Download Algebra 1 - Berlin Community School

Berlin Community School
8 Algebra 1
Teacher: Middle School (6-8) Math
Month
September
2010
Content
A. Problem Solving with the 4 Step
Process
B. Tesselations and Fractals
Skills
A. Use the 4 Step Process to solve
problems, Choose an appropriate method
of computation
Materials
Algebra 1,Glencoe, 2006
http://library.thinkquest.org/16661
/
B. Indentify and Construct Tesselations
C. Variables and Expressions
C. Write mathematical expressions for
verbal expressions, Write verbal
expressions for mathematical
expressions
D. Order of Operations
D. Evaluate numerical expressions by
using the order of operations, Evaluate
algebraic expressions by using the order of
operations
E. Open Sentences
E. Solve open sentence equations, Solve
open sentence inequalities
F. Identity and Equality Properties
F. Recognize the properties of identity and
equality, Use the properties of identity and
equality
G. The Distributive Property
G. Use the Distributive Property to
evaluate expressions, Use the Distributive
Property to simplify expressions
H. Commutative and Associative
Properties
H. Recognize the Commutative and
Associative Properties, Use the
Commutative and Associative Properties to
simplify expressions
I . Logical Reasoning
Assessment
A-K. Teacher Observation-Dry Erase
Boards, Quiz, Test
-Dry Erase Boards
-Paper (Colored, Graphing)
-Tape
-Rulers
-Sissors
-Colored Pencils, Markers
-Journals
-Calculators
-Graphing Calculators
I. Identify the hypothesis and conclusion in
a conditional statement, Use a
counterexample to show that an assertion is
false
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8 Algebra 1
Math
Month
Content
Skills
J. Graphs and Functions
J. Interpret graphs of functions, Draw
graphs of functions
K. Statistics: Analyzing Data by Using
Tables and Graphs
K. Analyze data given in tables and graphs
(bar, line, and circle), Determine whether
graphs are misleading
Mathematical Processes (Daily/On-going)
October
2010
Berlin Community School
A. Rational Numbers on the Number Line
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas
A. Graph rational numbers on a number
line, Find absolute values of rational
numbers.
B. Adding and Subtracting Rational
Numbers
B. Add integers and rational numbers,
Subtract integers and rational numbers.
C. Multiplying and Dividing Rational
Numbers
C. Multiply and divide integers, Multiply
and Divide rational numbers.
D. Statistics: Displaying and Analyzing
Data
D. Interpret and create line plots and stemand leaf plots, Analyze data using mean,
median, and mode.
E. Probability: Simple Probability and
Odds
Assessment
A-O. Teacher Observation-Dry Erase
Boards, Quiz, Test
Materials
Algebra 1,Glencoe, 2006
-Dry Erase Boards
-Paper (Colored, Graphing)
-Rulers
-Journals
-Calculators
-Graphing Calculators
E. Find the probability of a simple event,
Find the odds of a simple event.
F. Find square roots, Classify and order
real numbers.
F. Square Roots and Real Numbers
G. Writing Equations
G.Translate verbal sentences into
equations, Translate equations into verbal
sentences.
H. Solve equations by using addition and
subtraction.
H. Solving Equations by Using Addition
and Subtraction
I. Solve equations by using multiplication
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8 Algebra 1
Math
Month
Content
Berlin Community School
Skills
Assessment
Materials
and division.
I. Solving Equations by Using
Multiplication and Division
J. Solving Multi-Step Equations
K. Solving Equations with the Variable on
Each Side
J. Solve problems by working backward,
Solve equations involving more than one
operation.
K. Solve equaitons with the variable on
each side, Solve equations involving
grouping symbols.
L. Determine whether two ratios form a
proportion, Solve proportions.
L. Ratios and Proportions
M. Percent of Change
M. Find percents of increase and decrease,
Solve problems involving percents of
change.
N. Solve equations for given variables, Use
formulas to solve real-world problems.
N. Solving Equations and Formulas
O. Solve mixtures problems, Solve uniform
motion problems.
O. Weighted Averages
Mathematical Processes (Daily/On-going)
November
2010
A. The Coordinate Plane
B. Transformations on the Coordinate
Plane
C. Relations
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas.
A. Locate points on the coordinate plane,
Graph points on a coordinate plane.
B. Transform figures by using reflections,
translations, dilations, and rotations,
Transform figures on a coordinate plane by
using reflections, translations, dilations,
and rotations.
A-E. Teacher Observation-Dry Erase
Boards, Quiz, Test
Algebra 1,Glencoe, 2006
-Dry Erase Boards
-Paper (Colored, Graphing)
-Rulers
-Journals
-Calculators
-Graphing Calculators
C. Represent relations as sets of ordered
pairs, tables, mappings, and graphs, Find
the inverse of a relation.
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8 Algebra 1
Math
Month
Content
D. Equations as Relations
E. Graphing Linear Equations
Mathematical Processes (Daily/On-going)
December
2010
January
2011
A. Functions
Berlin Community School
Skills
Materials
E. Determine whether an equation is linear,
Graph linear equations.
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas.
A. Determine whether a relation is a
function, Find function values.
B. Arithmetic Sequences
B. Recognize arithmetic sequences, Extend
and write formulas for arithmetic
sequences.
C. Writing Equations from Patterns
C. Look for a pattern, Write an equation
given some of the solutions.
D. Venn Diagrams
D. Use Venn Diagrams to solve problems
involving two and three sets.
Mathematical Processes (Daily/On-going)
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas.
A. Find the slope of a line, Use rate of
change to solve problems.
A. Slope
Assessment
D. Use an equation to determine the range
for a given domain, Graph the solution set
for a given domain.
B. Slope and Direct Variation
B. Write and graph direct variation
equations, Solve problems involving direct
variation.
C. Slope-Intercept Form
C. Write and graph linear equations in
slope-intercept form, Model real world data
with an equation in slope intercept form.
A-D. Teacher Observation-Dry Erase
Boards, Quiz, Test
Algebra 1,Glencoe, 2006
-Dry Erase Boards
-Paper (Colored, Graphing)
-Rulers
-Journals
-Calculators
-Graphing Calculators
A-H. Teacher Observation-Dry Erase
Boards, Quiz, Test
Algebra 1,Glencoe, 2006
-Dry Erase Boards
-Paper (Colored, Graphing)
-Rulers
-Journals
-Calculators
-Graphing Calculators
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8 Algebra 1
Math
Month
February
2011
Content
Berlin Community School
Skills
D. Writing Equations in Slope-Intercept
Form
D. Write an equation of a line given the
slope and one point on a line, Write an
equation of a line given two points on the
line.
E. Writing Equations in Point-Slope Form
E. Write the equation of a line in pointslope form, Write linear equations in
different forms.
F. Geometry: Parallel and Perpendicular
Lines
F. Write an equation of the line that passes
through a given point, parallel or
perpendicular to a given line.
G. Statistics: Scatter Plots and Lines of Fit
G. Interpret Points on a scatter plot, Write
equations for lines of fit.
H. Solving Multi-step Inequalities
H. Solve linear inequalities by using
addition, subtraction, multiplication, and
division, Solve linear inequalities involving
more than one operation, and involving the
Distributive Property.
Mathematical Processes (Daily/On-going)
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas.
A. Solve compound inequalities containing
the words 'and' or 'or' and graph their
solution sets.
A. Solving Compound Inequalities
B. Solving Open Sentences Involving
Absolute Value
B. Solve absolute value equations and
absolute value inequalites.
C. Graphing Inequalities in Two Variables
C. Graph inequalities on the coordinate
plane, Solve real world problems involving
linear inequalities.
Assessment
A. -H. Teacher Observation-Dry Erase
Boards, Quiz, Test
Materials
Algebra 1,Glencoe, 2006
-Dry Erase Boards
-Paper (Colored, Graphing)
-Rulers
-Journals
-Calculators
-Graphing Calculators
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8 Algebra 1
Math
Month
March
2011
Content
Berlin Community School
Skills
D. Graphing Systems of Equations
D. Determine whether a system of linear
equations has 0,1, or infinitely many
solutions, Solve systems of equations by
graphing.
E. Substitution
E. Solve systems of equations by using
substitution, Solve real world problems
involving systems of equations.
F. Elimination
F. Solve systems of equations by using
elimination with addition, subtraction,
multiplication and division, Determine the
best method for solving systems of
equations.
G. Graphing Systems of Inequalities
G. Solve systems of inequalities by
graphing, Solve real-world problems
involving systems of inequalities.
H. Multiplying and Dividing Monomials
H. Multiply and divide monomials,
Simplify expressions involving powers of
monomials, Simplify expressions involving
the quotient of monomials, and those
containing negative exponents.
Mathematical Processes (Daily/On-going)
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas
A. Express numbers in scientific notation
and standard notation, Find products and
quotients of numbers expressed in
scientific notation.
A. Scientific Notation
Assessment
A. -Q. Teacher Observation-Dry Erase
Boards, Quiz, Test
Materials
Algebra 1,Glencoe, 2006
Success Work-a-text in Mathematics,
Instructivision, Inc., c.1998
B. Polynomials
B. Find the degree of a polynomial,
Arrange the terms of a polynomial in
ascending or descending order.
The New Jersey GEPA Mathematics
Coach, by Mervine Edwards, Educational
Design, c. 2000
C. Adding and Subtracting Polynomials
C. Add and subtract polynomials.
Preparing for the Proficiency Assessment:
NJ Grade 8 GEPA Mathematics, Prentice
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8 Algebra 1
Math
Month
Content
D. Multiplying a Polynomial by a
Monomial
Berlin Community School
Skills
D. Find the product of a monomial and a
polynomial, Solve equations involving
polynomials.
E. Multiplying Polynomials
E. Multiply two binomials by using the
FOIL Method, Multiply two polynomials
by using the Distributive Property.
F. Special Products
F. Find the squares of sums and
differences, Find the product of a sum and
a difference.
G. Place Value
G. Identifying, reading, and writing
numbers using correct notation and
vocabulary.
H. Rounding Numbers
I. Percents and Decimals
J. Percent of a Number
K. Compound Interest
L. Primes, Multiples, and Factors
Assessment
Materials
Hall, c. 2007
-Dry Erase Boards
-Paper (Colored, Graphing)
-Rulers
-Journals
-Calculators
-Graphing Calculators
H. Rounding numbers to the nearest ten,
hundred, thousand, dollar, cent, tenth,
hundredth, thousandth; Finding the
smallest and largest possible value that will
round to a given number and place value.
I. Writing percents as equivalent decimals
and fractions.
J. Solving a variety of problems using
percents, Comparing effects of percent
increase and decrease in a variety of
situations.
K. Applying exponential growth and decay
formulas (compound interest, bacteria,
population, etc.); Recognizing and
Describing the difference between linear
and exponential growth.
L. Applying concepts of factoring a
number into primes, Applying concepts of
multiples of a number, Using inequalities
of represent and describe relationships
between numbers.
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8 Algebra 1
Math
Month
Content
Berlin Community School
Skills
M. Temperature
M. Converting Temperatures between
Fahrenheit and Celsius Scales.
N. Adding, Subtracting, Multiplying and
Dividing with Integers
N. Solving problems that involve Adding,
Subtracting, Multiplying and Dividing with
Integers.
O. Absolute Value
O. Applying the definition of absolute
value to solve problems.
Assessment
Materials
P. Solving problems involving factorial.
P. Factorial
Q. Ratio and Proportion
Mathematical Processes (Daily/On-going)
April 2011
A. Two Dimensional Figures
Q. Illustrate, model, and solve problems
involving ratios and proportions.
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas
A. Using properties, definitions, and
relationships to classify and identify two
dimensional figures. Applying
relationships of perpendicularity and
parallelism, determining angle measures
for 2 dimensional figures.
B.Three Dimensional Visualization
B. Using properties, definitions, and
relationships to identify, classify, and
describe three dimensional figures and
their parts.
C. Units of Measurement
C. Converting from smaller to larger units
and vice versa in a system, Finding
approximate equivalents between systems,
Solving problems requiring calculations
that involve different units of
measurement, Selecting appropriate units
for a given situation and using appropriate
A. -O. Teacher Observation-Dry Erase
Boards, Quiz, Test
Success Work-a-text in Mathematics,
Instructivision, Inc., c.1998
The New Jersey GEPA Mathematics
Coach, by Mervine Edwards, Educational
Design, c. 2000
Preparing for the Proficiency Assessment:
NJ Grade 8 GEPA Mathematics, Prentice
Hall, c. 2007
-Dry Erase Boards
-Paper (Colored, Graphing)
-Rulers
-Journals
-Calculators
-Graphing Calculators
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8 Algebra 1
Math
Month
Content
Berlin Community School
Skills
Assessment
Materials
tools to measure various quantities,
Recognizing the degree of precision
needed for a given problem.
D. Surface Area and Volume of Three
Dimensional Figures
D. Calculating the surface area and volume
for three dimensional figures.
E. Perimeter, Area, and Circumference
E. Applying a variety of strategies to
determine perimeter, area, and
circumference of regular and irregular
figures.
F. Transformations
F. Finding an image or pre-image,
Applying reflections, rotations,
translations, and dilations to a pre-image,
Mapping figures on to others using
transformations.
G. Probability
G. Interpreting probablities as ratios,
percents, and decimals, Determining
probabilities of independent and dependent
compound events, Designing and analyzing
simulations, Classifying probablilites as
Experimental or Theoretical, Determining
fairness and expected values.
H. Permutations and Combinations
H. Using the Multiplication Principle of
Counting to find the total number of
possibilities, Determining whether order is
important for a situation, Finding the
permutations and combinations for real life
situations.
I.Counting Procedures: Trees and
Networks
J. Data Displays
I. Using techniques of counting,
constructing networks and trees, analyzing
and applying networks to real-life
situations, Determining traversibility.
J. Creating, Reading and interpreting Data
from data displays: bar graphs, circle
graphs, box-and-whisker plots, scatter
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8 Algebra 1
Math
Month
Content
Berlin Community School
Skills
Assessment
Materials
plots, and frequency tables, Drawing lines
of best fit and using them to predict
results.
K. Fractals
K. Recognizing and constructing fractals at
various stages.
L. Patterns
L. Recognize, describe, extend and create
patterns using tables, rules, graphs,
expressions and equations.
M. Graphing Equations and Functions
M. Graph, understand and describe
behaviors of functions involving two
variables.
N. Slope
N. Determine the slope of a line given 2
points, a graph of a line, or the equation of
a line.
O. Linear and Exponential Growth
O. Recognize and Describe the difference
between exponential and linear growth
using tables, graphs, and equations.
Mathematical Processes (Daily/On-going)
May 2011
A. Factors and Greatest Common Factors
B. Factoring Using the Distributive
Property
C. Factoring Trinomials: x^2 + bx+ c
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas
A. Find prime factorizations of integers
and monomials, Find the greatest common
factors of integers and monomials.
B. Factor polynomials by using the
Distributive Property, Solve quadratic
equations of the form ax^2 +bx=0.
C. Factor trinomials of the form x^2 +
bx+c, Solve equations of the form x^2 +
bx+c=0.
A. -J. Teacher Observation-Dry Erase
Boards, Quiz, Test
Algebra 1,Glencoe, 2006
-Dry Erase Boards
-Paper (Colored, Graphing)
-Rulers
-Journals
-Calculators
-Graphing Calculators
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8 Algebra 1
Math
Month
Content
D. Factoring Trinomials: ax^2 + bx + c
Berlin Community School
Skills
Assessment
Materials
D. Factor trinomials of the form
ax^2+bx+c, Solve equations of the form
ax^2 +bx+c=0.
E. Factoring Differences of Squares
E. Factor binomials that are the differences
of squares, Solve equations involving
differences of squares.
F. Perfect Squares and Factoring
G. Simplifying Radical Expressions
F. Factor perfect square trinomials, Solve
equations involving perfect squares.
A.-F.
G. Simplify radical expressions using the
Product Property of Square Roots, Simplify
radical expressions using the Quotient
Property of Square Roots.
H. Operations with Radical Expressions
H. Add and subtract radical expressions,
Multiply radical expressions.
I. Radical Equations
J. The Distance Formula
Mathematical Processes (Daily/On-going)
June 2011
A. Rational Expressions
I. Solve radical equations, Solve radical
equations with extraneous solutions.
G.-I.
J. Find the distance between two points on
the coordinate plane using the Pythagorean
Theorem and using the Distance
Formula.
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas.
A. Identify values excluded from the
domain of a rational expression, Simplify
rational expressions.
B. Multiplying Rational Expressions
B. Multiply rational expressions.
C. Review of all content covered
C. All Skills covered September through
A.-B. Teacher Observation-Dry Erase
Boards
Algebra 1,Glencoe, 2006
C. Cumulative Final for the Course
-Dry Erase Boards
-Paper (Colored, Graphing)
-Rulers
-Journals
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8 Algebra 1
Math
Month
Content
Berlin Community School
Skills
September through June
June.
Mathematical Processes (Daily/On-going)
Problem Solving, Communicating, Making
Connections, Reasoning, Making and
Analyzing, Representations, and Using
Technology to Solve Problems and
Communicate Mathematical Ideas
Assessment
Materials
-Calculators
-Graphing Calculators
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