Transcript 2. Reason abstractly and quantitatively.

Algebraic Expressions
Writing Equations
Pythagorean Theorem
How do I use what I learned about algebraic
expressions and equations in different real
life situations?
 1.
Make sense of problems and persevere in
solving them.
 2. Reason abstractly and quantitatively.
 3. Construct viable arguments and critique
the reasoning of others.
 4. Model with mathematics.
 5. Use appropriate tools strategically.
 6. Attend to precision.
 7. Look for and make use of structure.
 8. Look for and express regularity in
repeated reasoning.
 What
is an algebraic expression?
 How do I evaluate an expression?
 What is a variable?
 Why do I have to use opposite operation in
an equation?
 Why do we solve equations?
 An
algebraic expression is a mathematical
expression that consists of variables,
numbers and operations. The value of this
expression can change.
 Calculating the value of an expression is
called ‘evaluating’ the expression.
 A variable is a symbol used to represent a
number in an expression or an equation. The
value of this number can change.
 The
goal in solving an equation is to get the
variable by itself on one side of the equation
and a number on the other side of the
equation.
 To isolate the variable, we must reverse the
operations acting on the variable. We do this
by performing the inverse of each operation
on both sides of the equation. Performing the
same operation on both sides of an equation
does not change the validity of the equation,
or the value of the variable that satisfies it.
 The
process of finding out the variable
value that makes the equation true is
called ‘solving’ the equation.
 Write
and solve an
equation to find
the measure of
angle x.

Find the measure of
angle b.

A triangle has an area
of 6 square feet. The
height is four feet.
What is the length of
the base?

The surface area of a
cube is 96 in2. What
is the volume of the
cube?

The distance from
Jonestown to Maryville is
180 miles, the distance
from Maryville to Elm City
is 300 miles, and the
distance from Elm City to
Jonestown is 240 miles.
Do the three towns form a
right triangle? Why or why
not?

The Irrational Club wants
to build a tree house.
They have a 9-foot ladder
that must be propped
diagonally against the
tree. If the base of the
ladder is 5 feet from the
bottom of the tree, how
high will the tree house be
off the ground?

Find the length of
segment AB
The expression 20(4x) + 500
represents the cost in
dollars of the materials
and labor needed to build
a square fence with side
length x feet around a
playground. Interpret the
constants and coefficients
of the expression in
context.
The Tindell household contains three people of
different generations. The total of the ages of
the three family members is 85.
 Find reasonable ages for the three Tindells.
 Find another reasonable set of ages for them.
 One student, in solving this problem, wrote
C + (C+20)+ (C+56) = 85
 What does C represent in this equation?
 What do you think the student had in mind when
using the numbers 20 and 56?
 What set of ages do you think the student came
up with?

Simplify the fol owing.
a.
b.
REVIEW: Algebra Competency
 How
do I use what I learned on Unit 2 on
problem solving?
 1.
Make sense of problems and persevere in
solving them.
 2. Reason abstractly and quantitatively.
 3. Construct viable arguments and critique
the reasoning of others.
 4. Model with mathematics.
 5. Use appropriate tools strategically.
 6. Attend to precision.
 7. Look for and make use of structure.
 8. Look for and express regularity in
repeated reasoning.
 Simplify
the following:
1(x + 3) + (x + 5)
2. (2x + 1) - (3x – 4)
3. (4 x  1)
2
4. ( x  1)(3x  5x  6)
2
 Which
of the following expressions are
equivalent to (2x+3)2 ; Choose all that apply
A) 4x2 +12x + 9
B) (2x+3)(2x+3)
C) 4x2 + 9
D) (2x)2 + 2(6x) + 32
 Express 2(x3 – 3x2 + x – 6) – (x – 3)(x + 4) in
factored form and use your answer to say for
what values of x the expression is zero.
 Given that (2^x)^2 + (2^x) −12 can be written
as (2^x + a)(2^x + b), where a, b are
integers, find the value of a and of b.
Simplify the following expressions
2
2
1. x  5 x  4  x  2 x  8
x 2  16 x 2  x  2
3.
1 3

4a 8a 2
1 x

6. x y
1
1
y
3x 2
3x
2.
 2
x2 x 4
4x x  4
2x 1
4

 2
4.
5.
x  4 x 1
x  5 x  3x  10
2
2
7. x  4
3
1
x4
Express
in the form
, where a(x) and b(x) are polynomials
Rewrite the rational exponents as a radical; Rewrite the radicals with rational exponents.
2
1
1. 8 3
5. (32)
3
5
:
Simplify:
1)
3
125x 9
2.
4
813
6.
9
10 x 3 y 5
2.
4
810 x 5 y 2
3.. 216 3
7. Rewrite
3. Rewrite
4.
x
5
a2
in at least three alternate forms.
x
2
3
x3  3x2  3x  1 in simplest form.
Review: UNIT 2
Introduction to geometry
 How
do I use definitions, postulates to write
a proof?
 1.
Make sense of problems and persevere in
solving them.
 2. Reason abstractly and quantitatively.
 3. Construct viable arguments and critique
the reasoning of others.
 4. Model with mathematics.
 5. Use appropriate tools strategically.
 6. Attend to precision.
 7. Look for and make use of structure.
 8. Look for and express regularity in
repeated reasoning.
Identify and describe the basic undefined terms
of geometry.
 Represent and analyze angles and angle
relationships including vertical, adjacent,
complementary, supplementary, obtuse, acute,
right, interior, and exterior.
 Represent and analyze line/segment/plane
relationships including parallel, perpendicular,
intersecting, bisecting, and midpoint.
 Represent and analyze point relationships
including collinear

 Construct
a simple formal deductive proof
using properties of equality and congruence.
If 3x + 28 = 58, then x = 10.
 Write the correct statements and reasons in
the flowchart ( and two-column proof) to
prove the conditional above.
 Proving
Statements about segments
 Proving statements about angles
 Proving vertical angles theorem