Download Algebra Curriculum Map

Algebra
Curriculum Map
2011-2012
Week
#
Dates
Standard(s)
Topic/Objective
Textbook
Connections
1
8/22-26,
To evaluate variable expressions To
use the established order of operations
(d=rt)
1.1
1.3
2
8/29 – 9/ 2
15.0 Students apply algebraic techniques to solve rate
problems, work problems, and percent mixture
problems.
25.2 Students use properties of the number system to
judge the validity of results, to justify each step of a
procedure, and to prove or disprove statements and
judge the validity of an argument according to whether
the properties of the real number system and the order
of operations have been applied correctly at each step.
5.0 Students solve multistep problems, including word
problems, involving linear equations and linear
inequalities in one variable and provide justification
for each step.
2.0a Understand and use such operations as taking the
opposite and finding the reciprocal of a number.
1.1: Use properties of numbers to demonstrate whether
assertions are true or false.
1.4, 1.5
2.1, 2.2
Supplement
The Real #
System and
2.3, 2.4
3
9/6-9
1.1: Use properties of numbers to demonstrate whether
assertions are true or false.
4.0 Students simplify expressions before solving linear
equations and inequalities in one variable.
4
9/12-16
24.2 Students use and know simple aspects of a logical
argument: Identify the hypothesis and conclusion in
logical deduction.
5.0a Students solve multistep problems, including
word problems, involving linear equations and linear
inequalities in one variable and provide justification
for each step.
2.0a Understand and use such operations as taking the
opposite and finding the reciprocal of a number.
2.0a Understand and use such operations as taking the
To check solutions of equations and
inequalities. To translate words into
mathematical symbols.
To graph, compare and order real
numbers. To find the opposite and
absolute value of a real number.
To add and subtract real numbers. To
understand the real number system (i.e.
Natural Numbers, Whole Numbers,
Integers) To use the properties of real
numbers. (i.e., commutative property
of addition)
To multiply real numbers. To use the
properties of real numbers.
To use the distributive property.
To simplify an expression by
combining like terms.
To divide real numbers.
To find the hypothesis and conclusion
in logical deduction.
To solve linear equations using
addition and subtraction.
To solve linear equations using
multiplication and division.
To find the reciprocal of a number.
To use 2 or more steps to solve a linear
equation.
2.5
2.6
2.7
2.8
2 ext
3.1
3.2
3.3
Number of
Questions
on CST
Algebra
Curriculum Map
2011-2012
5
9/19-23
6
9/26-30
7
10/3-7
8
10/10-14
opposite and finding the reciprocal of a number.
5.0a Students solve multistep problems, including
word problems, involving linear equations and linear
inequalities in one variable and provide justification
for each step.
4.0 Students simplify expressions before solving linear
equations and inequalities in one variable.
15.0 Students apply algebraic techniques to solve rate
problems, work problems, and percent mixture
problems.
3.0 Students solve equations and inequalities involving
absolute values.
4.0 Students simplify expressions before solving linear
equations and inequalities in one variable.
5.0b Students solve multistep problems, including
word problems, involving linear equations and linear
inequalities in one variable and provide justification
for each step.
3.0 Students solve equations and inequalities involving
absolute values.
3.0 Students solve equations and inequalities involving
absolute values.
Review
BENCHMARK #1
To solve equations that have variables
on both sides. To solve multi-step
word problems.
To solve more complicated equations
that have variables on both sides. To
solve multi-step word problems.
To solve work problems.
3.4
3.5
supp. mat'l
To solve and graph one step
inequalities in one variable using
multiplication and division. (Including
word problems)
To solve multi-step inequalities in one
variable. (including word problems)
To solve and graph compound
inequalities involving "and".
To solve and graph compound
inequalities involving "or".
To solve absolute value equations in
one variable.
To solve absolute value inequalities in
one variable.
6.1, 6.2
6.3
6.4
6.5
6.6
6.7
Algebra
Curriculum Map
2011-2012
Week
#
Dates
Standard(s)
Topic/Objective
Textbook
Connections
9
10/17-21
To use 4 different ways to represent
functions.
To decide whether a relation is a
function and use function notation.
To graph a linear equation using a
table of values.
To graph horizontal and vertical lines.
To find the intercepts of the graph of a
linear equation, and then, use them to
make a quick graph of the equation.
1.8, 4.8
4.1, 4.2
4.3
4.4
10
10/24-28
To find the slope of a line.
To graph a linear equation in slopeintercept form.
To use slope-intercept form to write an
equation of a line. To use point-slope
to write an equation of a line.
4.5
4.7
5.1, 5.2
11
10/31 – 11/4
16.0 Students will understand the concepts of a relation
and a function, determine whether a given relation
defines a function, and give pertinent information
about given relations and functions.
17.0 Determine the domain of independent variables
and the range of dependent variables defined by a
graph, a set of ordered pairs, or a symbolic expression.
6.0a Students graph a linear equation and compute the
x- and y- intercepts.
6.0a Students graph a linear equation and compute the
x- and y- intercepts.
6.0a Students graph a linear equation and compute the
x- and y- intercepts.
6.0a Students graph a linear equation and compute the
x- and y- intercepts.
8.0 Understand the concepts of parallel lines and
perpendicular lines and how their slopes are related.
Students are able to find the equation of a line
perpendicular to a given line that passes through a
given point.
7.0b Students are able to derive linear equations by
using the point-slope formula.
8.0 Understand the concepts of parallel lines and
perpendicular lines and how their slopes are related.
Students are able to find the equation of a line
perpendicular to a given line that passes through a
given point.
7.0a Verify that a point lies on a line, given an
equation of the line.
7.0b Students are able to derive linear equations by
using the point-slope formula.
8.0 Understand the concepts of parallel lines and
perpendicular lines and how their slopes are related.
Students are able to find the equation of a line
perpendicular to a given line that passes through a
given point.
To write an equation of a line given
two points on a line.
Supplement: To verify that a point lies
on a line, given an equation of the line.
To write an equation of a line in
standard form.
To write equations of perpendicular
lines.
5.3 and
Supplement
5.4
5.6
Number of
Questions
on CST
Algebra
Curriculum Map
2011-2012
12
11/7-10
13
11/14-18
14
11/21-22
15
11/28–12/2
16
12/5-9
6.0b Students are able to sketch the region defined by
linear inequality.
15.0a Students apply algebraic techniques to solve rate
problems, work problems, and percent mixture
problems.
15.0c Students apply algebraic techniques to solve rate
problems, work problems, and percent mixture
problems.
9.0 Students solve a system of two linear equations in
two variables algebraically and are able to interpret the
answer (to a system) graphically. Students are able to
solve a system of two linear inequalities in two
variables and to sketch the solution sets.
9.0 Students solve a system of two linear equations in
two variables algebraically and are able to interpret the
answer graphically. Students are able to solve a
system of two linear inequalities in two variables and
to sketch the solution sets.
9.0 Students solve a system of two linear equations in
two variables algebraically and are able to interpret the
answer graphically. Students are able to solve a
system of two linear inequalities in two variables and
to sketch the solution sets.
9.0 Students solve a system of two linear equations in
two variables algebraically and are able to interpret the
answer graphically. Students are able to solve a
system of two linear inequalities in two variables and
to sketch the solution sets.
25.2 Use properties of the number system to judge the
validity of results, to justify each step of a procedure,
and to prove or disprove statements: Use properties of
numbers to construct simple, valid arguments (direct
and indirect) for, or formulate counterexamples to
claimed assertions.
Review
To graph linear inequalities in 2
variables.
To solve rate problems.
To solve percent mixture problems.
6.8
supp. mat'l
supp. mat'l
To estimate the solution of a system of
linear equations by graphing.
To solve a linear system by
substitution.
To solve a system of linear equations
by linear combinations.
7.1
7.2
7.3
To identify how many solutions a
linear system has.
To graph a system of linear
inequalities.
7.5
7.6
To formulate counterexamples to
assertions.
Supplement
Algebra
Curriculum Map
2011-2012
Week
#
Dates
17
18
12/12-16
12/19-1/2
1/3-6
19
1/9-12
20
1/17-20
Standard(s)
Topic/Objective
Textbook
Connections
2.0c: Understand and use such operations
as the rules of exponents.
2.0b: Understand and use such operations
as the rules of exponents.
Use the multiplication
properties of exponents to
simplify expressions with zero
and negative exponents
Use the division properties of
exponents to simplify
exponents
Use the properties of square
roots to simplify expressions
Solve quadratic equations
using the properties of square
roots
Use the properties of radicals
to simplify expressions
Graph quadratic functions
to find solutions or roots
Determine the number of
solutions of a quadratic
function using the discriminant
and compare to number of
solutions on the graph
Solve Quadratic Equations
using the quadratic formula
8.1, 8.2
8.4
9.1
9.2
BENCHMARK #2
Winter Recess
2.0b: Understand and use such operations
as taking a root of a number.
21.0: Graph quadratic functions and know
that their roots are the
x-intercepts.
22.0: Use the quadratic formula or
factoring techniques or both to determine
whether the graph of a quadratic function
will intersect the x-axis in zero, one or two
points.
19.0: Know the quadratic formula and
become familiar with its proof by
completing the square.
20.0: Use the quadratic formula to find the
roots of a second-degree polynomial and to
solve quadratic equations.
10.0: Add, subtract, multiply, and divide
monomials and polynomials; solve
multistep problems, including word
problems, by using these techniques.
Solve Quadratic Equations
using the quadratic formula
Add and subtract polynomials
Multiply polynomials
Multiply polynomials with
special products (Connect to
10.7)
9.3
9.4 +
calculators
Introduction
(tested on BM
#4)
9.7
9.6
9.6
10.1
10.2 +
manipulatives
10.3
Number of
Questions
on CST
Algebra
Curriculum Map
2011-2012
21
1/23-27
22
1/30–2/3
23
2/6-10
24
2/14-17
25
2/21-24
26
2/27–3/2
10.0: Add, subtract, multiply, and divide
monomials and polynomials; solve
multistep problems, including word
problems, by using these techniques.
14.0 Solve a quadratic equation by
factoring or completing the square.
11.0: Apply basic factoring techniques to
second and simple third degree
polynomials; e.g. find a common factor for
all terms in a polynomial, recognize the
difference of two squares, and recognize
perfect squares of binomials.
11.0: Apply basic factoring techniques to
second and simple third degree
polynomials; e.g. find a common factor for
all terms in a polynomial, recognize the
difference of two squares, and recognize
perfect squares of binomials.
14.0: Solve a quadratic equation by
factoring or completing the square.
19.0: Know the quadratic formula and
become familiar with its proof by
completing the square.
10.0: Add, subtract, multiply, and divide
monomials and polynomials; solve
multistep problems, including word
problems, by using these techniques.
12.0: Simplifying fractions with
polynomials in the numerator and
denominator by factoring both and reducing
them to the lowest terms.
REVIEW
BENCHMARK #3
Solving quadratic equations in
Factored Form
Factor (x2 + bx + c)
expressions and equations.
Make connections to graphs of
quadratic functions.
Factor (ax2 + bx + c)
expression and equations
Find a common factor before
factoring
Factor special products, such
as the difference of two
squares and perfect squares in
expressions and equations
Factoring Cubic Polynomials
10.4
10.5 +
manipulatives
10.6 +
manipulatives
10.7
10.8
Completing the Square and
Quadratic Proof (pg. 717)
12.5
Divide polynomials
*supp.
Simplify rational expressions
11.3
Algebra
Curriculum Map
2011-2012
Week
#
Dates
Standard(s)
Topic/Objective
Textbook
Connections
27
3/5-9
Proportions
Multiplying and Dividing
Rational Expressions
Adding and Subtracting with
Like Denominators
11.1
11.4
11.5
28
3/12-16
Adding and Subtracting with
Unlike Denominators
Rational Equations
Rational Functions
11.6
11.7
11.8
29
3/19-23
13.0: Add, subtract, multiply and divide
rational expressions functions; solve both
computationally and conceptually
challenging problems by using these
techniques.
13.0: Add, subtract, multiply and divide
rational expressions functions; solve both
computationally and conceptually
challenging problems by using these
techniques.
13.0: Add, subtract, multiply and divide
rational expressions functions; solve both
computationally and conceptually
challenging problems by using these
techniques.
13.0: Add, subtract, multiply and divide
rational expressions functions; solve both
computationally and conceptually
challenging problems by using these
techniques.
13.0: Add, subtract, multiply and divide
rational expressions functions; solve both
computationally and conceptually
challenging problems by using these
techniques.
2.0d: Understand and use such operations
as raising a number to a fractional power.
Functions Involving Square
Roots
Operations with Radical
Expressions
Solving Radical Equations
Rational Exponents
12.1
12.2
12.3
12.4
30
3/26-30
4/2-6
Relations/Functions REVIEW
Counter examples/Number
4.8
*supp.
Spring Break
18.0: Determine whether a relation
defined by graph, a set of ordered pairs, or
Number of
Questions
on CST
Algebra
Curriculum Map
2011-2012
31
4/9-13
32
33
34
35
36
37
38
39
4/16-20
4//23-27
4/30 – 5/4
5/7-11
5/14-18
5/21-25
5/29-6/1
a symbolic expression is a function and
justify the conclusion
24.3: Use and know simple aspects of
logical argument: Use counterexamples to
show that an assertion is false and
recognize that a single counter example is
sufficient to refute an assertion.
25.3: Use properties of the number system
to judge the validity of results, to justify
each step of a procedure, and to prove or
disprove statements: Given a specific
algebraic statement involving linear,
quadratic, or absolute value expressions or
equations or inequalities, determine
whether the statement is true sometimes,
always, or never.
24.1: Use and know simple aspects of
logical argument: Explain the difference
between inductive and deductive reasoning
and identify and provide examples of each.
21.0: Graph quadratic functions and know
that their roots are the x-intercepts.
23.0: Apply quadratic equations to
physical problems, such as the motion of
an object under the force of gravity.
23.0: Apply quadratic equations to
physical problems, such as the motion of
an object under the force of gravity.
21.0: Graph quadratic functions and know
that their roots are the x-intercepts.
STAR testing
REVIEW FOR BENCHMARK
BENCHMARK #4
Properties/Assertions/Inductive
and Deductive Reasoning (old
Alg. Book pg. 187 and 188)
Solving Quadratic Equations by
Graphing
9.5
Quadratic Equations and
Problem Solving
Graph quadratic functions
Include finding the vertex, axis
of symmetry
*supp.
9.4
Algebra
Curriculum Map
2011-2012