Mathematics TEKS Refinement 2006 – 9 -12
Tarleton State University
Foundations for Functions
Activity:
Right or Left?
TEKS:
(A.2) Foundations for functions. The student uses the properties and
attributes of functions.
The student is expected to:
(D) collect and organize data, make and interpret scatterplots
(including recognizing positive, negative, or no correlation for
data approximating linear situations), and model predict, and
make decisions and critical judgments in problem situations.
Overview:
In this lesson, students will perform an activity to test right- and lefthandedness, collect data from the activity, organize it into a table, and use
the table to create a scatterplot. Using the scatterplot, they will draw
conclusions about the percentage of the class that is right- or left-handed,
and interpret different parts of the graph in the context of right- or lefthandedness.
Materials:
Square grid paper for each student
Student Data Table (large poster or transparency)
Student Data Table (one for each student)
Graph paper for each student
Graphing calculator (for Extension)
Grouping:
None
Time:
1 class period
Lesson:
1.
2.
Procedures
Collect the data
For 20 seconds, have each student use
his/her right hand to write the first letter of
his/her name in each square on a piece of
square grid paper. Then have each student
repeat this procedure on another piece of
square grid paper using his or her left hand.
Next have students count and record the
number of letters that each one was able to
write using each hand in the 20 seconds
allotted.
Organize the data
Collect and record the data from each
student on the poster or transparency
Foundations for Functions
Right or Left?
Notes
It is probably best to have all
students use only capital letters.
Make sure that students write
legibly; any illegible letters should
be excluded in the counts.
Before class make a Student Data
Table on a transparency or poster
Algebra I
Page 1
Mathematics TEKS Refinement 2006 – 9 -12
Procedures
Student Data Table.
Hand out individual Student Data Table
sheets to each student so that he/she can
keep his/her own record of the data
collected.
3.
4.
Graph the data
Using the number of legible letters written by
the right hand as x and the number of legible
letters written by the left hand as y. Have
students create a scatterplot, with each point
representing a different student.
Tarleton State University
Notes
board. Determine a procedure for
collecting and recording the data
from each student.
It might be helpful to label the two
columns containing the data on the
classroom table. Ask students
what is the meaning for each point.
This would be a good time to
discuss with the class the
differences in discrete and
continuous data. Ask students
whether or not they should
connect the points they are
plotting. (This is discrete data, so
they should conclude that it is NOT
appropriate to connect the points.)
Analyze the data
Looking at the scatterplot, have students
answer each of the following questions:
a. On their scatterplots, have students draw
the line, y = x. Ask students why the line
could be called the ambidextrous line.
Points on this line represent those who
are equally skilled with their left hand as
right hand. They are ambidextrous.
b. What do the points above the line
represent? Persons who are left-handed
Below the line? Persons who are righthanded.
c. What is the significance of points being
near the line? Points near the line but
above it represent those who are almost
as skilled with their right hand as their
left. Points near the line but below it
represent those who are almost as skilled
with their left hand as their right.
d. What percentage of the class is lefthanded? Answers will vary from class to
Foundations for Functions
Right or Left?
Algebra I
Page 2
Mathematics TEKS Refinement 2006 – 9 -12
Procedures
Tarleton State University
Notes
class.
e. Is anyone ambidextrous, or close to being
ambidextrous? How could you tell from
the scatterplot? Anyone who is on the
line y = x or very close.
5.
Have each student use his/her pencil to
determine a best fit line and answer the
question: “Does this scatterplot appear to
have a linear correlation?” The scatterplots
will vary from class to class.
The scatterplot could appear to have no
linear correlation. Even if the scatterplot
appears linear, would the line have any real
meaning in the context of this situation? Is
there a causal relationship between the two
variables graphed?
Some observations the teacher
might want to help the students
discuss:
• Does the x value have to be
the right-hand data?
Choosing which value to
place on the x axis and which
to place on the y axis is
arbitrary.
• How would placing the lefthand data on the x-axis
change the results? The
points above the line
represent Right-handed
people and the points below
the line represent Left-handed
people.
• Are there dependent and
independent variable in this
situation? No, the right and
left hand numbers are
independent of each other.
Homework: Have students write a short paper explaining and describing the
conclusions drawn from exploring this data.
Extensions: Have students enter the data on a graphing calculator and use the linear
regression feature of the calculator to find an equation. Then answer the
following question: How can using information produced by the CALC
LinReg (ax+b) function lead to incorrect conclusions and/or decisions?
Resources: Adapted from Cynthia Lanius’ activity at
http://www.math.rice.edu/~lanius/Algebra/rightleft.html
A terrific website for graph paper is
http://www.mathematicshelpcentral.com/graph_paper.htm. The graph
paper is free, and you can customize it to the size and features you want.
(One type is included in this activity.)
Foundations for Functions
Right or Left?
Algebra I
Page 3
Mathematics TEKS Refinement 2006 – 9 -12
Tarleton State University
Student Data Table
Name of Student
Foundations for Functions
Right or Left?
Number of Letters
(Right)
(x)
Number of Letters
(Left)
(y)
Algebra I
Page 4
Mathematics TEKS Refinement 2006 – 9 -12
Foundations for Functions
Right or Left?
Tarleton State University
Algebra I
Page 5
Mathematics TEKS Refinement 2006 – 9 -12
Foundations for Functions
Right or Left?
Tarleton State University
Algebra I
Page 20