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Advanced Math
Chapter 1: Exploring and Communicating Mathematics
Section 1.2: Investigating PatternsA variable is a letter used to represent one
or more numbers.
Sample 1Peter earns $12 an
hour. Write a variable expression for the amount he earns in h hours. Look for pattern…
12 (1) = 1212 (2) = 2412 (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
Sample 2A 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.
Sample 3: Evaluating Variable ExpressionsSuppose 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?8901000
64 hours 720 hours 8000 hours
Section 1.3: Patterns with PowersNumbers 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.
Sample 1Write 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
8x8x8x8x8x8x8x8x8x8eight to the tenth
power
Sample 2Write an
expression for the area covered by the tiles.
Evaluate your expression for each value of x.X = 5X = 10
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
29X = 8
89
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.
Sample 3Larry 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
Section 1.4: Writing and Evaluating ExpressionsThe 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
Sample 1Calculate
according to the order of operations.
Try this one on your own…
11
8)812(48 2 9)1218(72 2
Sample 2Insert
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 = 222 + (8 / 4) + (6 x 3)
= 22
2 + 8 /4 + 6 x 3 = 3(2 + 8) / (4 + 6) x 3
= 3
Sample 3
Write an expression for the area covered by the tiles.
Evaluate the expression when x = 5.
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
352 2 xx
Section 1.5: Modeling the Distributive PropertySample 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 19000 – 98991
12 (1003)12 x 1000 + 12 x 312000 + 3612036
Sample 2 Illustrate expression 3
(x + 2) using algebra tiles.
Rewrite the expression without parentheses.3x + 6
Try this one on your own…Illustrate the expression 4(x + 1) using
algebra tiles.
Then, rewrite the expression without parentheses.4x + 1
Combining Like TermsThe 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.
Sample 3Simplify…
5 ( x + 4) – 3x
5x + 20 – 3x2x + 20
Try this one on your own…Simplify…
4 ( x + 3) – 2x
4x + 12 – 2x 2x + 12
Section 1.6: Working Together on Congruent PolygonsTwo 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.
Exploration 1How 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
Exploration 2Can you work with others to find new ways
to divide the square?4 people in a group10 Minute Time Limit
Section 1.7: Exploring Quadrilaterals and Symmetry