Algebraic Expressions and Integers

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Algebraic Expressions and Integers

• Chapter 1

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Aim 1-1 How do we write expressions for word
phrases?

• Key terms
• Variable
• Variable expression ex. 3 - c
• Numerical expression ex. 4 - 3

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• Guided Practice
• 1. Bagels cost .50 each. Write a variable
  expression for the cost of b bagels.
• 2. Write a variable expression for the number of
  hours in m minutes.

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Practice Write a variable expression for
each word phrase.

• The product of a number n and 8
• K divided by 20
• Six less than a number h
• The value, in cents, of d dimes
• A telephone call costs c cents per minute. Write
  a variable expression for the cost of a 15 minute
  call.

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Summary Answer in complete sentences.

• What is a variable?
• What is a variable expression?
• How are variable expressions and numerical
  expressions alike? How are they different?

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Aim 1-2 How do we use the order of operations?

• What is the value of 3 5 x 2?
• What is the order of operations?

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• Simplify.
• 4 15 3
• 12 3 1
• 10 1 x 7
• 3 5 8 4 6
• 4 1 2 6 3

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Simplifying with Grouping Symbols

• 10 9 (2 2)
• 2(13 - 4) 3
• 1 (10 2)/ 4

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Geometry

• 3 km
• 4km 2km
• 6km
• What is the area of the shaded region?
• Is there another way to find the area?

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Summary

• What is the order of operations? Create your own
  mnemonic device for remembering the order.
• Example Please Excuse My Dear Aunt Sally.

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Warm-up Simplify each expression.

• 2 (13 - 4) 3
• 4 3 (2 x 3)
• (17 12) 5 (4 - 2)
• 16 (8 - 4) 2

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Aim 1-2b How do we find the square root?

• Key Terms
• Perfect Square
• Is the product of a whole number times itself.
• Examples 1, 4, 9, 16, 25, etc.
• Can you think of some other examples of perfect
  squares?

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• Radical Sign (v )
• It is to find the square root of a number.
• Radicand
• It is the number inside the radical sign. Ex.
  v9

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• Principal Root
• It is the positive root to a square root.
• Ex.
• Because 3 3 9 and 3 -3 9
• How do you know when to give 3 as your answer?
  When you see
• When do you 3 as an answer?
• When you see

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Order of Operations with Square roots

• 1.
• 2.
• 3.

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Summary

• Explain how to solve an expression with the
  radical sign. (i.e. what is the order of
  operations?) Provide an example with a
  step-by-step explanation.

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Ticket Out

• Write your name on the post-it note. Then
  complete the following question. Show all work.

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Warm-up Solve.

• The following show the incorrect answers the
  students gave on a quiz. Describe the error and
  correct it.
• 1. 12 6 3 6
• 2. 3 x 8 - 4 x 5 100
• 3.

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Aim 1-3 How do we evaluate variable expressions?

• Key term
• Evaluate
• Ex. Evaluate 4y 15 for y 9
• Substitute y for 9. Remember to insert
  parentheses. 4 (9) 15 Then solve.

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• Evaluate each expression.
• 63 - 5x for x 7
• 2. 4 ( t 3) 1, for t 8

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Replacing More Than One Variable
for a 2, b5 and c 10.
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Evaluate each expression

• 6 (g h) for g 8 and h 7
• 2xy z for x 4, y 3 and z 1
• for r13 and s 11

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Solving problems by Evaluating Expressions

• Energy drinks come in cases of 24 bottles.
• Write a variable expression for the number of
  cases a store should order to get b bottles of
  energy drinks.
• 2. Evaluate the expression for 120 bottles.

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Extension

• The store pays 29 for each case of energy
  drinks.
• Write a variable expression for the cost of c
  cases.
• Evaluate the expression to find the cost of five
  cases.

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Online Shopping

• An online music store charges 14 for each CD.
  Shipping costs 6 per order.
• Write a variable expression for the cost of
  ordering CDs.
• Find the cost of ordering four CDs.

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Summary

• List examples of how you can use variable
  expressions in your own life.
• Then pick one example and write a variable
  expression and evaluate a variable expression for
  it.

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Warm-up

• A carnival charges 5 for admission plus 2 per
  ride.
• Write an expression for the cost of admission
  plus r rides.
• Find the cost of admission plus six rides.
• How many rides can you afford if you have 15 to
  spend?

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Aim 1-4 How do we find opposites and absolute
value?

• Key terms
• 1. Integers are whole numbers and
• their opposites.
• Example -4, -3, -2, -1, 0, 1, 2, 3, 4

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• 2. Opposites are numbers that are same distance
  from zero.
• Example -2 and 2, -15 and 15

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• 3. Absolute Value is the distance a number is
  from zero.
• Example

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Summary

• Complete each sentence with a word that makes it
  true.
• 1. An integer is negative, positive or ___.
• 2. All __ integers are less than zero.
• 3. The opposite of a __ number is negative.
• 4. The absolute value of an integer is never ___.?

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• Name two consecutive integers between the given
  integers.
• -6, 2
• 0, -4
• -8, -12

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Warm-up

• Evaluate each expression.
• 3d 3 for d 7 b. 55y for y 8
• 2. Compare. Use lt,gt or to complete each
  statement.
• 5 10 5 _ (5 10) 5
• (9 - 6) (2 1) _ 9 6 2 1
• 3. Arrange the integers from least to greatest.
  0, 3, -17, -25

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Aim 1-5 How do we use tiles to model integer
addition?

• Activity

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Rules for Adding Integers

• The sum of two positive integers is positive. Ex.
  2 3 5
• The sum of two negative integers is negative. Ex.
  2 -6 -8
• To add two integers with different signs, find
  the difference of their absolute values. The sum
  has the sign of the integer with the greater
  absolute value.
• Ex. 2 6 4 or 10 4 -6

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Practice

• 2 -6
• -4 9
• -5 -1
• -12 (-31)
• 7 (-18)
• -20 (-15)

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Summary

• What is the sign of the sum when you add two
  integers of the same sign?
• Provide an example.
• What is the sign of the sum when you add two
  integers of unlike signs?
• Provide an example.

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Warm-up Find each sum.

• 1. 8 -9
• 2. -11 (-18)
• -4 (-6)
• 14 (-3)
• 6 (-6)
• -13 (-10)

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Aim 1-6 How do we subtract integers?

• 7 3
• Modeling using tiles
• -5 (-2)
• - - - - -

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• 6 (-2)
• - -
• 5 8
• - - -

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Rules for Subtracting Integers

• To subtract an integer, you add its opposite.
• Ex. 2 5 2 -5 -3
• 4 (-3) 4 3 7

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Practice

• -3 4
• -7 4
• -11 4
• -15 4

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Additional Practice

• 1. 6 (-2)
• 2. 6 2
• 3. 2 6
• 4. 2 (-6)
• 5. -2 6
• 6. 5 11
• 7. 75 (-25)

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Summary

• Explain how to solve and solve it.
• 2 - 48

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Aim 1-7 How do we write rules for patterns?

• Key Terms
• Inductive reasoning
• Conjecture

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Looking at Number Patterns

• 30, 25, 20, 15, .
• 2, -2, 2, -2, 2
• 1,3,4, 12, 13,

• Whats the pattern?

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Write a rule for each pattern.

• 1. 4, 9, 14, 19,
• 3, 9, 27, 81,
• 1, 1, 2, 3, 5, 8,
• 1, 4, 9, 16, 25,
• 1, 8, 27,
• 2, 3, 5, 7,

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Extending a Pattern

• 640, 320, 160, 80,
• 1, 3, 5, 7,
• 1, 2, 4, 7,

• Write a rule for the pattern.
• Then find the next two numbers in the pattern.

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Analyzing Conjectures

• Counterexample is an example that proves a
  statement false.

• True or false. If false, give a counterexample.
• Every four sided figure is a rectangle.

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Is each conjecture true? If false, give a
counterexample.

• The absolute value of any integer is positive.
• The last digit of the product of 5 and a whole
  number is either 0 or 5.

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Summary

• Write a rule for the pattern below. Then find the
  next three numbers.
• 1, 4, 10, 22,46, 94,

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Warm-up

• Write a rule for the pattern. Then find the next
  three numbers.
• 8, 11, 14, 17,
• 1, 5, 4, 8, 7,
• 3, 5, 10, 12, 24,
• 1, 4, 7, 10,

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Aim 1-8 How do we use patterns to solve
real-world problems?

• What do songs on the radio, computer code and
  your bodys DNA have in common?

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Information

• News spreads quickly at Riverdale High. Each
  student who hears a story repeats it 15 minutes
  later to two students who have not yet heard it,
  and then tells no one else. Suppose one student
  hears some news at 800 a.m. How many students
  will know the news at 900 a.m.?

• Read and Understand
• 1. How many students does each student tell?
• How long does the news take to reach the second
  and third students?
• Plan and Solve
• Make a table to organize the numbers. Then look
  for a pattern.

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• Practice
• Page 42 problems 1-5 Test Prep

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Summary

• What are two ways to solve a problem that
  involves a pattern?
• List and explain at least 5 different problem
  solving strategies.

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Warm-up

• Each student on a committee of five students
  shakes hands with every other committee member.
  How many handshakes will there be in all?

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Aim 1-9 How do we multiply and divide integers?

• Rules for multiplying and dividing integersThe
  product or quotient of two integers with the same
  signs is positive.
• The product or quotient of two integers with
  opposite signs is negative.

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Summary

• Create a mini-poster for remembering the rules
  for multiplying and dividing integers using
  examples and color.

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Aim 1-10 How do we graph on the coordinate
plane?

• Key Terms
• Coordinate plane (Cartesian Plane)
• X-axis
• Y-axis
• Quadrants
• Origin
• Ordered pair
• X-coordinate
• Y-coordinate

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Summary

• In which quadrant does P (x, y) lie?
• X is positive, y is negative.
• X is positive, y is positive.
• X is negative, y is positive.
• X is negative, y is negative.

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Warm-up

• Fill-in the blank with the best word or phrase.
• The ordered pair(0,0) represents the location of
  the ___.
• A letter that stands for a number in an
  expression is a (n) ___.
• The vertical axis in the coordinate plane is
  known as the ___.
• The coordinate plane is divided into four __.
• All whole numbers and their opposites are __.

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Chapter Review

• Part 1 In groups
• Create a graphic organizer.
• Person 1 starts drawing a rectangle in the center
  of the paper with the first concept. Person 2
  provides an example. Person 3 list another
  concept and person 4 provides an example.
  Continue this until all concepts have been
  listed.
• Try to draw connections between the concepts
  whenever possible.