1. Chairs
You walk into a restaurant with a large group of friends. To accommodate you,
the restaurant will push a bunch of tables together—but how many tables
will be needed to ensure that everyone has a seat? This applet will let you
explore that question.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=144
Reviewed by Jennifer Sollman and Yessica

2. How the applet works…
Students have the opportunity to
explore how many chairs sit around
the table. The variables that students
can choose from are: arrangement of
tables, how many chairs fit around
each table, and whether to explore
with the applet or solve/guess the
problem answer.

3. Instructions on how to use the
applet..
The menus at the top of the applet allow investigation in a variety
of ways. Mode: Allows the user to select Exploration, in which the
number of chairs needed for a particular arrangement is
displayed; or Guess, in which the user is able to construct an
arrangement and then predict the number of chairs.
Table: The applet allows two types of tables, 1 × 1 tables which
accommodate one chair per side, and 2 × 1 tables, which hold
two chairs on the longer sides.
Arrangement: The user can choose a straight line arrangement
(tables are placed side-by-side) or a rectangular arrangement
(tables are placed along the border of a rectangle).
The Increase/Decrease buttons allow the size of the arrangement
to change.

4. Exploration of Applet
Set the menus at the top to Exploration, Six Chairs, and
Rectangle. Using only the Length buttons, adjust the size of the
arrangement. How do the number of chairs change with each
increase in length?
Using only the Width buttons, adjust the size of the arrangement.
How do the number of chairs change with each increase in width?
What pattern exists between the number of tables and the number
of chairs? Describe a rule for the number of chairs based on what
you observed.
How many chairs are needed for a 10 × 5 arrangement?
How many chairs are needed for a 13 × 8 arrangement?
How many chairs are needed for an m × n arrangement?

5. Analysis
Strengths Weaknesses
•Simple and easy to use •Limited table
•Interactive arrangements
•Options to explore •Limited number of
problem questions you can pose
•Not focused on getting to about the tables
an answer. •What about round tables?

6. Evaluation of Applet
• The chairs applet is a free, easy to use applet
that allow students explore chairs around a
table without frills. The exploration, along with
the different ways you can change the chair
setting, gives students the ability to
conceptually explore patterns, and
expressions. It is limited in its use, but is great
for the task that is linked to it.

7. A Problem-Based Task
• Task:
• Set the menus at the top to Exploration, Six Chairs, and Rectangle. Using only
the Length buttons, adjust the size of the arrangement. How do the number of
chairs change with each increase in length? Using only the Width buttons,
adjust the size of the arrangement. How do the number of chairs change with
each increase in width? What pattern exists between the number of tables and
the number of chairs? Describe a rule for the number of chairs based on what
you observed.
• How many chairs are needed for a 10 × 5 arrangement?
• How many chairs are needed for a 13 × 8 arrangement?
• How many chairs are needed for an m × n arrangement?
• Connection to the standards and/or big ideas:
• CCSS.Math.Content.5.OA.B3 Generate two numerical patterns using two given
rules. Identify apparent relationships between corresponding terms. Form
ordered pairs consisting of corresponding terms from the two patterns, and
graph the ordered pairs on a coordinate plane.

8. Questions to Ask to Assess
and Advance Student
•
Thinking can you find while
Launch (Task Set-Up): What patterns
exploring this applet? Could you explain to someone how the
number of chairs change for any amount of tables?
• Explore (During Task Implementation):
• What do you notice to the number of chairs when you add or
subtract a table? What changes when you change the shape of
the table arrangement?
• Summarize (As students share findings, strategies,
reasoning, etc.): Can you show us how you saw the pattern?
Are both peoples expressions equivelent?