LESSON PLAN (Linda Bolin) - Granite School District

LESSON PLAN (Linda Bolin)
Lesson Title: Representing Patterns and Evaluating Expressions
Course: Pre-Algebra Date: November Lesson 1
Utah State Core Content and Process Standards:
3.1c Create and extend simple numeric and visual patterns
a) 3.1b Describe patterns using mathematical rules and algebraic expressions
3.2a Evaluate algebraic expressions, including those with whole number exponents, when
given values for the variables
Lesson Objective(s): Students will create and extend patterns, write algebraic expressions
to model rules or patterns, and evaluate algebraic expressions for a given value.
Enduring Understanding (Big
Ideas):
Patterns and sequences
Algebraic representation
Skill Focus:
Create and extend patterns.
Write and evaluate algebraic
expressions to model patterns.
Essential Questions:
• What real-world patterns can be modeled by a sequence
of terms? How can I use a rule to find more terms in a
sequence?
• How can an algebraic expression be used to model the
rule for a pattern?
• When do we use substitution in the real-world?
• Given a value for the variable, what is the value for the
algebraic expression?
• How does changing the value of the variable affect the
value of an expression?
Vocabulary Focus:
Fibonacci numbers, triangular numbers, variable, algebraic
expression, substitution, evaluate
Materials:
• “Writing the Rule” cards for students, TI-73’s
• Color Tiles
• Pattern Blocks Smart Pals
• Stand Up Card packet for each team
• One deck of cards
• Worksheets: Patterns In Our World, Building A Square Patio Patterns, Polygon Trains
• Journal page: Defining Algebraic Expression
• Game worksheets (Optional Practice) : Evaluating Expressions Tic Tac Toe, Evaluating
Expressions War
Assessment (Traditional/Authentic): observation, questions, task performance
Ways to Gain/Maintain Attention (Primacy): manipulatives, game, patterns, technology,
cooperative activities, connections to real world
Written Assignment:
• Patterns In Our World
• Writing the rule game (Can be written on the back of the Patterns worksheet)
• Building A Square Patio Patterns
• Pattern Block: Polygon Train
• Team Challenge
• McDougal Littell p.695/3-8; p696/29, 30a or other appropriate practice.
List the vocabulary on the board
Starter: simplify each
Content Chunks
1. -2[3 • (5² – 15)] 2. -0.25 ÷ 0.5 + 1.5 3. ¾ + (- ½ )

Lesson Segment 1: What real-world patterns can be modeled by a sequence
of terms? How can an algebraic rule be used to find more terms for the
sequence?
Patterns are all around us. Finding patterns and sequences helps pharmacists
develop medicines, builders build structures, farmers plant crops, and even helps you
know when to go to classes. (every 90 min a bell rings).
Do Team List where a Round Robin is used to have team members suggest
anywhere they might see a pattern in the world. Scribe writes list. Team with longest
after 2 minutes wins. Have that team scribe read their list. Scribes from other teams
each read one idea that hasn’t been mentioned yet.
Introduce the Patterns In Our World Worksheet. Do Four Corners where a student
from each team goes to a corner to meet with other team’s students to complete the
pattern or sequence shown in one of the problems on worksheet (attached) and to
write a rule for the pattern they found to help them. Each person then returns to their
team and teaches the team about their one problem, so all four problems get
discussed. Students are all accountable to write the next two terms and the
description of the pattern on their own worksheet.
TI-73 activity: All patterns can be modeled using verbal or written rules, and by using
math symbols. That is why mathematics is such a powerful language.
Q. Think-Team-Share For example, in this pattern: 1, 2, 3, 4, 5, 6…, what operation is
happening to one number to get the next term in the sequence?
We can write the rule for finding the next term using math symbols. So if n was a
number in the pattern, n + 1 would be the rule to help us find the next number.
Q. What would the next number be if the number you were looking at were 52? 65?
Demonstrate using the graphing calculator to find terms of a sequence and write the
rule (algebraic expression) for finding the next term. Then play “Writing The Rule”.
Instructions are attached.
Lesson segment 2: How can algebraic expressions be used to model a rules or
patterns? Given a value for a variable, what is the value for the expression?
Have students look at these two columns and identify characteristics that would qualify
an expression for being in one column or the other. The expressions on the left are
algebraic since they include at least one variable. The expressions on the right are
numeric since they only include numbers and operations having no variable.
y + 1 3 + 5.8
r*t 12 • (-4)
lwh 2 • 3 • 6
2(3x -2) 2(6 – 2)
Algebraic or variable expressions can help us describe patterns and extend them to find
other possible values.
Journal: Work with students to complete the Frayer Model for defining Algebraic
Expression (attached)

Manipulative Patterns
Color Tiles: Have student pairs work with Color Tiles to complete the first five rows in
the “Building A Square Patio Patterns” table. The activity is a review of the
manipulative activity found in the exponential lesson with additional patterns included.
Discuss the patterns they find. Ask them to look for a rule that would involve
operations on the length of the side of a square to find the information for the table.
Use the “X” row to write algebraic expressions modeling the rule for the patterns.
(# added on = 2x-1. Perimeter = 4x, Area = x², Radical expression = √x² = x)
Pattern Blocks, Smart Pals: Use the attached Pattern Blocks: Polygon Trains
worksheet for discussion, Having the students work with a partner. Students should
take turns building the trains and sketching and labeling on the Smart Pal. Guide them
in recording the data in the tables on the worksheet and discuss the pattern for each
train. Again, ask them to look for a rule to help them find the number of windows by
operating on the number of cars in the train. Let x represent the number of cars in the
train.
Writing Expressions from Tables Using The TI-73
To find patterns leading to the writing of single variable expressions, type an
equation in the &. Select -'and set the dependent and independent variables
to Aask@. Select -*and push bto type a value in the X column. Tell students
you have performed an operation on that value to get a result. Place the curser in the
Y column and push b. Discuss what operation(s) might have been performed to
get that result. Type another value in the X column and push b in the
corresponding position in the Y column. Ask students if the same operation they
discussed was used on this new value for x to get the resulting value in the Y column.
If not, tell them you want them to find an operation(s) that could be used for both x
values to get the result in the table. Have them describe a “rule”. Then, type a third
value in the X column. Ask them if their rule works for that value. Then enter the
corresponding value in the Y column and see if they got the same result.
Enter two or three more values in the x column. Have them write an expression
that would produce the given value for each x value. For example if the “rule” were to
add 5 to X to get a result the expression would be 5 + X . Some possible functions you
may wish to try might be:
y = x + 1, y = 2x, y = x – 4, y = 2 x, y = 2x + 1, y = x/2
Lesson segment 3: When do we use substitution in life? Given a value for a
variable, what is the value for the expression? How does changing the value
for the variable affect the value of the expression?
Have you ever been in a class where you were surprised when you came in to find a
substitute teacher was there?
Think-Team-Share Q: What do we mean when we say the word “substitute”?
Think-Team-Share Q: Where do we see substituting things going on in the real
world? (Splenda for sugar, Pinch-hit at a ball game)

Have you ever been in a class where the teacher was gone more than one day, and
you had a different substitute each day?
Think-Team-Share Q: How did changing a substitute change the class?
In mathematics we can substitute too. In an algebraic expression, we can
substitute values for the variable.
Have you ever gone to the store and tried to decide how many of something you
could buy? For example, if a candy bar is 25 cents, you know you will have to pay
$0. 25 x the number of candy bars (write 0.25c on the board).
Let’s do some mental math. How much would you have to pay if you bought 2 candy
bars? 3 candy bars? 6 candy bars? You have been doing mental substitution. First,
you replaced the c with a 2 to get $0.50. (Write $0.25(2) = $0.50 on the board) Then
you substituted a 3 for the c and got $0.75. (Write $0.25(3) = $0.75). Finally, you
substituted a 6 for the c and got $1.50. (Write $0.25(6) = $1.50 on the board).
Have students write the expression $0.25c on their paper and choose any
number of candy bars and evaluate their expression. Then select several students to
tell what value they chose for c and tell the class the cost of the candy bars.
Think-Team-Share Q: How did changing the value of c change the amount you had to
pay?
Team Challenge Game: (materials: Stand-Up cards, one card deck, TI-73’s)
Give each team a pack of Stand-Up Cards (Large cards numbered from 1-20,
operation signs cards, right and left parenthesis cards, a couple of variable cards, and a
negative sign card. Have each team use the cards to create an algebraic expression
(not an equation). The challenger team stands holding their cards to show the
expression they have created. The class and teacher write the expression. The
challenger team then asks a classmate to come to the front of the class and pick a
card(s) from a playing card deck the teacher is holding. The picker selects a card for
each variable in the challenger team’s expression. Red cards in the deck represent
negative numbers. Black cards represent positive numbers.
All the students then work to evaluate the expression using the drawn card(s) as
value(s). The challengers then pick one student to show explain how they evaluated
the expression. If that student is correct, his/her team gets a point. If not, the
challengers must show how to evaluate the expression correctly to earn the point.
Remind students to use the correct order of operations. Model this procedure
once with the class.
Assign: Practice Writing and Evaluating Expressions Using The Ti-73. For additional
practice assign Writing Expressions Tic Tac Toe, and Writing Expressions War (all
attached). McDougal Littell 2005 p. 7, # 1-31 odd. or any appropriate text practice for
evaluating expressions
Rules for the practice problems on the Writing and Evaluating Expressions Practice
page are
1. 2x + 1
2. x – 2.5
3. x + 4
4. – 1 x

Name__________________
Patterns can be found all around you. Sketch the next two pictures for the patterns
shown below, and then describe the pattern that helped you know what to sketch.
1. A pattern that often occurs in building is called a triangular pattern. Here’s what
this pattern looks like:
9 9 9 9 9
999 999 999 999
99999 99999 99999
9999999 9999999
999999999
2. Some Native American designs include square patterns that look like this
• • • •
• • • •
• • • •
• • • •
3. The number of petals on a pinecone or sections around a pineapple increase in a
sequence known as a Fibonacci Sequence named for the mathematician who
discovered it. If the sections were unwound and laid in rows, they would look like this:
− −− −−− −−−−− −−−−−−−−
4. A game where a ball moves through a maze to an end point can have several paths
the ball could follow to get there. The number of paths can often be modeled by
another famous sequence known as Pascal’s Sequence named for the mathematician
who discovered it.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
5. On the back of this paper, sketch a pattern of your own. Explain how you know
what each step of the pattern will be.

Writing The Rule
Hand several students a card. See examples below. Each card has a beginning
number and a rule written on the card. The person getting the card starts with the
beginning number and applies the rule to generate three more numbers in the
sequence. That person then tells the class the beginning number and the next three
numbers in the sequence. Class members are given time to guess a rule by writing
that rule on their calculator and on their paper. The person with the card then reads
the next number in the sequence and gives the class time to change or refine the rule
they had originally written. This process continues until someone in the class is ready
to guess the rule. The guesser using the teacher=s overhead screen types the rule and
shows the sequence. Then next person with a card then challenges the class in the
same manner.
Calculator steps: Press original number, then press X I b. Next, type the
rule algebraically (ex. x + 3 ). Then press X I b. Continue pushing b to
generate more terms of the sequence.
Begin with: 1.5
Begin with: 10
Begin with: ½
Rule: add 2 to each
term
Rule: add - 2 to
each term
Rule: Multiply each
term by 3
Begin with: 24
Begin with: 2
Begin with: 3
Rule: Multiply each
term by ¼
Rule: square each
term
Rule: Multiply each
number by 3
Begin with: 1.12
Begin with: 4
Begin with: 6.45
Rule: Add 0.03 to
each term
Rule: subtract 0.25
from each term
Rule: subtract 0.15
from each term

Defining ______________
Name ____________________________
Date________
1. Sketch, drawing or connection 2. Facts about the
(this reminds me of…)
word
Algebraic
3a. Two examples
Expression
4. Definition in your
own words
3b. Two non-examples

Building A Square Patio Patterns
Name_________________
Date ________
As you build a model for a patio using square tiles, you notice some
patterns that help you predict. Write expressions to find each. Work with
your team to build each model in the table. Look for a rule that includes
operating on the length of a side of the patio.
Sketch the Length of # of tiles Perimeter Area Radical
patio one side added to expression
last patio
1" 1 4 1² √1² = 1
2" 3 8 2² √2² = 2
3"
4”
5"
X”
1. What would the area be if x = 8? 5½ ?
2. What would the perimeter if x = 50? 10.2?
3. What would the number added on be when x = 32? 3.5?
4. What would x be if the area were 400? 0.25?

Pattern Blocks: Polygon Trains
Name____________________
You are the designer of a unique train ride attraction using
polygon shaped cars. Each exposed side of a polygon will need
to have a window for a passenger. Complete a table. Beside
each table, write an algebraic expression for finding the number
of windows if X represents the number of cars. Then find the
number of windows if there are 20 cars, 50 cars, 100 cars.
1) This train will have triangular cars
Cars in the
train (X)
Total
windows
1 3
2 4
3 5
4
x
2) This train will have square cars
Cars in the
train (X)
Total
windows
1 4
2 6
3
4
x
3) This train will have trapezoidal
cars
4) This train will have rhombus
cars
Cars in the
train (X)
Total
windows
Cars in the
train (X)
Total
windows
5) This train will have hexagonal
cars
6) This train will have octagonal
cars
Cars in the
train (X)
Total
windows
Cars in the
train (X)
Total
windows

Practice Writing and Evaluating
Expressions from Tables
Name _________________
Date ________
For each of the tables below
a) Explain in words what operations you see must be performed on the
x variable to get the result in the Y column.
b) Write an expression to the right of the = sign below the table to
show the operation(s)
c) Use the expression to fill in the missing values in the Y column.
Show your justification.
1. 2.
3. 4.

Name__________________________ Date______
Evaluating Expressions Tic Tac Toe
First: Arrange these numbers in any order in the little boxes in each square. Use only
one number per square please. 0, 1, 3, 4, 5, 8, 10, 20, 48
Next: Evaluate each expression below. Show how you substituted the value given.
Write each expression in the square above where you have placed its value.
3b², when b = 1 3b², when b = - 4 3b², when b = 0
2m 0 + 3, if m = 6 2m + 3, if m = - 1 2m + 3, if m = ½
2(5 – X), if X = 0 2(5 – X), if X = 1 2(5 – X), if X = - 5
Teacher will now draw values from a box. When you get three in a row, say “I have
Tic, Tac, Toe”

Evaluating Expressions War
Name ____________________
Date________
Players: 2
Materials: One deck of cards (Black cards represent positive numbers; red are
negative.), worksheet for each player.
Procedure: Both players draw 1 card for each variable. Substituting the card(s)
drawn, each player evaluates their expression . The player whose
expression has the greatest value wins all cards for that expression. The
player with the most cards wins the game. If a tie occurs, leave the
cards. The winner of the next round gets all these cards, too.
1. -3m² + 4 2. ½ w – 4
3. r + r – p 4. _Y_ + (-2)
2
5. -3 – d 6. b + 3c – a³
4
7. _x + y_ 8. -8k ÷ jk
w – z