HCPSS Curriculum Framework
Common Core Mathematics 8
Unit 4: Patterns of Association
Overview (Big Ideas):
Until Grade 8, almost all of students’ statistical topics and investigations have dealt with
univariate data, e.g., collections of counts or measurements of one characteristic. Eighth graders
apply their experience with the coordinate plane and linear functions in the study of association
between two variables related to a question of interest. As in the univariate case, analysis of
bivariate measurement data graphed on a scatter plot proceeds by describing shape, center, and
spread. But now “shape” refers to a cloud of points on a plane, “center” refers to a line drawn
through the cloud that captures the essence of its shape, and “spread” refers to how far the data
points stray from this central line. Students extend their understanding of “cluster” and “outlier”
from univariate data to bivariate data. They summarize bivariate categorical data using two-way
tables of counts and/or proportions, and examine these for patterns of association.
Source:
http://commoncoretools.me/2011/12/26/progression-for-statistics-and-probability-grades-6-8/
Enduring Understandings:
1.
Formulating questions, designing studies, and collecting data about a characteristic
shared by two populations or different characteristics within one population.
2.
Selecting, creating, and using appropriate graphical representations of data, including
histograms, box plots, and scatter plots.
3.
Finding, using, and interpreting measure of center and spread, including mean and interquartile range.
4.
Discussing and understanding the correspondence between data sets and their graphical
representations, especially histograms, and scatter plots.
5.
Using observations about differences between two or more samples to make conjectures
about the populations from which samples were taken.
6.
Making conjectures about possible relationships between two characteristics of a sample
on the basis of scatter plots of the data and approximate lines of fit.
7.
Using conjectures to formulate new questions and plan new studies to answer them.
8.
Understanding and using appropriate terminology to describe complementary and
mutually exclusive events.
9.
Using proportionality and a basic understanding of probability to make and test
conjectures about the results of experiments and simulations.
10.
Computing probabilities for simple compound events, using such methods as organized
lists, tree diagrams, and area models.
Source:
Bright, G. W., Frierson, D., Tarr, J. E., & Thomas, C. (2003) Navigating through Probability in
Grades 6-8. Reson, VA: The National Council of Teacher of Mathematics, Inc.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
Essential Questions:
o Visually, how do a non-linear association and a linear association differ on a scatter plot?
o What can data clustering reveal on a scatter plot?
o When estimating line of best fit, how should the line be positioned?
o What does the line of best fit represent?
o How can the line of best fit be used to make predictions about a set of data?
o What kind of data is displayed in a two-way table?
o What types of information can be gathered from a two-way table?
Curriculum Standards:
8.SP.A Investigate patterns of association in bivariate data.
1. 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.
2. Know that straight lines are widely used to model relationships between two
quantitative variables. For scatter plots that suggest a linear association, informally fit
a straight line, and informally assess the model fit by judging the closeness of the data
points to the line.
3. Use the equation of a linear model to solve problems in the context of bivariate
measurement data, interpreting the slope and intercept. For example, in a linear model
for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional
hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
4. Understand that patterns of association can also be seen in bivariate categorical data
by displaying frequencies and relative frequencies in a two-way table. Construct and
interpret a two-way 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 two variables. For example, collect data from
students in your class on whether or not they have a curfew on school nights and whether
or not they have assigned chores at home. Is there evidence that those who have a curfew
also tend to have chores?
Common Misconceptions:
o When plotting data on a scatter plot, students may confuse the independent (y) and the
dependent (x) variable and on what axis each should be placed.
o The language used in questions to help students interpret two-way tables can be very
confusing. Be sure to help students break down questions and understand how to
determine what information each question is asking for.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.