Download Math Algebra Grade 8 - Morgan County School District Re-3

Morgan County School District Re-3
Month
August
Content and Essential
Questions
What is algebra?
This chapter develops some of the
basic symbolism and terminology that
students may have seen before but still
need to master. The concepts of
variables, expressions, and equations
are presented in meaningful examples
in an intuitive manner. This in turn
leads to an introduction to algebraic
problem solving that will be the basis
for problem solving throughout the
course.
Standard 1 - (1.1, 1.2, 1.5, 1.6)
Standard 3 - (3.6)
Standard 4 - (4.1, 4.5)
Standard 5 - (5.1,5.4, 5.6)
Standard 6 - (6.2, 6.3, 6.4)
September
Working with real numbers Working with real numbers This chapter focuses on using the
four operations and properties of real
numbers to simplify numerical and
algebraic expressions.
Standard 1 - (1.1, 1.5, 1.6)
Standard 6 - (6.2, 6.3, 6.4)
Math Algebra Grade 8
Skills
Students will be able to simplify
numerical expressions and evaluate
algebraic expressions. (M)
Assessment
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Students will be able to simplify
expressions with or without grouping
symbols. (M)
Students will be able to calculate and
identify solution sets of equations over
a given domain. (M)
Students will be able to translate
phrases into variable expressions,
translate word sentences into
equations, and translate simple word
problems into equations. (R)
Students will be able to analyze
number properties in order to simplify
expressions. (M)
Students will be able to demonstrate
and calculate the addition of real
numbers using a number line or
properties about opposites. (R)
Students will be able to demonstrate
and calculate the addition of real
numbers using rules of addition. (R)
Students will be able to demonstrate
and calculate the subtraction of real
numbers. (M)
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Resources
Text Book
Title: Algebra - Structure and
Method, Book 1
Copyright: 2000
Publisher: McDougal Littell
Morgan County School District Re-3
Month
October
Content and Essential
Questions
Working with real numbers - (cont.)
Math Algebra Grade 8
Skills
Students will be able to simplify and
analyze expressions involving
differences, using the distributive
property to simplify expressions. (R)
Students will be able to analyze and
calculate multiplication problems
involving real numbers. (R)
Assessment
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Text Book
Title: Algebra - Structure and
Method, Book 1
Copyright: 2000
Publisher: McDougal Littell
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Text Book
Title: Algebra - Structure and
Method, Book 1
Copyright: 2000
Publisher: McDougal Littell
Students will be able to construct and
apply equations to represent
relationships among integers. (M)
November
Solving Equations and Problems Algebraic methods of solving
equations are developed using the
properties of equality. Multistep
solutions require the use of many
properties from earlier in the year.
Standard 1 - (1.5, 1.6)
Standard 4 - (4.5)
Standard 5 - (5.1, 5.4)
Standard 6 - (6.2, 6.3, 6.4)
Students will be able to simplify
expressions involving reciprocals, and
evaluate problems involving the
division of real numbers and solving
expressions involving quotients. (M)
Students will analyze and solve
equations using addition, subtraction,
multiplication and division by
applying more than one
transformation. (R)
Students will create and apply a fivestep plan to solve work story problems.
(I)
Students will solve equations with
variables on both sides of an equation.
(M)
Students will solve problems involving
cost, income, and value. (M)
Polynomials
The concept of an exponent and the
first rules of exponents are
introduced. The addition, subtraction,
and multiplication of polynomials are
Students will solve, convert, and
simplify expressions involving
Resources
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Morgan County School District Re-3
Month
Content and Essential
Questions
developed and applied in conjunction
with additional rules of exponents.
See December for Standards.
December
Math Algebra Grade 8
Polynomials (con't)
Skills
Students will solve polynomials
through means of addition,
subtraction, multiplication, and
division. (I)
Students will also be expected to
evaluate problems by multiplying
monomials, and determine the powers
of monomials. (I)
(con't) Students will be able to analyze and
solve problems by multiplying a
polynomial by a monomial. (R)
Standard 1 - (1.1, 1.2, 1.3, 1.5, 1.6)
Standard 3 - (3.6)
Standard 4 - (4.1, 4.5)
Standard 5 - (5.1, 5.4)
Standard 6 - (6.2, 6.3, 6.4)
Students will be able to transform
formulas. (I)
This chapter develops the
factorization of composite numbers,
monomials, and polynomials. Division
of monomials is presented as a related
skill along with the rule of exponents
for division. Several lessons are
devoted to special techniques of
factoring polynomials, and one lesson
provides practice in multiplying
Resources
exponents. (R)
The concept of an exponent and the
first rules of exponents are
introduced. The addition, subtraction,
and multiplication of polynomials are
developed and applied in conjunction
with additional rules of exponents.
Factoring Polynomials
Assessment
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Students will be able to analyze and
solve problems by multiplying
polynomials. (I)
Students will solve word problems
using uniform motion. (I)
Students will be able to analyze and
solve word problems involving area
and recognize problems with no
solutions. (I)
Students will factor integers and
determine the Greatest Common
Factor (GCF) of integers. (R)
Students will simplify quotients of
monomials and demonstrate the GCF
of several monomials. (M)
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Text Book
Title: Algebra - Structure and
Method, Book 1
Copyright: 2000
Publisher: McDougal Littell
Morgan County School District Re-3
Month
Content and Essential
Questions
binomials mentally. The last part of
the chapter uses factoring and the
zero-product property to solve
polynomial equations and application
problems.
See January for Standards.
Math Algebra Grade 8
Skills
Assessment
Resources
Students will divide polynomials by
monomials and record monomial
factors of polynomials. (I)
Students will calculate the product of
two binomials mentally. (I)
Students will factor the difference of
two perfect squares and find their
products. (I)
Students will find the squares of
binomials and factor perfect square
trinomials. (I)
January
Factoring Polynomials (Con't)
This chapter develops the
factorization of composite numbers,
monomials, and polynomials. Division
of monomials is presented as a related
skill along with the rule of exponents
for division. Several lessons are
devoted to special techniques of
factoring polynomials, and one lesson
provides practice in multiplying
binomials mentally. The last part of
the chapter uses factoring and the
zero-product property to solve
polynomial equations and application
problems.
Standard 1 - (1.3)
Standard 2 - (2.3)
Students will factor quadratic
trinomials whose quadratic coefficient
is 1 and whose constant term is
positive. (I)
Students will factor quadratic
trinomials whose quadratic coefficient
is 1 and whose constant term is
negative. (I)
Students will factor general quadratic
trinomials with integral coefficients. (I)
Students will factor a polynomial by
grouping terms, factor polynomials
completely, and solve problems by
factoring quadratic equations. (I)
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Text Book
Title: Algebra - Structure and
Method, Book 1
Copyright: 2000
Publisher: McDougal Littell
Morgan County School District Re-3
Month
Content and Essential
Questions
Math Algebra Grade 8
Skills
Assessment
Resources
Standard 4 - (4.1, 4.5)
Standard 5 - (5.1, 5.4)
Standard 6 - (6.4)
February
Fractions
A thorough treatment of algebraic
fractions and operations with
fractions and mixed expressions is
presented in this chapter. Emphasis is
placed on expressing fractions in
simplest form and on dividing
polynomials using the long division
form.
Standard 1 - (1.2, 1.3, 1.4, 1.5, 1.6)
Standard 4 - (4.3, 4.5)
Standard 6 - (6.2, 6.4)
March
Students will simplify algebraic
fractions, and multiply and divide
algebraic fractions. (M)
Students will express two or more
fractions with their least common
denominator, and add and subtract
algebraic fractions. (R)
Students will construct mixed
expressions as fractions in simplest
form. (R)
Students will simplify problems by
dividing polynomials. (M)
CSAP Awareness
Developing methods geared towards
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Text Book
Title: Algebra - Structure and
Method, Book 1
Copyright: 2000
Publisher: McDougal Littell
Students will investigate data
collection and analysis, statistics, and
Individual class time, teacher
observation, discussion, and individual
work.
CSAP released items, sample
problems, and problems collected by
the teacher needed to address
Morgan County School District Re-3
Month
Math Algebra Grade 8
Content and Essential
Questions
Skills
understanding, interpreting, and
answering CSAP type questions using
released items and practice tests. In
addition, due to the specificity of the
algebra class, other topics such as
geometry, statistics and probability,
graphing data, and data analysis will
be covered.
probability in problem solving
situations and interpret the reasoning
used in solving these problems. (R)
Assessment
Resources
standards not covered in the text.
Students will apply geometric
concepts, properties, and relationships
in problem solving situations and
analyze the reasoning used in solving
these problems. (R)
Standard 1 - (1.1, 1.2, 1.4, 1.5, 1.6)
Standard 2 - (2.1, 2.2, 2.3, 2.5)
Standard 3 - (3.1, 3.2, 3.3, 3.4, 3.5,
3.7)
Standard 4 - (4.2, 4.4, 4.6)
Standard 5 - (5.2, 5.3, 5.5)
Standard 6 - (6.1)
Applying Fractions
This chapter presents a wide variety of
equations and word problems related
to algebraic fractions. Ratios are
introduced and proportions are solved
as a special case of fractional
equations. Extensive treatment is
given to solving equations with
fractional coefficients and fractional
equations.
Percents, decimals, mixture problems,
and scientific notation are also
specifically covered.
April
Standard 1 - (1.1, 1.2, 1.4, 1.5, 1.6)
Standard 2 - (2.2, 2.3)
Standard 4 - (4.3)
Standard 5 - (5.2)
Standard 6 - (6.1, 6.2, 6.3, 6.4)
Introduction to Functions
Students will solve problems involving
ratios and proportions. (M)
Class participation, teacher
observation, homework, quizzes, and
chapter test.
Text Book
Title: Algebra - Structure and
Method, Book 1
Copyright: 2000
Publisher: McDougal Littell
Class participation, teacher
Text Book
Students will solve equations with
fractional coefficients. (M)
Students will solve fractional
equations. (M)
Students will convert problems
involving percents and decimals. (M)
Students will analyze mixture and
word problems. (I)
Students will solve equations with two
Morgan County School District Re-3
Month
Content and Essential
Questions
This chapter introduces the basic tools
for working with linear equations in
two variables. Solution sets of linear
equations are represented graphically
using the coordinate plane. The slope
of a line is defined, and the standard
and slope-intercept forms of a line's
equation are examined. Lines are
graphed from given equations, and
equations are determined from given
facts about a line.
Functions are defined by tables,
graphs, and equations. Special
attention is given to linear and
quadratic functions.
Standard 2- (2.1, 2.2, 2.3, 2.4, 2.5)
Standard 6- (6.2, 6.3)
Math Algebra Grade 8
Skills
variables over given domains of the
variables. (R)
Assessment
observation, homework, quizzes, and
chapter test.
Students will graph ordered pairs and
linear equations. (R)
Students will determine the slope of a
line using the slope, y-intercept form
of a linear equation. (M)
Given the slope of a line and one point,
or given two points of a line, students
will determine the equation of a line.
(I)
Students will identify a function,
define a function by using tables and
graphs, and equations. (R)
Students will graph both linear and
quadratic functions. (M, I)
May
Systems of Linear Equations
This chapter shows how to find the
solutions that are common to two
linear equations in two variables.
Three methods of solving a system of
linear equations are introduced: the
graphing method, the substitution
method, and the addition and
subtraction method.
Problem solving skills are extended
to include many types of problems
associated with systems of linear
equations such as wind and water
current problems, age, digit, and
fraction puzzle problems.
Standard 2- (2.1, 2.2, 2.3, 2.4, 2.5)
Students will use graphs to solve
systems of linear equations. (R)
Students will use the substitution
method to solve systems of linear
equations. (I)
Students will use the addition or
subtraction method with multiplication
or division to solve systems of linear
equations. (I)
Students will use the multiplication
with the addition or subtraction method
to solve systems of linear equations. (I)
Students will use systems of equations
to solve wind and water current
Test, quizzes, and homework.
Resources
Title: Algebra - Structure and
Method, Book 1
Copyright: 2000
Publisher: McDougal Littell
Morgan County School District Re-3
Month
Content and Essential
Questions
Standard 6- (6.2, 6.4)
Math Algebra Grade 8
Skills
Assessment
problems, and using systems of
equations to solve digit, age and
fraction puzzle problems. (I)
Inequalities
The introduction to inequality
symbols from Chapter 1 provides the
background for a more formal study
of inequalities in this chapter. The
order of the real numbers leads to the
study of inequalities with one variable
and their graphs.
Techniques for solving inequalities
are developed. Methods for solving
simple inequalities are extended to
include conjunctions, disjunctions,
and absolute value.
Linear inequalities in two variables
and systems of such inequalities are
investigated with emphasis on their
graphs.
Students will determine the relative
value of real numbers by placing them
on a number line. (R)
Students will solve absolute value
problems and absolute values of
products in an open sentence. (I)
Students will graph linear inequalities
and systems of linear inequalities. (M)
Standard 1- (1.2, 1.5, 1.6)
Standard 2- (2.1, 2.2, 2.3, 2.4, 2.5)
Standard 6- (6.2)
Rational and Irrational numbers
Rational numbers and their properties
are defined and then examined in
both the decimal and square root
form. Irrational numbers are then
introduced in terms of irrational
square roots. Finding the square root
of a variable expression leads to the
Pythagorean Theorem and its
Students will examine and
demonstrate the properties of rational
numbers, decimal forms of rational
numbers, rational square roots,
irrational square roots, square roots
with variable expressions, the
Pythagorean theorem, and multiplying,
Test, quizzes, and homework
Resources
Morgan County School District Re-3
Month
Content and Essential
Questions
applications.
Math Algebra Grade 8
Skills
Assessment
dividing, and simplifying radicals. (I,
R, M)
Test, quiz, and homework
Quadratic Functions
Students will be introduced to the
quadratic equation as an alternative
method of solving quadratic
equations.
Students will be able to solve quadratic
equations by using the quadratic
equation.
(I)
Final Comprehensive Test
Summary of yearly content
Final Test
Resources