Download Algebra II coded

Grade: High School
Course: Algebra II
District Adopted Materials: Algebra 2 (Glencoe/McGraw-Hill) 2003
Standard 1: Number and Computation – The student uses numerical and computational concepts and procedures in a variety of situations.
Benchmark 1: Number Sense – The student demonstrates number sense for real numbers and algebraic expressions.
Benchmark 2: Number Systems and Their Properties – The student demonstrates an understanding of the real number system; recognizes,
applies, and explains their properties, and extends these properties to algebraic expressions.
Benchmark 3: Estimation – The student uses computational estimation with real numbers in a variety of situations.
Benchmark 4: Computation – The student models, performs, and explains computation with real numbers and polynomials in a variety of
situations.
Standard 2: Algebra – The student uses algebraic concepts and procedures in a variety of situations.
Benchmark 1: Patterns – The student recognizes, describes, extends, develops, and explains the general rule of a pattern in a variety of
situations.
Benchmark 2: Variables, Equations, and Inequalities – The student uses variables, symbols, real numbers, and algebraic expressions to
solve equations and inequalities in variety of situations.
Benchmark 3: Functions – The student analyzes functions in a variety of situations.
Benchmark 4: Models – The student develops and uses mathematical models to represent and justify mathematical relationships found in a
variety of situations involving tenth grade knowledge and skills.
Standard 3: Geometry – The student uses geometric concepts and procedures in a variety of situations.
Benchmark 1: Geometric Figures and Their Properties – The student recognizes geometric figures and compares and justifies their
properties of geometric figures in a variety of situations.
Benchmark 2: Measurement and Estimation – The student estimates, measures and uses geometric formulas in a variety of situations.
Benchmark 3: Transformational Geometry – The student recognizes and applies transformations on two- and three-dimensional figures in a
variety of situations.
Benchmark 4: Geometry From An Algebraic Perspective – The student uses an algebraic perspective to analyze the geometry of two- and
three-dimensional figures in a variety of situations.
Standard 4: Data – The student uses concepts and procedures of data analysis in a variety of situations.
Benchmark 1: Probability – The student applies probability theory to draw conclusions, generate convincing arguments, make predictions
and decisions, and analyze decisions including the use of concrete objects in a variety of situations.
Benchmark 2: Statistics – The student collects, organizes, displays, explains, and interprets numerical (rational) and non-numerical data sets
in a variety of situations.
Indicators
The student…
 HS.1.1.K1 knows, explains, and uses equivalent representations for real
numbers and algebraic expressions including integers, fractions, decimals,
percents, ratios; rational number bases with integer exponents; rational
numbers written in scientific notation; absolute value; time; and money
(2.4.K1a) ($), e.g., –4/2 = (–2); a(-2) b(3) = b3/a2
 HS.1.1.A1 generates and/or solves real-world problems using equivalent
representations of real numbers and algebraic expressions (2.4.A1a) ($),
e.g., a math classroom needs 30 books and 15 calculators. If B represents
the cost of a book and C represents the cost of a calculator, generate two
different expressions to represent the cost of books and calculators for 9
math classrooms
 HS.1.2.K3▲names, uses, and describes these properties with the real
number system and demonstrates their meaning including the use of
concrete objects (2.4.K1a) ($):
o commutative (a + b = b + a and ab = ba), associative [a + (b + c) =
(a + b) + c and a(bc) = (ab)c], distributive [a (b + c) = ab + ac], and
substitution properties (if a = 2, then 3a = 3 x 2 = 6);
o identity properties for addition and multiplication and inverse
properties of addition and multiplication (additive identity: a + 0 =
a, multiplicative identity: a • 1 = a, additive inverse: +5 + –5 = 0,
multiplicative inverse: 8 x 1/8 = 1);
o symmetric property of equality (if a = b, then b = a);
o addition and multiplication properties of equality (if a = b, then a +
c = b + c and if a = b, then ac = bc) and inequalities (if a > b, then
a + c > b + c and if a > b, and c > 0 then ac > bc);
o zero product property (if ab = 0, then a = 0 and/or b = 0)
 HS.1.2.A1 generates and/or solves real-world problems with real numbers
using the concepts of these properties to explain reasoning (2.4.A1a) ($):
o commutative, associative, distributive, and substitution properties,
e.g., the chorus is sponsoring a trip to an amusement park. They
need to purchase 15 adult tickets at $6 each and 15 student
tickets at $4 each. How much money will the chorus need for
tickets? Solve this problem two ways.
o identity and inverse properties of addition and multiplication, e.g.,
the purchase price (P) of a series EE Savings Bond is found by
the formula ½ F = P where F is the face value of the bond. Use the
formula to find the face value of a savings bond purchased for
$500.
o symmetric property of equality, e.g., Sam took a $15 check to the
Teaching
Time
On-going
Bloom’s
Strand
Sequence
Synthesis
Variables,
Equations, and
Inequalities;
Advanced
R
M
Analysis
Equivalent
Represent
R
M
S(9-12)
.5
Knowledge
Number
Systems and
Properties
S(9-11)
.25
bank and received a $10 bill and a $5 bill. Later Sam took a $10
bill and a $5 bill to the bank and received a check for $15. $
addition and multiplication properties of equality, e.g., the total
price for the purchase of three shirts in $62.54 including tax. If the
tax is $3.89, what is the cost of one shirt, if all shirts cost the
same?
o addition and multiplication properties of equality, e.g., the total
price for the purchase of three shirts is $62.54 including tax. If the
tax is $3.89, what is the cost of one shirt?
T = 3s + t
$62.54 = 3s + $3.89 - $3.89
$62.54 - $3.89 = 3s
$58.65 = 3s
$58.65 = 3s = 3s ÷ 3
$19.55 = s
o zero product property, e.g., Jenny was thinking of two numbers.
Jenny said that the product of the two numbers was 0. What could
you deduct from this statement? Explain your reasoning.
 HS.1.2.K4 uses and describes these properties with the real number system
(2.3.K1a) ($):
o transitive property (if a = b and b = c, then a = c),
o reflexive property (a = a).
 HS.1.3.K2 uses various estimation strategies and explains how they were
used to estimate real number quantities and algebraic expressions (2.4.K1a)
($)
 HS.1.4.K1c A student will be able to solve and graph equations and
absolute value equations and inequalities. [1-6]
 HS.1.4.K3 finds prime factors, greatest common factor, multiples, and the
least common multiple of algebraic expressions (2.4.K1b)
 HS.2.1.K1 identifies, states, and continues the following patterns using
various formats including numeric (list or table), algebraic (symbolic
notation), visual (picture, table, or graph), verbal (oral description),
kinesthetic (action), and written
o arithmetic and geometric sequences using real numbers and/or
exponents (2.4.K1a); e.g., radioactive half-lives;
o patterns using geometric figures (2.4.K1h);
o algebraic patterns including consecutive number patterns or
equations of functions, e.g., n, n + 1, n + 2, ... or f(n) = 2n – 1
(2.4.K1c,e);
o special patterns (2.4.K1a), e.g., Pascal’s triangle and the
Fibonacci sequence
Knowledge
Number
Systems and
Properties
S(9-11)
Application
Advanced
R
S(9-11)
Comprehension
Analysis
Variables,
Equations,
Inequalities
Advanced
Application
Advanced
I
R
M
RM
S(9-11)
R
S(9-11)
.25
1
1.5
1
1
 HS.2.2.K1 knows and explains the use of variables as parameters for a
specific variable situation (2.4.K1f), e.g., the m and b in y = mx + b or the h,
k, and r in (x – h)2 + (y – k)2 = r2
Analysis
 HS.2.2.A1 represents real-world problems using variables, symbols,
expressions, equations, inequalities, and simple systems of linear equations
(2.4.A1c-e) ($).
 HS.2.2.K2 manipulates variable quantities within an equation or inequality
(2.4.K1e), e.g., 5x – 3y = 20 could be written as 5x – 20 = 3y or 5x(2x + 3) =
8 could be written as 8/(5x) = 2x + 3
Application
 HS.2.2.K2 solves (2.4.K1d) ($):
o N linear equations and inequalities both analytically and
graphically;
o quadratic equations with integer solutions (may be solved by trial
and error, graphing, quadratic formula, or factoring);
o ▲N systems of linear equations with two unknowns using integer
coefficients and constants;
o radical equations with no more than one inverse operation around
the radical expression;
o equations where the solution to a rational equation can be
simplified as a linear equation with a nonzero denominator, e.g.,
__3__ = __5__.
(x + 2) (x – 3)
o equations and inequalities with absolute value quantities
containing one variable with a special emphasis on using a
number line and the concept of absolute value.
o exponential equations with the same base without the aid of a
calculator or computer, e.g., 3x + 2 = 35
 HS.2.2.A2 represents and/or solves real-world problems with (2.4.A1c) ($):
o ▲N linear equations and inequalities both analytically and
graphically, e.g., tickets for a school play are $5 for adults and $3
for students. You need to sell at least $65 in tickets. Give an
inequality and a graph that represents this situation and three
possible solutions.
o quadratic equations with integer solutions (may be solved by trial
and error, graphing, quadratic formula, or factoring), e.g., a fence
is to be built onto an existing fence. The three sides will be built
with 2,000 meters of fencing. To maximize the rectangular area,
what should be the dimensions of the fence?
o systems of linear equations with two unknowns, e.g., when
comparing two cellular telephone plans, Plan A costs $10 per
Analysis
Analysis
Variables,
Equations,
Inequalities;
Advanced
Variables,
Equations, and
Inequalities
Variables,
Equations,
Inequalities;
Advanced
Variables,
Equations,
Inequalities;
Advanced
I
R
On-going
R
M
S(9-12)
R
M
S(9-11)
On-going
I
R
S(9-11)
3
On-going
month and $.10 per minute and Plan B costs $12 per month and
$.07 per minute. The problem is represented by Plan A = .10x +
10 and Plan B = .07x + 12 where x is the number of minutes.
o radical equations with no more than one inverse operation around
the radical expression, e.g., a square rug with an area of 200
square feet is 4 feet shorter than a room. What is the length of the
room?
o a rational equation where the solution can be simplified as a linear
equation with a nonzero denominator, e.g., John is 2 feet taller
than Fred. John’s shadow is 6 feet in length and Fred’s shadow is
4 feet in length. How tall is Fred?
 HS.2.3.K2 matches equations and graphs of constant and linear functions
and quadratic functions limited to y = ax2 + c (2.4.K1d,f)
Analysis
Advanced
 HS.2.3.K4 determines x- and y-intercepts and maximum and minimum
values of the portion of the graph that is shown on a coordinate plane
(2.4.K1f)
Analysis
 HS.2.3.K5 identifies domain and range of:
o relationships given the graph or table (2.4.K1e-f)
o linear, constant, and quadratic functions given the equation(s)
(2.4.K1d)
 HS.2.3.K7 uses function notation
Analysis
Variables,
Equations,
Inequalities;
Advanced
Relations and
Functions;
Advanced
 HS.2.3.K8 evaluates function(s) given a specific domain ($)
Comprehension
Application
 HS.3.4.K2 determines if a given point lies on the graph of a given line or
parabola without graphing and justifies the answer (2.4.K1f)
Analysis
 HS.3.4.K4 ▲finds and explains the relationship between the slopes of
parallel and perpendicular lines (2.4.K1f), e.g., the equation of a line 2x + 3y
= 12. The slope of this line is ‫־‬2/3. What is the slope of a line perpendicular
to this line?
 HS.3.4.K6 ▲ recognizes the equation of a line and transforms the equation
into slope-intercept form in order to identify the slope and y-intercept and
uses this information to graph the line (2.4.K1f).
Analysis
 HS.3.4.K7 recognizes the equation y = ax2 + c as a parabola; represents
and identifies characteristics of the parabola including opens upward or
opens downward, steepness (wide/narrow), the vertex, maximum and
Analysis
Analysis
Relations and
Functions;
Advanced
Relations and
Functions;
Advanced
Advanced
Variables,
Equations,
Inequalities;
Advanced
Variables,
Equations,
Inequalities;
Advanced
Variables,
Equations,
Inequalities;
I
R
S(9-11)
I
R
.5
R
M
On-going
R
M
On-going
I
R
.5
R
M
S(9-11)
R
M
S(9-11)
.5
R
M
S(9-11)
.5
R
M
S(9-11)
1
.5
.5
minimum values, and line of symmetry; and sketches the graph of the
parabola (2.4.K1f).
 HS.3.4.K8 explains the relationship between the solution(s) to systems of
equations and systems of inequalities in two unknowns and their
corresponding graphs (2.4.K1f), e.g., for equations, the lines intersect in
either one point, no points, or infinite points; and for inequalities, all points in
double-shaded areas are solutions for both inequalities
 ACT 2-6, 6-6 A student will recognize and graph relations, functions, and
special functions and identify the domain and range.
Advanced
Analysis
Variables,
Equations,
Inequalities;
Advanced
R
M
S(9-11)
1.5
Comprehension
Advanced
2
 ACT 4-1 A student is able to organize data in matrix form and solve
equations involving matrices.
Comprehension
Advanced
 ACT 4-2, 4-3 A student is able to add, subtract, and multiply matrices.
Comprehension
Advanced
 ACT 4-7, 4-8 A student is able to evaluate determinants.
Comprehension
Advanced
 ACT 4-6 A student is able to solve systems by Cramer's Rule.
Comprehension
Advanced
 ACT 5-1, 5-2 A student is able to do operations of polynomials.
Comprehension
Advanced
 ACT 5-4 A student is able to factor polynomials.
Comprehension
Advanced
 ACT 5-5, 5-6 A student is able to simplify radical and radical equations.
Comprehension
Advanced
 ACT 5-9 A student is able to do the operations of radicals and complex
numbers.
Comprehension
Advanced
 ACT 6-3, 6-4, 6-5 A student will solve quadratic equations by several
methods.
Comprehension
Advanced
 ACT 7-1 A student is able to graph a polynomial function. (ACT) [7-1]
Comprehension
Advanced
 ACT 7-4, 7-5, 7-6 A student is able to use synthetic division to evaluate
functions, determine whether a binomial is a factor, and find the zeros of the
Comprehension
Advanced
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
1
2
1
2
1
3
2
4
6
1
2
polynomial function.
 ACT 7-7 A student is able to find the sum, difference, product, quotient,
and composition of functions.
Comprehension
Advanced
 ACT 7-8 A student is able to find the inverse of functions and proving the
functions are inverses.
Comprehension
 ACT 6-6, 8-2, 8-3, S3B4, S2B4 The student will write equations of
parabolas and circles
Comprehension
Relations
and
Functions;
Advanced
Advanced
 ACT 8-4, 8-5, 8-6 The student will recognize equations and sketch graphs
of conics including ellipse and hyperbola.
Comprehension
Advanced
 ACT 9-1, 9-2, 9-3 The student will add, subtract, multiply, and divide
rational expressions.
Comprehension
Advanced
 ACT 10-1, 10-2 The student is able to solve exponential and logarithmic
equations.
Comprehension
Advanced
 ACT 10-1 The student is able to graph exponential functions.
Comprehension
Advanced
 ACT 10-3 The student is able to evaluate logarithmic equations using
properties of logarithms.
Comprehension
Advanced
 ACT 10-4 The student is able to solve exponential equations and
inequalities using common logarithms.
Comprehension
Advanced
 ACT 10-5 The student is able to solve growth and decay application
problems.
Comprehension
Advanced
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
I
R
M
1
1
2
1
3
1
1
1
1
1