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- Growth: Grades 6+ Math - Data, Statistics, and Probability (2017)

# Growth: Grades 6+ Math - Data, Statistics, and Probability (2017)

### 5: Data, Statistics, and Probability

5.1: Collect, Represent, and Analyze Data

5.1.1: Bivariate Data

5.1.1.1: [RIT 199 - 243] Describes data in a scatter plot, including the interpretation of outliers and clusters

Correlation

Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Least-Squares Best Fit Lines

Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines

Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots

Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview

5.1.1.2: [RIT 206 - 249] Describes the correlation or association between two variables, including the direction and strength of linear and nonlinear relationships

Correlation

Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Least-Squares Best Fit Lines

Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines

Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots

Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview

5.1.1.3: [RIT 213 - 239] Constructs scatter plots of bivariate data

Correlation

Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview

Graphing Skills

Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview

Least-Squares Best Fit Lines

Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Trends in Scatter Plots

Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview

5.1.1.5: [RIT 220 - 238] Approximates the line of best fit on a scatter plot

Correlation

Least-Squares Best Fit Lines

Trends in Scatter Plots

5.1.1.6: [RIT 220 - 246] Determines whether two quantitative variables have a positive linear, negative linear, or zero association

Correlation

Graphing Skills

Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview

Least-Squares Best Fit Lines

Solving Using Trend Lines

Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview

Trends in Scatter Plots

5.1.1.7: [RIT 221 - 221] Distinguishes between linear and nonlinear relationships in scatter plots

Correlation

5.1.1.8: [RIT 222 - 222] Understands the relationship between the value of the correlation coefficient and the strength and direction of a linear relationship

Correlation

5.1.1.9: [RIT 231 - 247] Determines a pair of quantitative variables that has either a positive, negative, or zero correlation

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

5.1.1.11: [RIT 234 - 267] Interprets the meaning of the slope or y-intercept of a line of best fit or regression line

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

5.1.1.12: [RIT 244 - 263] Analyzes linear trends in scatter plots to make predictions

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

5.1.1.14: [RIT 246 - 254] Estimates the slope of a line of best fit

Correlation

Least-Squares Best Fit Lines

Trends in Scatter Plots

5.1.1.15: [RIT 261 - 276] Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a scatter plot

Correlation

5.1.1.16: [RIT 261 - 261] Identifies the correlation coefficient that best approximates the relationship between two quantitative variables represented in a real-world context

Correlation

5.1.1.17: [RIT 262 - 262] Approximates the equation of the line of best fit

Correlation

Least-Squares Best Fit Lines

Trends in Scatter Plots

5.1.1.18: [RIT 271 - 271] Compares two sets of bivariate data to draw conclusions

Correlation

Graphing Skills

Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview

5.1.2: Data Analysis

5.1.2.3: [RIT 152 - 184] Compares categories in bar graphs with multi-unit scales to determine which is greater than or greatest

Graphing Skills

Mascot Election (Pictographs and Bar Graphs)

A brand new school is opening and it is time to elect the school mascot! Students can choose the Eagle, Lion, Bear, or Wolf. Voting results can be displayed in a table, tally chart, pictograph, bar graph, circle graph, or dot plot. You can change student votes by selecting a group of students and clicking a mascot. 5 Minute Preview

Reaction Time 1 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median. 5 Minute Preview

5.1.2.5: [RIT 157 - 176] Compares categories in tables or charts to determine which is greater than or greatest

Mascot Election (Pictographs and Bar Graphs)

A brand new school is opening and it is time to elect the school mascot! Students can choose the Eagle, Lion, Bear, or Wolf. Voting results can be displayed in a table, tally chart, pictograph, bar graph, circle graph, or dot plot. You can change student votes by selecting a group of students and clicking a mascot. 5 Minute Preview

5.1.2.6: [RIT 158 - 176] Compares categories in pictographs with multi-unit scales to determine which is greater than or greatest

Mascot Election (Pictographs and Bar Graphs)

A brand new school is opening and it is time to elect the school mascot! Students can choose the Eagle, Lion, Bear, or Wolf. Voting results can be displayed in a table, tally chart, pictograph, bar graph, circle graph, or dot plot. You can change student votes by selecting a group of students and clicking a mascot. 5 Minute Preview

5.1.2.7: [RIT 163 - 215] Reads and interprets data from a circle graph

Graphing Skills

Mascot Election (Pictographs and Bar Graphs)

5.1.2.10: [RIT 167 - 167] Reads pictographs with single-unit scales to determine how many in a category

Mascot Election (Pictographs and Bar Graphs)

5.1.2.12: [RIT 169 - 192] Reads tables or charts to determine how many in a category

Mascot Election (Pictographs and Bar Graphs)

5.1.2.14: [RIT 171 - 201] Compares multiple categories in bar graphs with multi-unit scales to answer questions

Graphing Skills

5.1.2.15: [RIT 172 - 179] Compares categories in tables or charts to determine which is less than or least

Graphing Skills

5.1.2.16: [RIT 172 - 194] Reads bar graphs with multi-unit scales to determine how many in a category

Graphing Skills

Mascot Election (Pictographs and Bar Graphs)

5.1.2.18: [RIT 173 - 208] Compares multiple categories in tables or charts to answer questions

Mascot Election (Pictographs and Bar Graphs)

5.1.2.19: [RIT 175 - 200] Determines the question to ask in order to collect data for a given purpose

Box-and-Whisker Plots

Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview

Describing Data Using Statistics

Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview

Histograms

Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview

Stem-and-Leaf Plots

Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview

5.1.2.21: [RIT 176 - 193] Compares categories in bar graphs with multi-unit scales to determine which is less than or least

Graphing Skills

5.1.2.22: [RIT 177 - 177] Compares multiple categories in pictographs with multi-unit scales to answer questions

Mascot Election (Pictographs and Bar Graphs)

5.1.2.26: [RIT 180 - 180] Reads line or dot plots with whole-number scales to determine how many in a category

Mascot Election (Pictographs and Bar Graphs)

5.1.2.27: [RIT 182 - 234] Reads and interprets data in a scaled line graph

Elevator Operator (Line Graphs)

Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 5 Minute Preview

Graphing Skills

5.1.2.29: [RIT 185 - 205] Reads pictographs with multi-unit scales to determine how many in a category

Mascot Election (Pictographs and Bar Graphs)

5.1.2.37: [RIT 196 - 212] Reads and interprets data from line or dot plots with whole-number scales

Mascot Election (Pictographs and Bar Graphs)

5.1.2.40: [RIT 198 - 221] Reads and interprets data from a scatter plot

Correlation

Graphing Skills

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

5.1.2.45: [RIT 204 - 204] Interprets data in a table or chart

Graphing Skills

Mascot Election (Pictographs and Bar Graphs)

5.1.2.47: [RIT 205 - 240] Identifies the median, quartiles, extreme values, and outliers from a box plot

Box-and-Whisker Plots

Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview

5.1.2.48: [RIT 209 - 227] Reads and interprets data from a histogram

Histograms

Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview

5.1.2.54: [RIT 222 - 248] Reads and interprets data from a stem-and-leaf plot

Stem-and-Leaf Plots

Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview

5.1.2.56: [RIT 228 - 228] Determines the range from a stem-and-leaf plot

Stem-and-Leaf Plots

Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview

5.1.2.57: [RIT 231 - 231] Determines the median from a stem-and-leaf plot

Stem-and-Leaf Plots

5.1.2.58: [RIT 233 - 233] Determines the mode from a stem-and-leaf plot

Stem-and-Leaf Plots

5.1.2.63: [RIT 243 - 243] Compares the means and medians of related data sets from random samples represented in histograms

Populations and Samples

Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview

5.1.3: Data Representation

5.1.3.2: [RIT 174 - 200] Represents data in tables or charts

Mascot Election (Pictographs and Bar Graphs)

Reaction Time 1 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median. 5 Minute Preview

Reaction Time 2 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview

5.1.3.4: [RIT 189 - 189] Represents data in pictographs with single-unit scales

Mascot Election (Pictographs and Bar Graphs)

5.1.3.5: [RIT 192 - 211] Represents data in line or dot plots with whole-number scales

Histograms

Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview

Mascot Election (Pictographs and Bar Graphs)

Reaction Time 1 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median. 5 Minute Preview

Reaction Time 2 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview

5.1.3.6: [RIT 194 - 201] Represents data in pictographs with multi-unit scales

Mascot Election (Pictographs and Bar Graphs)

5.1.3.7: [RIT 196 - 224] Represents data in circle graphs

Graphing Skills

Mascot Election (Pictographs and Bar Graphs)

5.1.3.8: [RIT 197 - 197] Represents data in line graphs

Elevator Operator (Line Graphs)

Operate an elevator in an old apartment building. Pick up and drop off residents where they want to go. A line graph shows where the elevator traveled over time. Operate the elevator either by using the standard up and down controls, or by building a graph to program where you want it to go. 5 Minute Preview

Graphing Skills

5.1.3.9: [RIT 198 - 219] Identifies the data display that best represents a given set of data or scenario

Mascot Election (Pictographs and Bar Graphs)

5.1.3.10: [RIT 204 - 204] Represents data in picture graphs with multi-unit scales

Mascot Election (Pictographs and Bar Graphs)

5.1.3.13: [RIT 213 - 239] Constructs scatter plots of bivariate data

Correlation

Graphing Skills

Least-Squares Best Fit Lines

Trends in Scatter Plots

5.1.3.15: [RIT 225 - 227] Represents data in frequency tables

Mascot Election (Pictographs and Bar Graphs)

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview

5.1.3.16: [RIT 226 - 226] Represents data in stem-and-leaf plots

Stem-and-Leaf Plots

5.1.3.17: [RIT 228 - 254] Represents data in histograms

Histograms

Real-Time Histogram

Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected. 5 Minute Preview

Sight vs. Sound Reactions

Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. 5 Minute Preview

5.1.4: Measures of Center and Spread (Variability)

5.1.4.1: [RIT 199 - 214] Interprets the mode in the context of a data set

Mean, Median, and Mode

Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

5.1.4.2: [RIT 202 - 216] Interprets the median in the context of a data set

Mean, Median, and Mode

Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview

Movie Reviewer (Mean and Median)

Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance model. Students can also find the median, mode, and range of the data set. 5 Minute Preview

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

5.1.4.3: [RIT 204 - 226] Determines the median of a data set that is ordered

Describing Data Using Statistics

Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview

Mean, Median, and Mode

Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview

Movie Reviewer (Mean and Median)

Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance model. Students can also find the median, mode, and range of the data set. 5 Minute Preview

5.1.4.4: [RIT 205 - 240] Identifies the median, quartiles, extreme values, and outliers from a box plot

Box-and-Whisker Plots

Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview

5.1.4.5: [RIT 209 - 222] Determines the mode of a data set

Describing Data Using Statistics

Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

5.1.4.6: [RIT 213 - 237] Determines the mean of a data set

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance model. Students can also find the median, mode, and range of the data set. 5 Minute Preview

5.1.4.7: [RIT 215 - 215] Defines the mode

Describing Data Using Statistics

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

5.1.4.8: [RIT 216 - 222] Describes how the median is calculated

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

5.1.4.9: [RIT 216 - 216] Describes how the mean is calculated

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

5.1.4.10: [RIT 217 - 248] Determines the median of a data set that is not ordered

Mean, Median, and Mode

Reaction Time 2 (Graphs and Statistics)

5.1.4.11: [RIT 219 - 248] Determines the range of a data set

Describing Data Using Statistics

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

5.1.4.12: [RIT 221 - 221] Defines the median

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

5.1.4.14: [RIT 228 - 228] Determines the range from a stem-and-leaf plot

Stem-and-Leaf Plots

5.1.4.15: [RIT 231 - 231] Determines the median from a stem-and-leaf plot

Stem-and-Leaf Plots

5.1.4.17: [RIT 233 - 233] Determines the mode from a stem-and-leaf plot

Stem-and-Leaf Plots

5.1.4.19: [RIT 238 - 243] Explains why the mean and median differ in a single data set

Mean, Median, and Mode

5.1.4.21: [RIT 243 - 243] Compares the means and medians of related data sets from random samples represented in histograms

Populations and Samples

Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview

5.2: Probability and Sample Spaces

5.2.2: Probability

5.2.2.1: [RIT 168 - 201] Identifies a simple event given the likelihood of the event as more likely, less likely, neither likely nor unlikely, impossible, or certain

Spin the Big Wheel! (Probability)

Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview

5.2.2.2: [RIT 185 - 213] Describes the likelihood of simple events occurring

Probability Simulations

Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview

Spin the Big Wheel! (Probability)

Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview

5.2.2.3: [RIT 193 - 225] Makes predictions based on theoretical probabilities of simple events

Probability Simulations

Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview

Spin the Big Wheel! (Probability)

Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview

5.2.2.4: [RIT 196 - 249] Determines theoretical probabilities of simple events

Geometric Probability

Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview

Lucky Duck (Expected Value)

Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview

Spin the Big Wheel! (Probability)

5.2.2.5: [RIT 208 - 236] Identifies the likelihood of a simple event as more likely, less likely, neither likely nor unlikely, impossible, or certain, given the probability of the event

Geometric Probability

Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview

5.2.2.7: [RIT 215 - 238] Determines the probability of the complement of an event

Probability Simulations

Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview

Theoretical and Experimental Probability

Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview

5.2.2.8: [RIT 215 - 247] Determines experimental probabilities of simple events

Probability Simulations

Spin the Big Wheel! (Probability)

Theoretical and Experimental Probability

Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview

5.2.2.10: [RIT 224 - 232] Describes the likelihood of compound events occurring

Independent and Dependent Events

Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview

Spin the Big Wheel! (Probability)

5.2.2.11: [RIT 224 - 224] Writes proportions to make predictions based on experimental probabilities

Estimating Population Size

Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview

Polling: Neighborhood

Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

5.2.2.12: [RIT 224 - 224] Determines the odds of simple events

Probability Simulations

5.2.2.13: [RIT 229 - 245] Makes predictions based on experimental probabilities of simple events

Probability Simulations

5.2.2.14: [RIT 230 - 239] Understands independence as it relates to previous outcomes

Independent and Dependent Events

Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview

5.2.2.17: [RIT 238 - 269] Determines probabilities of compound independent events

Independent and Dependent Events

Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview

5.2.2.18: [RIT 239 - 242] Determines conditional probabilities of events without replacement

Independent and Dependent Events

5.2.2.19: [RIT 240 - 240] Modifies sample space to change the probability of an event

Independent and Dependent Events

Lucky Duck (Expected Value)

Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview

5.2.2.20: [RIT 245 - 266] Determines probabilities using geometric models

Geometric Probability

Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview

5.2.2.21: [RIT 246 - 246] Makes predictions based on probability distributions

Lucky Duck (Expected Value)

Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value. 5 Minute Preview

5.2.2.22: [RIT 253 - 278] Determines conditional probabilities of compound events using relative frequencies

Independent and Dependent Events

5.2.2.23: [RIT 257 - 257] Makes predictions based on theoretical probabilities of compound events

Independent and Dependent Events

5.2.2.24: [RIT 257 - 278] Determines probabilities using the general Multiplication Rule of probability

Independent and Dependent Events

5.2.2.25: [RIT 258 - 266] Determines probabilities of compound dependent events

Independent and Dependent Events

5.2.3: Sample Spaces

5.2.3.1: [RIT 193 - 219] Determines the sample space for a simple event using lists, tree diagrams, or charts

Probability Simulations

Theoretical and Experimental Probability

5.2.3.2: [RIT 196 - 227] Determines the sample space for two compound events using organized lists, tree diagrams, or charts

Independent and Dependent Events

Permutations and Combinations

Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview

5.2.3.4: [RIT 211 - 232] Determines the sample space for more than two compound events using organized lists, tree diagrams, or charts

Independent and Dependent Events

Permutations and Combinations

Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview

5.2.3.6: [RIT 243 - 272] Uses permutations and combinations to determine the number of possible outcomes

Permutations and Combinations

Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle. 5 Minute Preview

5.3: Population Sampling and Research Design

5.3.1: Populations/Random Processes

5.3.1.1: [RIT 187 - 217] Identifies a data collection method that best answers a question

Polling: City

Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood

Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

5.3.1.2: [RIT 202 - 210] Identifies random samples

Polling: City

Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood

Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

5.3.1.5: [RIT 217 - 250] Writes and solves proportions to make inferences about populations

Estimating Population Size

Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview

Polling: Neighborhood

5.3.1.6: [RIT 230 - 257] Identifies a sampling method that produces the most representative sample

Polling: City

Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood

5.3.1.7: [RIT 231 - 232] Identifies an appropriate research design, including surveys, experiments and observational studies, to answer a question

Polling: City

Polling: Neighborhood

How Free Gizmos Work

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**20-40 Free Gizmos**. See the full list.

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**Free Gizmos change each semester.** The new collection will be available January 1 and July 1.

About STEM Cases

Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.

Each STEM Case uses realtime reporting to show live student results.

Introduction to the Heatmap

STEM Cases take between 30-90 minutes for students to complete, depending on the case.

Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.

Multiple grade-appropriate versions, or levels, exist for each STEM Case.

Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.

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