Course 3 Online!
Henrico County Public Schools, Virginia
8.13 - Graphical Methods
Number and Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
Probability and Statistics
Focus: Statistical Analysis of Graphs and Problem Situations


The student will
a)   make comparisons, predictions, and inferences, using information displayed in graphs; and
b)   construct and analyze scatterplots. 
Essential Knowledge and Skills 
  • Collect, organize, and interpret a data set of no more than 20 items using scatterplots. Predict from the trend an estimate of the line of best fit with a drawing.
  • Interpret a set of data points in a scatterplot as having a positive relationship, a negative relationship, or no relationship.
Essential Understandings
  • Why do we estimate a line of best fit for a scatterplot? A line of best fit helps in making interpretations and predictions about the situation modeled in the data set.
  • What are the inferences that can be drawn from sets of data points having a positive relationship, a negative relationship, and no relationship? Sets of data points with positive relationships demonstrate that the values of the two variables are increasing. A negative relationship indicates that as the value of the independent variable increases, the value of the dependent variable decreases. 
Vertical Articulation
  1. SOL 6.14abc - a) construct circle graphs; b) draw conclusions/make predictions, using circle graphs; c) compare/contrast graphs
  2. SOL 7.11ab - a) construct/analyze histograms; b) compare/contrast histograms
  3. SOL A.10 - compare/contrast multiple univariate data sets with box-and-whisker plots
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Graphs  (PDF) - Using graphs to make comparisons, predictions, and inferences (Word)
  2. VDOE Enhanced Scope and Sequence Lesson: Scatterplots (PDF) - Constructing and analyzing scatterplots (Word)
  3. Notes: Vocabulary (flipchart)
  4. Notes: Scatterplots (flipchart)
  5. Activity: Hands vs. Feet Scatter Plots (doc)
  6. Activity: Making Scatter Plots (doc)
  7. VDOE Algebra Readiness Curriculum Companion: Exploring Statistics (pdf)
Real World Lessons
Practice
  1. Worksheet: Drawing Scatter Plots (doc)
  2. Worksheet: Interpreting and Drawing Scatter Plots (doc)
  3. Worksheet: Scatter Plots (doc)
  4. Worksheet: Histograms (doc)
  5. Worksheet: Line Graphs (doc)
Self-Assessments
  1. SOL 8.13a Mini-Quiz: Graphical Displays
  2. SOL 8.13b Mini-Quiz: Scatterplots
Skills
  1. Mathematics Assessment Project:
    • A07:Birds' Eggs - Apprentice - In this task, you use a scatter graph to look for patterns in the size of birds' eggs.
    • A09:Sugar Prices - Apprentice - In this task, you must use a graph showing the prices and weights of bags of sugar to find the bag offering the best value for money.
    • A23:Scatter Diagram - Apprentice - In this task, you will use a scatter diagram to compare the results of two school tests. 
    • A24:Shelves - Apprentice - In this task, you must figure out how many planks and bricks are needed to build a bookcase.
    • A26:Temperatures - Apprentice - In this task, you will use graphs and box diagrams to compare temperatures in California and Washington.
  2. Scatterplots: Heart Rate (doc)
Videos
  1. Virtual Nerd: Positive Correlation
  2. Virtual Nerd: Negative Correlation
  3. Virtual Nerd: No Correlation
  4. Virtual Nerd: Using a Scatter Plot to Determine the Line of Best Fit
  5. Virtual Nerd: Definition of a Scatter Plot
Explore Learning
  1. 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.
  2. 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.
  3. 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.
  4. 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. 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.
  6. Line Plots: Build a data set using a line plot. Find its mean, median, mode, and range. Change the data values by dragging the points, and watch how the mean, median, mode, and range change (or, in some cases, do not change).
  7. 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.
  8. 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.
  9. Scatter Plots - Activity A: 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.
  10. Stem-and-Leaf Plots: Build a data set and compare the line plot of the data set to the stem‑and‑leaf plot.
Websites
  1. Shodor: Scatter Plots
  2. Regents Prep: Scatter Plots
VDOE Interventions
  1. VDOE Algebra Readiness Curriculum Companion: Exploring Statistics - The lessons focus on methods of data collection and use of technology to represent data with various types of graphs. Students learn that different graphs represent different types of data effectively and to use measures of center and dispersion to analyze and interpret data. (pdf)
Common Core Standards
8.SP.1
8.SP.2
8.SP.3
N-Q.1
N-Q.2
N-Q.3
S-ID.1
S-ID.6a
S-ID.6b
S-ID.6c
S-ID.9