HCPSS Worthwhile Math Task
What is the Relationship?
Common Core Standard
8.SP.A.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.
MP1:
MP2:
MP3:
MP4:
MP6:
MP7:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Attend to precision.
Look for and make use of structure.
The Task
You and a friend would like to determine the relationship between two topics, such as a person’s
age and their height. You will use the Internet, books, surveys, or other research tools to gather
data about these topics. Once you have gathered data, create a visual representation of this
information and explain any relationship you see between the two topics. Be prepared to discuss
your findings with the class!
Facilitator Notes
1. Students should be given a set of two variables (topics that have numerical values) and
should determine if there is a relationship between the two items. This can be done by
brainstorming a list of topics, giving groups a particular set of variables to research, or by
having students draw slips of paper from two bags with the topics written on them. A set
of potential topics are listed below.
 height and weight
 age and weight
 age and income for adults
 years of education and income
 years of education and years in jail
 height and shoe size
 temperature and elevation
 height and age
 resting heart rate and weight
 population size of a species and temperature of climate
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
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HCPSS Worthwhile Math Task
2. Students can research their topics using the Internet, books, surveys, or class
measurements, depending on the topic. A list of web resources is included.
3. After collecting a set of data points (approximately 10-15), students should create a
presentation about their data. This would most likely be a scatter plot, but could vary
slightly. (Look for evidence of MP4.)
4. As students work on their presentation, monitor graphs to ensure students are using
appropriate scales. (Look for evidence of MP6.)
5. Encourage students to use words such as positive and negative to describe any linear
relationships.
6. Students should share their findings with the class through a gallery walk or group
presentations.
7. Once all groups have shared their work, ask students to organize their findings into
“linear” relationships (positive and negative) and “no relationship” categories. These
could be posted on the board and their visual representations can be posted under the
correct category. (Look for evidence of MP2.)
Follow-Up Questions
1. Why do you think your two topics have this kind of relationship? (Look for evidence of
MP7.)
a. Do you think these topics would always have this kind of relationship?
b. What might cause a change in this relationship?
2. Why did you choose to visually represent your data in this manner?
a. Discuss the different option chosen by students and compare and contrast their
benefits and drawbacks. (Look for evidence of MP3 and MP4.)
3. What does it mean for two variables to have a linear relationship? (Look for evidence of
MP7.)
a. What does a positive relationship mean?
i. What does a positive relationship look like on a graph?
b. What does a negative relationship mean?
i. What does a negative relationship look like on a graph?
4. Why do some sets of topics/variables have no relationship? (Look for evidence of MP7.)
a. How does this appear on a graph?
5. Expand upon student understanding by asking students to make inferences about their
graphs or other displays.
a. How does this relationship relate to a current event or topic in society?
b. What kind of careers might use this information?
c. What generalizations or decisions could be made based upon your graph?
d. Which of your teachers might use this graph in their classroom?
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.
HCPSS Worthwhile Math Task
Solutions
Note: Each solution will be different based on the topics explored.
Strategy #1:
Students will most likely determine relationships between these variables using a scatter plot or
another type of graph. Using these visual representations, students should be able to recognize a
correlation or lack thereof between the two variables.
Students should be able to recognize that data points which create a linear model have a linear
association. They may explain a positive association by stating “As __________ increases,
____________ also increases”. Students may explain a negative association by stating “As
___________increases, ___________decreases.”
If a set of data does not have an association, students should explain that the two variables do not
appear to be related.
Strategy #2:
Students may choose to organize their data in a table. The table should be ordered such that the
data for one variable is in order from least to greatest or greatest to least. Based on this
information, students should be able to explain the relationship between the two variables.
They may explain a positive association by stating “As __________ increases, ____________
also increases”. Students may explain a negative association by stating “As
___________increases, ___________decreases.”
If a set of data does not have an association, students should explain that the two variables do not
appear to be related. This would occur when the data for one variable is increasing but there is
no obvious increase or decrease among the data for the other variable.
Strategy #3:
Students may use a combination of the previous strategies by using a multiple representations
resource sheet to organize their data. These resource sheets include a graph, table, verbal
description, and equation to represent the data. As students complete these pieces of the resource
sheet, they should be able to determine whether there is a relationship between the two variables.
An example of this resource sheet is included at the end of this task.
Students may make observations of the table and/or graph as noted in the first two strategies.
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.
HCPSS Worthwhile Math Task
Students may notice that if they cannot create an equation to model the data, there is not a linear
relationship among the variables. On the other hand, they may note that they are able to create a
linear equation to model the relationship. If students are able to create an equation, they should
notice that a positive slope would imply a positive association and a negative slope would imply
a negative association.
Web Resources for Students:
http://www.disabled-world.com/artman/publish/height-weight-teens.shtml (Average heights and
weight tables from baby to teenager)
http://www.cdc.gov/growthcharts/ (CDC information on age, weight, and height-mostly graphs)
http://www.cdc.gov/nchs/fastats/bodymeas.htm (Body measurements-just data)
http://www.publicagenda.org/charts/income-age-and-gender (Salary data by age and gender-bar
graphs)
http://www.census.gov/compendia/statab/cats/income_expenditures_poverty_wealth.html
(Income levels)
http://www.infoplease.com/ipa/A0883617.html (Income and level of education chart)
https://www.ncjrs.gov/pdffiles1/nij/grants/202978.pdf (Incarceration and education level)
http://www.classzone.com/books/earth_science/terc/content/investigations/es1706/es1706page03
.cfm (Interactive temperature and elevation data)
http://www.indiainvites.com/temperature.html (Temperature and elevation charts for India)
http://www.topendsports.com/testing/heart-rate-resting-chart.htm (Resting heart rate data)
http://icb.oxfordjournals.org/content/44/2/152.full (Effects of temperature on animal species)
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.
HCPSS Worthwhile Math Task
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.
HCPSS Worthwhile Math Task
Multiple Representations Resource sheet
Verbal Description:
Table:
Graph:
Linear Equation:
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.