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Lesson 1.1Expressions and Variables
September 15, 2008
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Goal: Students will be able to evaluate and write variable expressions
Agenda: 1.Check hmwk with partner2.Review 1.13.Begin lesson 1.2
Review: How are numerical and variable expressions similar?
Numerical Variable
Vocabulary• numerical expression
• variable
• variable expression
• evaluate
• verbal model
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Expressions and Variables1.1 L
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Page 8 Number 51 (independent work)
Zach belongs to an online DVD rental
service. His yearly rental budget is
$200 (wow!). Each rental costs $4.00.
1. Copy and complete the table.
DVDs
1
2
3
4
Cost ($)
4
8
?
?
Amount left
196
192
?
?2. Write a variable expression for the cost of r rentals.
3. Write variable expression for the amount of his budget left after r rentals.
DVDs
1
2
3
4
Cost ($)
4
8
12
16
Amount left
196
192
188
184
Writing: How many DVDs will Zach be able to rent before the $200 is spent? Explain how you found your answer.
Sample Answer: Zach could rent 50 DVDs. There is a pattern with the number of DVDs rented and the cost—each number of DVDs rented is multiplied by 4. Therefore, 50 * 4 = 200, which allows Zach to spend the entire $200 without going over his budget.
Remember to show all work when completing problems
Lesson 1.2Powers and Exponents
September 15, 2008
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Goal:
Students will be able to use powers to describe repeated multiplication.
CB Standards We are Working Towards:
2.1 understand and apply concepts related to #s, # systems, and # relationships; 2.2 Understand and apply concepts related to computation; 2.8 Use algebraic methods to describe patterns
Assessment: Teacher Observation; Checkpoints
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Math Message
Heather sends an email to Morgan, Brianna, Nathan, and Brennan. Each then sends the email to 4 more friends. Each of those friends sends it to 4 friends. How many people have received that email?
What are a few ways you might go about solving this problem.
Table Talk
Vocabulary: Match the vocab wd to the
best definition
1. power
2. base
3. exponent
53
1. It is the result of a repeated multiplication of the same factor
2. Top number of the power
3. Bottom number of the power
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How to read powers
Power In Words Value
51
55 to the first power
(0.5)2
0.5 to the second power; 0.5 squared
(0.5)(0.5) = 0.25
53
54
5 to the third power; 5 cubed
5 to the fourth power
5*5*5= 125
5*5*5*5= 625
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Example 1: Write the product using an exponent
a. 2*2*2*2 = 24
b. (0.2)(0.2)(0.2)=______
c. n * n * n * n * n = ______
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Checkpoint-use dry erase board to solve
Directions: Write the produce using an exponent.
1. (4.3)(4.3) =_____
2. x * x * x * x =_____
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Example 2: Evaluating Powers with Variables
Evaluate the expression x when x = 0.54
CheckpointEvaluate the expression when x = 3
m
m
2
4
=
=
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Example 3: Using Powers in FormulasWhat formulas require the use of powers?
Area in square units; Volume in cubic units
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Example 3: Using Powers in Formulas
Brandon is going to use cube-shaped block of ice to make an ice sculpture for a competition. Find the volume of the ice.
20 in.
20 in.20 in.
V = s 3
Step 1: Write the formula
= (20) Step 2: substitute 20 for s
= (20)(20)(20) Step 3: evaluate the power
3
Answer: The volume of the block of ice is 8,000 cubic inches.
= 8,000 Step 4: multiply
Checkpoint
Find the area of a square with the given side length
• 9 meters
9 meters
A = 81 meters squared
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Math Message
Heather sends an email to Morgan, Brianna, Nathan, and Brennan. Each then sends the email to 4 more friends. Each of those friends sends it to 4 friends, and so on.
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How did you use powers in this problem to describe repeated multiplication?
Heather sends an email to Morgan, Brianna, Nathan, and Brennan. Each then sends the email to 4 more friends. Each of those friends sends it to 4 friends, and so on.
How would this chart look if we continued the pattern?
Stage Emails Sent as Power Value of Power1 4 4
2 4 16
3 ____ ___
4 ____ ___
1
2
94 262,144 emails9
Page 12 # 2
Page 12 #s 6, 8, 11
• I will be the reporter
• Need a volunteer to be the recorder at the front board
Math Matters Partner Work
• Page 12 #s 14-28 evens • Label notebook with page # • Read all directions• Show all work• Be neat• When finished you may play 24• We will check as whole group in
approximately 12 minutes
Closing
• Written Response
• Page 13 # 34
• Use complete sentences
• Will review as whole class
Homework
• Page 8 #39 (check in back of book)
• Page 9 #s 57-60 all and #67
• Label each piece of hmwk with page number
• Show all work in notebook
• Be neat
Lesson 1.2Powers and Exponents
September 16, 2008
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Goal:
Students will be able to use powers to describe repeated multiplication.Check hmwk with partner (star/circle items you’d like to review)• Page 8 #39 (check in back of book)• Page 9 #s 57-60 all and #67
CB Standards We are Working Towards:
2.1 understand and apply concepts related to #s, # systems, and # relationships; 2.2 Understand and apply concepts related to computation; 2.8 Use algebraic methods to describe patterns
Assessment: Teacher Observation; Checkpoints
Whole ClassRevisit Lesson 1.2
• Page 12 # 4 and # 12
• I need a recorder, please.
Powers and Exponents
p. 13 #36
• Properly label your notebook
• Be neat
• Show all work
• You may work with a partner
• Play 24 when finished; we will review as whole group in approximately 5 minutes
1.2 Practice A• #s 3, 6, 12, 16, 18, 25, 26• With a partner, create a problem similar to #31
– Be neat and creative– Solve showing all of your work
Powers and Exponents
Play 24 when finished
Will share problems in approximately 18 minutes
• Visit http://fvollman.wikispaces.com
• Helpful websites
• Portaportal for Math
• Textbook
• Section 1.2 online worksheet
• http://snipurl.com/3qlw2
Homework•Practice Wksh 1.2
•3-29 odds only
•Label notebook with Practice wksh 1.2
•Show all work in notebook
•Be neat
•Quiz on lessons 1.1-1.3 on Friday, September 19
Powers and Exponents
Label notebook for hmwk each night; example for tonight your notebook should look like:
Practice Wksh 1.2 #s 3-29 odds 9/16/08
3.
Lesson 1.3September 17, 2008
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Goal: Students will be able to use order of operations to evaluate numerical and variable expressions.
Check hmwk with partner(star items you’d like to review)• Practice Wksh 1.2• #5-29 odds
CB Standards We are Working Towards:
2.1 understand and apply concepts related to #s, # systems, and # relationships; 2.2 Understand and apply concepts related to computation; 2.8 Use algebraic methods to describe patterns
Assessment: Teacher Observation; Checkpoints
How does the order of
operations pertain to this
plant??!!
The Boojum Plant
It is a strange plant that is found in Baja, California. It was founded by Godfrey Sykes in 1922. He named it after a mythical creature in the poem “The Hunting of the Snark”. This creature was found in desolate, far away places. The name suits it quite well!
http://farm3.static.flickr.com/2318/2145881083_d46bb61fd8.jpg?v=0
http://www.bajainsider.com/baja-life/plants-animals-baja/insider_boojum.htm
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Order of operations:
1. Evaluate expressions inside grouping symbols
2. Evaluate powers
3. Multiply and divide from left to right
4. Add and subtract from left to right
PEMDAS
Please Excuse My Dear Aunt Sally
set of rules for evaluating expressions
involving more than one operation
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Table Talk: Why might order of operations be important when finding the total number of flowers in the flag?
•About 2,000 plants in each of the 50 stars of this flower flag.
•There about 64,100 plants in each of the 7 short stripes
•106,700 plants in each of the 6 long stripes
•The blue region contains about 198,900 plants
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There are about 2,000 plants in each of the 50 stars of this flower flag. There about 64,100 plants in each of the 7 short stripes and 106,700 plants in each of the 6 long stripes. The blue region contains about 198,900 plants. Write a numerical expression to find the total number of plants.
50 * 2000 + 7 * 64,100 + 6 * 106,700 + 198,900
100,000 + 448,700 + 640,200 + 198,900
Approximately 1,387,800 were used in this flower flag
Order of Operations1.3 L
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Order of operations:
1. Evaluate expressions inside grouping symbols
2. Evaluate powers
3. Multiply and divide from left to right
4. Add and subtract from left to right
PEMDAS
Please Excuse My Dear Aunt Sally
set of rules for evaluating expressions
involving more than one operation
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Using Grouping Symbols
Directions: Evaluate the expression
a) 8(17 – 2.3) =
= 8 (14.7)
= 117.6
Show all of your work
14.7
* 8
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Using Grouping Symbols
Directions: Evaluate the expression
14 + 612-7
= (14 + 16) (12-5) Rewrite the fraction as division
20 5 =
4
Evaluate within parentheses
Divide
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What other type of grouping symbol might you see this year?
Directions: Evaluate the expression
= 5 * [ 36 – ( 22)]
14
36
-22
c) 5 * [ 36 – ( 13 + 9 )] =
= 5 * 1414
• 5
70
70
Work from inner symbol
to the outer symbol
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Checkpoint
1. 10 ( 1.5 + 0.6)
2. 72 [(11 – 7) * 2]
21
9
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Page 18 1. Give three examples of grouping symbols.
•Numbers 4, 6, 7, 8
•We will use the board and the overhead.
•All eyes on board; you will be told when to write
Students will be able to use order of operations to evaluate expressions.
Page 19 Number 28
The Boojum Plant
http://farm3.static.flickr.com/2318/2145881083_d46bb61fd8.jpg?v=0
A boojum is a very slow-growing cactus. One fifty-year-old boojum is 1.5 meters tall, and has been growing about 0.03 meter each year. Assume the same pattern keeps going.
There are 3.28084 feet in a meter.
2. How tall will the boojum be 50 years from now?
1. Write an expression for the height in meters of the boojum y years from now.
Variable Expression:1.5 + 0.03y
1.5 + 0.03y1.5 + 0.03(50)1.5 + 1.5 =3The boojum would grow 3 meters.
Remember your goal: You will be able to use the order of operations to evaluate numerical and variable expressions.
With your Math Matters Partner you will visit
http://fvollman.wikispaces.com
“helpful websites”
Login as a guest—fvollman
Think through activities under Math-Order of Operations
Order of Operations1.3 L
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Students will be able to use order of operations to evaluate expressions.
The table shows the numbers of sets of twins, triplets, quadruplets, and
quintuplets registered at a twin convention. Write and evaluate an
expression for the total number of people who registered at the convention.
Type Sets
Twins 2697
Triplets 29
Quadruplets 2
Quintuplets 1
Wksh 1.3A#s 12-28 evens onlyShow all work neatly in notebook
Label notebook for hmwk each night; example for tonight your notebook should look like:
1.3 Practice A #s 12-28 even 9/17/08
12.
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