistics Data Analysis and Statistics Data Analysis and Statistics Interprets simple graphs or tables Interprets simple graphs or tables Interprets data using tally charts Solves simple problems based on data from tally Reads and interprets data from a pictograph* charts* Solves simple problems based on data from Solves simple problems based on data from pictographs pictographs Displays data appropriately - bar graph - scale is 1 to 1* Reads and interprets data from a bar graph Solves simple problems based on data from bar graphs Solves simple problems based on data from bar graphs Compares data from simple graphs (e.g., largest, smallest, most often, least often) Probability Probability Probability using a table* New Vocabulary: fewer, less, quart, taller New Signs and Symbols: cm centimeter/centimetre, in. inch, tally mark using a spinner with objects hidden in containers* New Vocabulary: average, consecutive, lowest, most likely, most often, spinner New Signs and Symbols: none Solves problems using tables Solves problems using tally charts* Reads and interprets data from a bar graph Reads and interprets dual bar graphs* Reads and interprets simple line graphs Reads and interprets data given in percent form on a circle graph* Draws conclusions from data - tally charts or frequency tables* using a spinner with a dart board* New Vocabulary: line graph New Signs and Symbols: a.m., F degrees Fahrenheit, g gram, lb pound, min minute, p.m., % percent, : used with time

6 RIT Score Range: Data Analysis and Statistics Data Analysis and Statistics Data Analysis and Statistics Interprets simple graphs or tables Solves simple problems based on data from tally charts* Solves simple problems based on data from pictographs Reads and interprets data from a bar graph Solves simple problems based on data from bar graphs Solves problems using tables Solves problems using tally charts* Reads and interprets data from a bar graph Reads and interprets dual bar graphs* Reads and interprets simple line graphs Reads and interprets data given in percent form on a circle graph* Draws conclusions from data - tally charts or frequency tables* Probability Probability Probability using a spinner with objects hidden in containers* using a spinner with a dart board* New Vocabulary: average, consecutive, lowest, most likely, most often, spinner New Signs and Symbols: none New Vocabulary: line graph New Signs and Symbols: a.m., F degrees Fahrenheit, g gram, lb pound, min minute, p.m., % percent, : used with time Reads and interprets tables* Solves problems using tables Understands how the omission or duplication of data affects the interpretation of results from a pictograph* Organizes data to create simple bar graphs Solves problems using bar graphs Solves problems using dual bar graphs* Solves problems using line graphs* Displays data appropriately - simple circle graph - no calculations necessary* Reads and interprets data given in percent form on a circle graph* Interprets data given in circle graphs to solve simple Solves problems using Venn diagrams Draws conclusions from data - bar graphs Predicts from pictographs and bar graphs* Predicts from simple charts and tables Recognizes events that are certain, likely, unlikely, possible, or impossible* Uses the concept of chance to determine the likelihood of an event* Determines the probability for a simple experiment using one or more coins Determines the probability for a simple experiment using objects - must determine size of sample space New Vocabulary: bar graph, below, less likely, maximum, random, square mile, times New Signs and Symbols: ft feet, kg kilogram

7 RIT Score Range: Data Analysis and Statistics Data Analysis and Statistics Data Analysis and Statistics Solves problems using tables Solves problems using tally charts* Reads and interprets data from a bar graph Reads and interprets dual bar graphs* Reads and interprets simple line graphs Reads and interprets data given in percent form on a circle graph* Draws conclusions from data - tally charts or frequency tables* Reads and interprets tables* Solves problems using tables Understands how the omission or duplication of data affects the interpretation of results from a pictograph* Organizes data to create simple bar graphs Solves problems using bar graphs Solves problems using dual bar graphs* Solves problems using line graphs* Displays data appropriately - simple circle graph - no calculations necessary* Reads and interprets data given in percent form on a circle graph* Interprets data given in circle graphs to solve simple Solves problems using Venn diagrams Draws conclusions from data - bar graphs Predicts from pictographs and bar graphs* Predicts from simple charts and tables Probability Probability Probability using a spinner with a dart board* Recognizes events that are certain, likely, unlikely, possible, or impossible* Uses the concept of chance to determine the likelihood of an event* Determines the probability for a simple experiment using one or more coins Determines the probability for a simple experiment using objects - must determine size of sample space Solves problems using pictographs* Solves problems using bar graphs Interprets data in line graphs (e.g., change over time) Solves problems using line graphs* Reads and interprets circle graphs* Interprets data given in circle graphs to solve simple Solves problems using circle graphs* Reads and interprets Venn diagrams Reads and interprets data in scatter plots Reads and interprets data in line plots* Determines the average (mean) of a simple set of data Solves simple problems involving mean Draws conclusions from data - charts* Predicts from pictographs and bar graphs* Predicts from plotted data* Determines the probability for a simple experiment using one die Determines probability from a real-world situation - number of possible outcomes given Determines the probabilities for a simple experiment using a frequency table - must determine size of sample space Determines probability when drawing objects from containers - must determine size of sample space Determines the complement of a simple event* Determines the possible outcomes for a simple probability experiment using spinners Solves problems involving permutations Determines the number of possible combinations of given items Predicts the sample space, based on the outcome of an

8 New Vocabulary: line graph New Signs and Symbols: a.m., F degrees Fahrenheit, g gram, lb pound, min minute, p.m., % percent, : used with time New Vocabulary: bar graph, below, less likely, maximum, random, square mile, times New Signs and Symbols: ft feet, kg kilogram experiment - tally sheet* Uses the results of probability experiments or events to predict future events* New Vocabulary: combinations, fastest, fitted line, likelihood, line of best fit, line plot, mean, number cube, outcome, positive linear relationship, prove, scatter plot, tails New Signs and Symbols: { } set notation, cent sign, d distance, hr hour, mph miles per hour, P( ) probability, t time

9 RIT Score Range: Data Analysis and Statistics Data Analysis and Statistics Data Analysis and Statistics Reads and interprets tables* Solves problems using pictographs* Solves problems using tables Solves problems using bar graphs Understands how the omission or duplication of data Interprets data in line graphs (e.g., change over time) affects the interpretation of results from a pictograph* Solves problems using line graphs* Organizes data to create simple bar graphs Reads and interprets circle graphs* Solves problems using bar graphs Interprets data given in circle graphs to solve simple Solves problems using dual bar graphs* Solves problems using line graphs* Solves problems using circle graphs* Displays data appropriately - simple circle graph - no Reads and interprets Venn diagrams calculations necessary* Reads and interprets data in scatter plots Reads and interprets data given in percent form on a Reads and interprets data in line plots* circle graph* Determines the average (mean) of a simple set of data Interprets data given in circle graphs to solve simple Solves simple problems involving mean Draws conclusions from data - charts* Solves problems using Venn diagrams Predicts from pictographs and bar graphs* Draws conclusions from data - bar graphs Predicts from plotted data* Predicts from pictographs and bar graphs* Predicts from simple charts and tables Probability Probability Probability Recognizes events that are certain, likely, unlikely, possible, or impossible* Uses the concept of chance to determine the likelihood of an event* Determines the probability for a simple experiment using one or more coins Determines the probability for a simple experiment using objects - must determine size of sample space Determines the probability for a simple experiment using one die Determines probability from a real-world situation - number of possible outcomes given Determines the probabilities for a simple experiment using a frequency table - must determine size of sample space Determines probability when drawing objects from containers - must determine size of sample space Determines the complement of a simple event* Determines the possible outcomes for a simple probability experiment using spinners Solves problems involving permutations Determines the number of possible combinations of Determines the most accurate sample for a situation* Interprets data given in tables to solve problems Interprets data given in circle graphs to solve complex Solves problems using circle graphs* Determines the average (mean) of a simple set of data Determines the mean of a complex set of data (e.g., fractions, integers, many data points) Estimates the mean from a set of data* Solves simple problems involving mean Solves problems with missing data when the mean is known Determines the middle value (median) from a simple set of data* Determines the mode of a set of data Explains rationale for determining the mean, median, or mode of a set of data* Draws conclusions from data - charts* Predicts from line graphs* Predicts from plotted data* Determines likelihood using tree diagrams* Determines probability - must determine size of sample space Determines the complement of a simple event* Determines the possible outcomes for a simple probability experiment using spinners Determines the possible outcomes for a simple probability experiment using dart boards* Solves problems involving combinations Determines the number of possible combinations of given items Determines the outcome of simple multiple events* Uses previous results to predict future events* Computes probability as a fraction, given equivalent

10 New Vocabulary: bar graph, below, less likely, maximum, random, square mile, times New Signs and Symbols: ft feet, kg kilogram given items Predicts the sample space, based on the outcome of an experiment - tally sheet* Uses the results of probability experiments or events to predict future events* New Vocabulary: combinations, fastest, fitted line, likelihood, line of best fit, line plot, mean, number cube, outcome, positive linear relationship, prove, scatter plot, tails New Signs and Symbols: { } set notation, cent sign, d distance, hr hour, mph miles per hour, P( ) probability, t time forms* Given probability as a decimal, estimates probability as a fraction* New Vocabulary: frequency table, median, mode, survey New Signs and Symbols: h hour (SI metric), - negative number, oz ounce, s second (SI metric)

11 RIT Score Range: Data Analysis and Statistics Data Analysis and Statistics Data Analysis and Statistics Solves problems using pictographs* Determines the most accurate sample for a situation* Solves problems using bar graphs Interprets data given in tables to solve problems Interprets data in line graphs (e.g., change over time) Interprets data given in circle graphs to solve complex Solves problems using line graphs* Reads and interprets circle graphs* Solves problems using circle graphs* Interprets data given in circle graphs to solve simple Determines the average (mean) of a simple set of data Determines the mean of a complex set of data (e.g., Solves problems using circle graphs* fractions, integers, many data points) Reads and interprets Venn diagrams Estimates the mean from a set of data* Reads and interprets data in scatter plots Solves simple problems involving mean Reads and interprets data in line plots* Solves problems with missing data when the mean is Determines the average (mean) of a simple set of data known Solves simple problems involving mean Determines the middle value (median) from a simple Draws conclusions from data - charts* set of data* Predicts from pictographs and bar graphs* Determines the mode of a set of data Predicts from plotted data* Explains rationale for determining the mean, median, or mode of a set of data* Draws conclusions from data - charts* Predicts from line graphs* Predicts from plotted data* Probability Probability Probability Determines the probability for a simple experiment using one die Determines probability from a real-world situation - number of possible outcomes given Determines likelihood using tree diagrams* Determines probability - must determine size of sample space Determines the complement of a simple event* Determines the probabilities for a simple experiment Determines the possible outcomes for a simple using a frequency table - must determine size of sample probability experiment using spinners space Determines the possible outcomes for a simple Determines probability when drawing objects from probability experiment using dart boards* Performs basic operations on matrices* Organizes data using tables* Interprets data given in tables to solve problems Determines appropriate intervals and/or scale for a bar graph* Interprets data given in horizontal and vertical bar graphs to solve problems Interprets data given in line graphs to solve problems* Interprets data given in circle graphs to solve complex Reads and interprets data in box-and-whisker plots Determines the mean of a complex set of data (e.g., fractions, integers, many data points) Estimates the mean from a set of data* Solves problems with missing data when the mean is known Determines the median from a complex set of data (e.g., not in order, many data points) Determines the range of a complex set of data Estimates line of best fit to make predictions Identifies outliers on a data display (e.g., uses interquartile range to identify outliers on a box-and-whisker plot)* Predicts from an analysis of data and statistical measures* Predicts from charts and tables Determines certainty from a set data* Determines sample space given probability of all possible outcomes* Determines probability - must determine size of sample space Modifies sample space to change the probability of an event* Determines the probability of independent simple

12 containers - must determine size of sample space Determines the complement of a simple event* Determines the possible outcomes for a simple probability experiment using spinners Solves problems involving permutations Determines the number of possible combinations of given items Predicts the sample space, based on the outcome of an experiment - tally sheet* Uses the results of probability experiments or events to predict future events* New Vocabulary: combinations, fastest, fitted line, likelihood, line of best fit, line plot, mean, number cube, outcome, positive linear relationship, prove, scatter plot, tails New Signs and Symbols: { } set notation, cent sign, d distance, hr hour, mph miles per hour, P( ) probability, t time Solves problems involving combinations Determines the number of possible combinations of given items Determines the outcome of simple multiple events* Uses previous results to predict future events* Computes probability as a fraction, given equivalent forms* Given probability as a decimal, estimates probability as a fraction* New Vocabulary: frequency table, median, mode, survey New Signs and Symbols: h hour (SI metric), - negative number, oz ounce, s second (SI metric) compound events Determines the complement of a complex event* Recognizes the relationship between events and probability - selects an experiment which matches a given probability* New Vocabulary: average salary, box-and-whisker plot, data point, interquartile range, lower quartile, matrix, meters per minute, middle, outlier, percentile, quartile, sample, successive, upper quartile New Signs and Symbols: ( ) ordered pair, \$ dollar sign, C degrees Celsius, m meter/metre, ml milliliter/millilitre,? next in sequence, outlier

13 RIT Score Range: Data Analysis and Statistics Data Analysis and Statistics Data Analysis and Statistics Determines the most accurate sample for a situation* Performs basic operations on matrices* Interprets data given in tables to solve problems Organizes data using tables* Interprets data given in circle graphs to solve complex Interprets data given in tables to solve problems Determines appropriate intervals and/or scale for a bar Solves problems using circle graphs* graph* Determines the average (mean) of a simple set of data Interprets data given in horizontal and vertical bar Determines the mean of a complex set of data (e.g., graphs to solve problems fractions, integers, many data points) Interprets data given in line graphs to solve problems* Estimates the mean from a set of data* Interprets data given in circle graphs to solve complex Solves simple problems involving mean Solves problems with missing data when the mean is Reads and interprets data in box-and-whisker plots known Determines the mean of a complex set of data (e.g., Determines the middle value (median) from a simple fractions, integers, many data points) set of data* Estimates the mean from a set of data* Determines the mode of a set of data Solves problems with missing data when the mean is Explains rationale for determining the mean, median, known or mode of a set of data* Determines the median from a complex set of data Draws conclusions from data - charts* (e.g., not in order, many data points) Predicts from line graphs* Determines the range of a complex set of data Predicts from plotted data* Estimates line of best fit to make predictions Identifies outliers on a data display (e.g., uses interquartile range to identify outliers on a box-and-whisker plot)* Predicts from an analysis of data and statistical measures* Predicts from charts and tables Probability Probability Probability Determines likelihood using tree diagrams* Determines certainty from a set data* Determines probability - must determine size of Determines sample space given probability of all sample space possible outcomes* Determines the complement of a simple event* Determines probability - must determine size of Determines the possible outcomes for a simple sample space probability experiment using spinners Modifies sample space to change the probability of an Determines the possible outcomes for a simple event* probability experiment using dart boards* Determines the probability of independent simple Performs basic operations on matrices* Reads and interprets data in tables Reads and interprets data in box-and-whisker plots Reads and interprets data in stem-and-leaf plots Determines the range of a complex set of data Determines the correlation for a set of data* Identifies a set of data with a given mean, median, and/or mode* Predicts from an analysis of data and statistical measures* Determines certainty from a set data* Determines probability using counting procedures* Determines probability using tables Determines the complement of a complex event* Determines probability using an area model Uses multiplication principle of counting to determine possibilities Uses counting procedures to determine possibilities*

14 Solves problems involving combinations Determines the number of possible combinations of given items Determines the outcome of simple multiple events* Uses previous results to predict future events* Computes probability as a fraction, given equivalent forms* Given probability as a decimal, estimates probability as a fraction* New Vocabulary: frequency table, median, mode, survey New Signs and Symbols: h hour (SI metric), - negative number, oz ounce, s second (SI metric) compound events Determines the complement of a complex event* Recognizes the relationship between events and probability - selects an experiment which matches a given probability* New Vocabulary: average salary, box-and-whisker plot, data point, interquartile range, lower quartile, matrix, meters per minute, middle, outlier, percentile, quartile, sample, successive, upper quartile New Signs and Symbols: ( ) ordered pair, \$ dollar sign, C degrees Celsius, m meter/metre, ml milliliter/millilitre,? next in sequence, outlier Uses theoretical probability to predict future events New Vocabulary: correlation, hyperbolic, mileage table, stem and leaf plot New Signs and Symbols: degrees, E east, multiplication, NE northeast, NNE north northeast, N north, NW northwest, S south, W west

15 RIT Score Range: Data Analysis and Statistics Data Analysis and Statistics Data Analysis and Statistics Performs basic operations on matrices* Performs basic operations on matrices* Organizes data using tables* Reads and interprets data in tables Interprets data given in tables to solve problems Reads and interprets data in box-and-whisker plots Determines appropriate intervals and/or scale for a bar Reads and interprets data in stem-and-leaf plots graph* Determines the range of a complex set of data Interprets data given in horizontal and vertical bar Determines the correlation for a set of data* graphs to solve problems Identifies a set of data with a given mean, median, Interprets data given in line graphs to solve problems* and/or mode* Interprets data given in circle graphs to solve complex Predicts from an analysis of data and statistical measures* Reads and interprets data in box-and-whisker plots Determines the mean of a complex set of data (e.g., fractions, integers, many data points) Estimates the mean from a set of data* Solves problems with missing data when the mean is known Determines the median from a complex set of data (e.g., not in order, many data points) Determines the range of a complex set of data Estimates line of best fit to make predictions Identifies outliers on a data display (e.g., uses interquartile range to identify outliers on a box-and-whisker plot)* Predicts from an analysis of data and statistical measures* Predicts from charts and tables Probability Probability Probability Determines certainty from a set data* Determines sample space given probability of all possible outcomes* Determines certainty from a set data* Determines probability using counting procedures* Determines probability using tables Determines probability - must determine size of Determines the complement of a complex event* sample space Determines probability using an area model Modifies sample space to change the probability of an Uses multiplication principle of counting to determine event* possibilities Determines the probability of independent simple Uses counting procedures to determine possibilities* Performs basic operations on matrices* Uses random sampling techniques* Displays data appropriately - circle graph - calculations necessary* Solves complex problems involving mean* Computes and compares mean, median, mode, and range in simple examples to demonstrate that they may differ for a given set of data* Evaluates how adding data to a set of data affects the measures of center* Uses the regression line method to make predictions* Determines certainty from a set data* Determines the probabilities of complex compound events (independent)*

16 compound events Determines the complement of a complex event* Recognizes the relationship between events and probability - selects an experiment which matches a given probability* New Vocabulary: average salary, box-and-whisker plot, data point, interquartile range, lower quartile, matrix, meters per minute, middle, outlier, percentile, quartile, sample, successive, upper quartile New Signs and Symbols: ( ) ordered pair, \$ dollar sign, C degrees Celsius, m meter/metre, ml milliliter/millilitre,? next in sequence, outlier Uses theoretical probability to predict future events New Vocabulary: correlation, hyperbolic, mileage table, stem and leaf plot New Signs and Symbols: degrees, E east, multiplication, NE northeast, NNE north northeast, N north, NW northwest, S south, W west New Vocabulary: none New Signs and Symbols: + addition

17 RIT Score Range: Data Analysis and Statistics Data Analysis and Statistics Data Analysis and Statistics Performs basic operations on matrices* Performs basic operations on matrices* Reads and interprets data in tables Uses random sampling techniques* Reads and interprets data in box-and-whisker plots Displays data appropriately - circle graph - calculations Reads and interprets data in stem-and-leaf plots necessary* Determines the range of a complex set of data Solves complex problems involving mean* Determines the correlation for a set of data* Computes and compares mean, median, mode, and Identifies a set of data with a given mean, median, range in simple examples to demonstrate that they may and/or mode* differ for a given set of data* Predicts from an analysis of data and statistical Evaluates how adding data to a set of data affects the measures* measures of center* Uses the regression line method to make predictions* Probability Probability Probability Determines certainty from a set data* Determines certainty from a set data* Determines probability using counting procedures* Determines the probabilities of complex compound Determines probability using tables events (independent)* Determines the complement of a complex event* Determines probability using an area model Uses multiplication principle of counting to determine possibilities Uses counting procedures to determine possibilities* Uses theoretical probability to predict future events New Vocabulary: correlation, hyperbolic, mileage table, stem and leaf plot New Signs and Symbols: degrees, E east, multiplication, NE northeast, NNE north northeast, N north, NW northwest, S south, W west New Vocabulary: none New Signs and Symbols: + addition Above 260 Reads and interprets interquartile range in box-and-whisker plots* Determines the probabilities of compound events (dependent) New Vocabulary: none New Signs and Symbols: none

18 RIT Score Range: Above Data Analysis and Statistics Performs basic operations on matrices* Uses random sampling techniques* Displays data appropriately - circle graph - calculations necessary* Solves complex problems involving mean* Computes and compares mean, median, mode, and range in simple examples to demonstrate that they may differ for a given set of data* Evaluates how adding data to a set of data affects the measures of center* Uses the regression line method to make predictions* Probability Determines certainty from a set data* Determines the probabilities of complex compound events (independent)* New Vocabulary: none New Signs and Symbols: + addition Above 260 Data Analysis and Statistics Reads and interprets interquartile range in box-and-whisker plots* Probability Determines the probabilities of compound events (dependent) New Vocabulary: none New Signs and Symbols: none

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