Name______________________________________________________ Period _____ Date ___________________________
Lesson: 7-6 Equivalent Expressions – Building Expressions From Patterns
Vocabulary
 Variable
 Constant
 Coefficient
 Vertical Pattern
 Horizontal Pattern
Directions:
Step 1: Open the Agile Mind Lesson “Topic 7-6 Exploring Equivalent Expressions.”
With your group, do the following: Use the paper hexagons to model the table layout.
Read the scenario on Page 1: Erlinda & Chris are continuing their work on the dance
committee. Erlinda just found out the hall where the tables will be located is long and narrow.
There is not enough room to spread the tables out. Chris suggests pushing the tables together in
a row.
a. Build or sketch some of the long banquet tables and count the number of people seated at
banquet tables of different lengths. Record your data in a table. Use a process column to keep
track of your strategy for counting the number of people. Be prepared to share your strategy.
Number of tables n
Process
Number of People seated, P
2
3
4
5
6
b. Write a rule in words that you can use to determine the number of people who can sit around
any number of tables that are pushed together.
Step 2: Go to Page 2
Another student, Pauline, is also on the dance committee. Erlinda, Chris, Pauline, and the caterer
each used a different strategy to figure out how many people could sit at 6 tables.
The following number sentences show how each person approached the problem.
Caterer:
Erlinda:
Chris:
Pauline:
1+(2•12)+1=26
5+(4•4)+5=26
1+(4•6)+1=26
(6•6)−(2•5)=26
Can you explain what each person was thinking? For each strategy, connect your explanation to
the picture of the tables. Be prepared to share your thoughts.
Caterer: __________________________________________________________________
Erlinda: __________________________________________________________________
Chris: ____________________________________________________________________
Pauline: __________________________________________________________________
Step 3: Look back at your rule from Step 1. Does your strategy match any of the strategies
above?
Step 4: Go to Page 3 – Explore the different strategies for determining the number of people
who can be seated with varying numbers of tables.

Use the pull down menu to select a person’s strategy. Use the animation to help you
understand and explain each person’s strategy.

Pay close attention to the values in the process column.
o Do any numbers stay the same?
o Do any change?
Step 5: Go to Page 4: Explore the patterns in the table as you play the animation. Answer the
following questions as you view the panels.
View Panels 1, 2 & 3: There are two types of patterns identified in the animation.
a) What is a vertical pattern?
b) What is a horizontal pattern?
View Panels 4 – 7:
c) What algebraic expression was developed from the table and written as a rule?
P = _____________________
d) Does the rule work for any number of tables?
_______________________________
3) If there were 12 tables, how many people could be seated?
______________________
Step 6: Go to Page 5:
Algebraic expressions are often made up of several terms.
Terms of an expression are separated by addition & subtraction symbols.
The expression for Chris’ strategy has ________________ terms:
What is the coefficient in the term 4n ?
4n and 2.
____________
Go to Page 6: Review what we have done so far. Can you write an algebraic expression for
your own strategy (from Step 1)?
__________________________________________________
Step 7: Go to Page 7
Play the animation and study each strategy.
Think about what stays the same and what changes?
Write algebraic rules for the caterer’s strategy and Pauline’s strategy.
Step 8: Go to Page 8:
Compare the algebraic rules you developed. How are they similar?
How are they different?
In each algebraic rule, the variable n represents a set of numbers.
Each algebraic expression models the same scenario.
a) What type of expressions model the same scenario? _______________________________
Practice Problems:
GA #5
Which algebraic rules accurately model the relationship between the number of tables and the
number of guests if each table has 5 sides?
In each rule, x represents the number of tables and y represents the number of guests.
Select all that apply.
GA # 6
A rectangular pool will be surrounded by square tiles as shown in
this diagram.
The pool designer wrote the following equations to try to
determine the number of tiles, t, around the pool.
Which equations do not correctly represent her problem?
Select all that apply.
MP #7
Courtney made the following pattern.
What rule will tell you how many white
hexagons, w, are needed for any given
number of black hexagons, b?