Unit Title: Samples and populations– Investigation 4 & Commom Core Investigation 3.5 & 3.6 Suggested Time: 8 Days (75- 90 minute Blocks)

Enduring understanding (Big Idea):applying the process of statistical investigation to pose questions, identify ways data are collected, determine strategies for analyzing data and interpreting the analysis In order to answer the question posed; explaining variability in categorical and numerical data; developing a linear equation to characterize a display of data on a scatter plot

Essential Questions: What is a scatter plot? What is the sample? What kinds of comparisons and relationships can I explore using data from the sample? Can I use my results to make predictions or generalizations about the population? What changes about a figure that is dilated? How does the scale factor affect a figure that is dilated? Does the location of the center of dilation affect the size of the dilated figure?

Unit Plans

Common Core Standards Alignment

Connection to 2003 Standards

Investigation 4
Problems 4.1, 4.2, 4.3
Math Reflections

Investigate patterns of association in bivariate data. 8.SP.1 - Construct and interpret scatter plots for bivariate measurementdata to investigate patterns of association between two quantities.Describe patterns such as clustering, outliers, positive or negativeassociation, linear association, and nonlinear association.

8.SP.2 - Know that straight lines are widely used to model relationshipsbetween two quantitative variables. For scatter plots that suggest alinear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Goal 4.01, 4.02, 4.03

CC Investigation 3: Transformation (Green Book)
Problems 3.5, 3.6

Understand congruence and similarity using physical models, transparencies, or geometry software.

8.GG.2- Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.GG.3- Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Prior Knowledge:Collecting and organizing data into different context; for numerical data: finding the range of distribution; using range and shape of distribution of data to make inferences and predictions: for categorical data: analyzing frequencies as counts or percents; collecting and organizing numerical data; understanding units of measure and counts; representing data with line plots, value or frequency bar graphs, stem-and-leaf plots, and coordinate graphs; finding measures of center, examining the behavior of mean and median and shapes of distribution; percents; using counts to report frequencies, tying together work with statistics and probability; comparing data sets using ratios, proportions, rates, or percents; exploring relationships between tables, graphs and equations and investigating linearity.

Mathematical Practices Standards for Common Core 1-Make sense of problems and persevere in solving them 2-Reason abstractly and quantitatively 3-Construct viable arguments and critique the reasoning of others 4-Model with mathematics 5-Use appropriate tools strategically 6-Attend to precision 7-Look for and make use of structure 8-Look for and express regularity in repeated reasoning

Essential Terms Developed in This Unit

Useful Terms Referenced in This Unit

Terms Developed in Previous Unit

Box-and-whisker plot, box plot
Convenience sample
Distribution
Five number summary
Histogram
Population
Random sample
Scatter plot
Stem-and-leaf plot, stem plot
Systematic sample
Voluntary-response sample

Compare

Measures of center

Predict

Prediction

Quartile

Categorical data

Distribution

Line plot

Equally likely

Frequency bar graph

Mean

Median

Mode

Numerical data

Probability

Random

Range

Stem and leaf plot

Variation

Samples and Populations

===Data and statistics

=

Samples and Populations extends the work done throughout sixth and seventh grade with probability and statistics to help students make connections between the two. Students investigate tools for grouping data and comparing distributions, such as line plots, histograms, and box and whisker plots. Students then explore how to collect data (sampling) in a fair method that truly represents the population they are trying to investigate. Finally, students look at relationships between two attributes to see if a pattern can be generated to explain or predict values.

For an in-depth explanation of unit goals, specific questions to ask your student and examples of core concepts from the unit, go to Samples and Populations.

Goals of the Unit The unit Samples and Populations was created to help students: • Use the process of statistical investigation to explore problems • Use information from samples to draw conclusions about populations • Explore the influence of sample size on the variability of the distribution of sample means or medians • Evaluate sampling plans • Use probability to select random samples from populations • Compare sample distributions using measures of center (mean, median), measures of variability (range, minimum and maximum data values, percentiles), and data displays that group data (histograms, box-and-whisker plots) • Explore relationships between paired values of numerical variables

Unit Title: Samples and populations– Investigation 4 & Commom Core Investigation 3.5 & 3.6Suggested Time: 8 Days (75- 90 minute Blocks)Enduring understanding (Big Idea):applying the process of statistical investigation to pose questions, identify ways data are collected, determine strategies for analyzing data and interpreting the analysis In order to answer the question posed; explaining variability in categorical and numerical data; developing a linear equation to characterize a display of data on a scatter plotEssential Questions:What is a scatter plot? What is the sample? What kinds of comparisons and relationships can I explore using data from the sample? Can I use my results to make predictions or generalizations about the population? What changes about a figure that is dilated? How does the scale factor affect a figure that is dilated? Does the location of the center of dilation affect the size of the dilated figure?Unit PlansCommon Core Standards AlignmentConnection to 2003 StandardsProblems 4.1, 4.2, 4.3

Math Reflections

Investigate patterns of association in bivariate data.8.SP.1 -Construct and interpret scatter plots for bivariate measurementdata to investigate patterns of association between two quantities.Describe patterns such as clustering, outliers, positive or negativeassociation, linear association, and nonlinear association.8.SP.2 -Know that straight lines are widely used to model relationshipsbetween two quantitative variables. For scatter plots that suggest alinear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.CC Investigation 3: Transformation (Green Book)Problems 3.5, 3.6

Understand congruence and similarity using physical models, transparencies, or geometry software.8.GG.2-Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.8.GG.3-Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.Prior Knowledge:Collecting and organizing data into different context; for numerical data: finding the range of distribution; using range and shape of distribution of data to make inferences and predictions: for categorical data: analyzing frequencies as counts or percents; collecting and organizing numerical data; understanding units of measure and counts; representing data with line plots, value or frequency bar graphs, stem-and-leaf plots, and coordinate graphs; finding measures of center, examining the behavior of mean and median and shapes of distribution; percents; using counts to report frequencies, tying together work with statistics and probability; comparing data sets using ratios, proportions, rates, or percents; exploring relationships between tables, graphs and equations and investigating linearity.Mathematical Practices Standards for Common Core1-Make sense of problems and persevere in solving them 2-Reason abstractly and quantitatively 3-Construct viable arguments and critique the reasoning of others 4-Model with mathematics 5-Use appropriate tools strategically 6-Attend to precision 7-Look for and make use of structure 8-Look for and express regularity in repeated reasoningEssential Terms Developed in This UnitUseful Terms Referenced in This UnitTerms Developed in Previous UnitConvenience sample

Distribution

Five number summary

Histogram

Population

Random sample

Scatter plot

Stem-and-leaf plot, stem plot

Systematic sample

Voluntary-response sample

Measures of center

Predict

Prediction

Quartile

Distribution

Line plot

Equally likely

Frequency bar graph

Mean

Median

Mode

Numerical data

Probability

Random

Range

Stem and leaf plot

Variation

## Samples and Populations

===Data and statistics## =

Samples and Populationsextends the work done throughout sixth and seventh grade with probability and statistics to help students make connections between the two. Students investigate tools for grouping data and comparing distributions, such as line plots, histograms, and box and whisker plots. Students then explore how to collect data (sampling) in a fair method that truly represents the population they are trying to investigate. Finally, students look at relationships between two attributes to see if a pattern can be generated to explain or predict values.## For an in-depth explanation of unit goals, specific questions to ask your student and examples of core concepts from the unit, go to Samples and Populations.

Online resources for Samples and Populations*Other online resourcesResourcesLab-Sheet

Additional Practice/Skills Worksheets

CMP2 Website –online & technology resources

Formal Assessment

Assessment Options

Parent Guide-Unit Letters

Spanish Assessment Resources

PHSchool.com

TeacherExpress CD-ROM

LessonLab Online Courses

Unit Technology Tips

Goals of the UnitThe unitSamples and Populationswas created tohelp students:• Use the process of statistical investigation toexplore problems• Use information from samples to drawconclusions about populations• Explore the influence of sample size on thevariability of the distribution of sample meansor medians• Evaluate sampling plans• Use probability to select random samples frompopulations• Compare sample distributions using measuresof center (mean, median), measures ofvariability (range, minimum and maximum datavalues, percentiles), and data displays that groupdata (histograms, box-and-whisker plots)• Explore relationships between paired values ofnumerical variables## Samples and Populations