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