Answer:
Opening (2 minutes)
Move students into groups of two or three, and distribute the bags of tiles.
Mathematical Modeling Exercise (15 minutes)
Today, we will model a problem that happens in restaurants every day: moving tables together so that
everyone in a group can sit together. Use the square tiles to represent square tables. One person can sit along
each edge of a table side, no crowding. Our first goal is to find how many people can sit at tables made of
various numbers of square tables pushed together end to end.
How many chairs can fit around one square table? What is the perimeter of the square if the edge length is
one yard? Record the results in your table.
4; 4 yards
If two square tables are pushed together to form a longer rectangular table, how many chairs will fit around
the new table? What is the perimeter of the rectangle? Record the results in your table.
6; 6 yards
Make sure that each student can connect the square model on the desk to the picture on the classwork sheet.
If there are twice as many square tables in the new rectangular table, why can’t twice as many chairs fit
around it?
No chairs will fit right where the tables come together.
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 6•4
Lesson 21: Writing and Evaluating Expressions―Multiplication and Addition
223
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Make a record of the number of chairs that will fit around longer rectangular tables when 3, 4, and 5 square
tables are pushed together to form long rectangular tables.
Mathematical Modeling Exercise
The Italian Villa Restaurant has square tables that the servers can push together to accommodate the customers. Only
one chair fits along the side of the square table. Make a model of each situation to determine how many seats will fit
around various rectangular tables.
Number of Square Tables Number of Seats at the Table
+ or ( + )
Are there any other ways to think about solutions to this problem?
Regardless of the number of tables, there is one chair on each end, and each table has two chairs opposite one another.
It is impractical to make a model of pushing tables together to make a long rectangle. If we did have a rectangle that
long, how many chairs would fit on the long sides of the table?
on each side, for a total of
How many chairs fit on the ends of the long table?
chairs, one on each end
How many chairs fit in all? Record it on your table.
chairs in all
Work with your group to determine how many chairs would fit around a very long rectangular table if square tables
were pushed together.
chairs on each side, totaling , plus one on each end; grand total
If we let represent the number of square tables that make one long rectangular table, what is the expression for the
number of chairs that will fit around it?
+
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 6•4
Lesson 21: Writing and Evaluating Expressions―Multiplication and Addition
224
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G6-M4-TE-1.3.0-09.2015
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Example (13 minutes)
Example
Look at Example 1 with your group. Determine the cost for various numbers of pizzas, and also determine the expression
that describes the cost of having pizzas delivered.
a. Pizza Queen has a special offer on lunch pizzas: $. each. They charge $. to deliver, regardless of how
many pizzas are ordered. Determine the cost for various numbers of pizzas, and also determine the
expression that describes the cost of having pizzas delivered.
Number of Pizzas Delivered Total Cost in Dollars
+
Allow the groups to discover patterns and share them.
What mathematical operations did you need to perform to find the total cost?
Multiplication and addition. We multiplied the number of pizzas by $ and then added the $ delivery fee.
Suppose our principal wanted to buy a pizza for everyone in our class. Determine how much this would cost.
Answers will vary depending on the number of students in your class.
b. If the booster club had $ to spend on pizza, what is the greatest number of pizzas they could order?
Students can use the “guess and check” method for answering this question. A scaffold question might be, “Could they
order 100 pizzas at this price?”
The greatest number of pizzas they could order would be . The pizzas themselves would cost
× $ = $, and then add $. for delivery. The total bill is $.
Step-by-step explanation:
because find the radius by dividing by pi and square-rooting, then multiplying the radius by 2 to get the diameter. Then multiply by pi to get the circumference