Transcript Chapter 1: Algebra Toolbox

Chapter 1: Exploring and
Communicating Mathematics
Advanced Math
Section 1.2: Investigating Patterns
 A variable is a letter used to represent one or more
numbers.
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
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.
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
 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
 30 : 12 (30) = 360 inches
 365 : 12 (365) = 4380 inches
 90
 1000
64 hours
 720 hours
 8000 hours

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.
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
Sample 2
 Write an expression for
the area covered by the
tiles.
 Evaluate your expression
for each value of x.
X=5
 X = 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
 29
X=8
 89
 Counterexamples
 Conjectures about
Powers of Ten
 A counterexample is an
example that shows that a
statement is false.
 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 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
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
Sample 1
 Calculate according to the
order of operations.
48  (12  8)  8
2
 Try this one on your
own…
72  (18  12) 2  9
 11
Sample 2
 Insert parentheses to
make each statement
true.
 Try these on your own…
 2 + 8 / 4 + 6 x 3 = 22
 2 + (8 / 4) + (6 x 3) = 22
 4 + 16 / 2 + 3 x 5 = 20
 4 + 16 / 2 + 3 x 5 = 59
 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.
2 x  5x  3
2
 Evaluate the expression
when x = 4.
 55 square units
Section 1.5: Modeling the Distributive
Property
 Sample 1
 Find each product using mental
 Try these on your own…
 9 (999)
math.
 9 x 1000 – 9 x 1
 7(108)
 9000 – 9
7 x 100 + 7 x 8
 700 + 56
 756

 8991
 12 (1003)
 12 x 1000 + 12 x 3
 15(98)
15 x 100 – 15 x 2
 1500 – 30
 1470

 12000 + 36
 12036
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 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.
Sample 3
 Simplify…
 Try this one on your own…
 Simplify…
 5 ( x + 4) – 3x
 5x + 20 – 3x
 2x + 20
 4 ( x + 3) – 2x
4x + 12 – 2x
 2x + 12

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.
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
Exploration 2
 Can you work with others to find new ways to divide the
square?
 4 people in a group
 10 Minute Time Limit
Section 1.7: Exploring Quadrilaterals
and Symmetry