Advanced Math

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Chapter 1 Exploring and Communicating Mathematics

• Advanced Math

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Section 1.2 Investigating Patterns

• A variable is a letter used to represent one or
  more numbers.

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Sample 1

• Peter earns 12 an hour. Write a variable
  expression for the amount he earns in h hours.
• Look for pattern
• 12 (1) 12
• 12 (2) 24
• 12 (3) 36
• Increasing each time by 12. 12h

• Try this one on your own
• Hitesh walks 3 miles in 1 hour. Write a variable
  expression for the number of miles he walks in h
  hours.
• 3h

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Sample 2

• A row of triangles is built with toothpicks.
  Write a variable expression of the perimeter of
  Shape N.

• Try this one on your own
• A row of squares is built with toothpicks. Write
  a variable expression for the perimeter of Shape
  N.

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Sample 3 Evaluating Variable Expressions

• Suppose a kudzo vine grows 12 inches a day. How
  long is the vine after each number of days?
• 7 12 (7) 84 inches
• 30 12 (30) 360 inches
• 365 12 (365) 4380 inches

• Try this one on your own
• Hector works 8 hours each day. How many hours
  does he work for the given number of days?
• 8
• 90
• 1000
• 64 hours
• 720 hours
• 8000 hours

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Section 1.3 Patterns with Powers

• Numbers multiplied together are called factors.
• When the same number is repeated as a factor, you
  can rewrite the product as a power of that
  number.
• The repeated factor is the base, and the number
  of times it appears as a factor is the exponent.

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Sample 1

• Write the product as a power. Then write how to
  say it in words.
• 2x2x2x2x2x2x2x2
• 6x6x6x6x6

• Try these on your own
• 3x3x3x3x3x3x3
• three to the seventh power
• 8x8x8x8x8x8x8x8x8x8
• eight to the tenth power

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Sample 2

• Write an expression for the area covered by the
  tiles.
• Evaluate your expression for each value of x.
• X 5
• X 10

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Try this one on your own

• Write an expression for the area covered by the
  tiles.
• Evaluate your expression for each value of x.
• X 4
• 29
• X 8
• 89

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• Counterexamples
• A counterexample is an example that shows that a
  statement is false.

• Conjectures about Powers of Ten
• A conjecture is a guess based on your past
  experiences.
• Make a conjecture about the number of zeros you
  need to write out 10 to the 9th power.

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Sample 3

• Larry makes a conjecture that x squared is
  greater than x for all values of x.
• Find a counterexample.
• You only need to find 1 example that makes it a
  false statement.
• Start at 0.

• Try this one on your own
• Nina makes a conjecture that x cubed is greater
  than x squared for all values of x.
• Find a counterexample.
• X 1

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Section 1.4 Writing and Evaluating Expressions

• The order of operations are a set of rules people
  agree to use so an expression has only one
  answer.
• P.E.M.D.A.S. Parentheses, Exponents,
  Multiplication/Division, Addition/Subtraction

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Sample 1

• Calculate according to the order of operations.

• Try this one on your own
• 11

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Sample 2

• Insert parentheses to make each statement true.
• 4 16 / 2 3 x 5 20
• 4 16 / 2 3 x 5 59

• Try these on your own
• 2 8 / 4 6 x 3 22
• 2 (8 / 4) (6 x 3) 22
• 2 8 /4 6 x 3 3
• (2 8) / (4 6) x 3 3

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Sample 3

• Write an expression for the area covered by the
  tiles.
• Evaluate the expression when x 5.

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Try this one on your own

• Write an expression for the area covered by the
  tiles.
• Evaluate the expression when x 4.
• 55 square units

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Section 1.5 Modeling the Distributive Property

• Sample 1
• Find each product using mental math.
• 7(108)
• 7 x 100 7 x 8
• 700 56
• 756
• 15(98)
• 15 x 100 15 x 2
• 1500 30
• 1470

• Try these on your own
• 9 (999)
• 9 x 1000 9 x 1
• 9000 9
• 8991
• 12 (1003)
• 12 x 1000 12 x 3
• 12000 36
• 12036

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Sample 2

• Illustrate expression 3 (x 2) using algebra
  tiles.
• Rewrite the expression without parentheses.
• 3x 6

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Try this one on your own

• Illustrate the expression 4(x 1) using algebra
  tiles.
• Then, rewrite the expression without parentheses.
• 4x 1

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Combining Like Terms

• The numerical part of a variable term is called a
  coefficient.
• Terms with the same variable part are called like
  terms.
• You use the distributive property in reverse to
  combine like terms.

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Sample 3

• Simplify
• 5 ( x 4) 3x
• 5x 20 3x
• 2x 20

• Try this one on your own
• Simplify
• 4 ( x 3) 2x
• 4x 12 2x
• 2x 12

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Section 1.6 Working Together on Congruent
Polygons

• Two figures that have the same size and shape are
  called congruent.
• Slide Translation
• Turn Rotation
• Flip Reflection
• Vertex Corner
• Two sides that have the same length are called
  congruent sides.

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Exploration 1

• How many different ways can you divide a square
  into four identical pieces?
• Use only straight lines.
• Square can only use 25 dots.
• 5 Minute Time Limit

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Exploration 2

• Can you work with others to find new ways to
  divide the square?
• 4 people in a group
• 10 Minute Time Limit

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Section 1.7 Exploring Quadrilaterals and Symmetry