Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community.
Course Number 405/406/407 Title Algebra I (A, B, C) Grade 9 # of Days 180Course Description / This is the essential foundation for all following Mathematics courses and for the bulk of preparation for the Grade 10 MCAS test. Algebra I will run the entire school year. Topics will include variables, solving equations and inequalities, linear sentences, graphing and systems. Symbolism is used to express abstract ideas. Real life applications will be included for all topics. This course addresses Whitman-Hanson Student Learning Expectations 1-6.
Instructional Strategies / Instructional Strategies include but may not be limited to the following:
1. Whole class instruction
2. Individual work: homework, classwork, assessments
3. Group work: activities, problem solving
4. Experiments, demonstrations, investigations
5. Video presentations
6. Use of technology (graphing calculators and computers)
7. Projects
Student Learning Expectations / 1.Read, write and communicate effectively.
2.Utilize technologies appropriately and effectively.
3.Apply critical thinking skills.
4.Explore and express ideas creatively.
5.Participate in learning both individually and collaboratively.
6.Demonstrate personal, social, and civic responsibility.
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Part A Major Concepts / Topics / Student ExpectationsTools of Algebra - Chapter 1
Variables / Definition of Variable / Identify variables in expressions and equations
Use of Variables in Expressions and Equations / Translate verbal descriptions to algebraic expressions
Write algebraic expressions from tabular data
Order of Operations / Simplifying Expressions / Apply Order of Operations to reduce to simplest form
Definition of Exponents / Translate between exponential and repeated multiplication forms
Evaluating Expressions with Parentheses & Exponents / Substitute and simplify expressions with parentheses and exponents
Exploring Real Numbers / Definitions of Number Sets / Identify or differentiate between naturals, wholes, integers, rationals, irrationals and reals
Inequality / Compare the values of two expressions
Use <, >, ≤, ≥, =, ≠ appropriately when comparing two real numbers
Absolute Value / Define absolute value as the distance from zero on a number line
Simplify an absolute value expression ex: |-4| = 4
Operations on Real Numbers / Addition and Subtraction / Know and apply the identity element for addition and subtraction is zero
Find the additive identity (opposite) of a number
State the Inverse Property of Addition ex: a + -a = 0
Use the number line model to add or subtract real numbers
Use the tile model to add or subtract real numbers
Multiplication and Division / Know and apply the identity element for multiplication and division is one
Find the multiplicative inverse (reciprocal) of a number
State the Inverse Property of Multiplication ex: a • 1/a = 1
Know and apply the Multiplication Property of 0 ex: a • 0 = 0
Know and apply the Multiplication Property of -1 ex: a • -1 = -a
Multiply and divide real numbers
Matrices / Define a matrix by the number of rows and columns
Determine whether two matrices can be added or subtracted
Perform scalar multiplication on a matrix
Properties of Real Numbers / The Distributive Property / Use the Distributive Property to simplify expressions
Define and use coefficient, constant, term and like term appropriately
Identify and combine like terms (similar terms) with multiply variables and exponents
Commutative Property / Know and apply the Commutative Property of Addition ex: a + b = b + a
Know and apply the Commutative Property of Multiplication ex: a • b = b • a
Associative Property / Know and apply the Associative Property of Addition
ex: (a + b) + c = a + (b + c)
Know and apply the Associative Property of Multiplication
ex: (a • b) • c = a • (b • c)
Coordinate Plane Graphing / Definitions / Identify x and y axes, the quadrants and the origin
Graphing / Plot ordered pairs (coordinates)
Scatter Plots / Create appropriate horizontal and vertical scales to plot real data points
Determine positive, negative or no correlation of the scatter plot
Sketch the trend line (line of best fit) for correlated data
Major Concepts / Topics / Student Expectations
Solving Equations - Chapter 2
One Step Equations / Properties of Equality / Name and apply the addition, subtraction, multiplication and division properties to solve equations
Inverse Operations / Determine the inverse operation for a given equation
Recognize division, and multiplication by the reciprocal, as equivalent steps
Use inverse operations to solve equations using real numbers
Two-Step Equations / Isolate the Variable Term, then Isolate the Variable / Use Algebra tiles to solve two-step equations
Use inverse operations in the correct order to solve equations using real numbers
Multi-Step Equations / Simplifying before Solving / Combine like terms before solving the equation
Use the Distributive Property to eliminate grouping symbols before solving
Multiply to eliminate fractions from all terms before solving
Multiply to eliminate decimals from all terms before solving
Variables on Both Sides / Equations with a Single Solution / Combine like terms: variable terms on one side, numbers on the other
Identities-Equations with Many Solutions / Recognize solutions of identities as 5=5 or any a=a
Equations with No Solution / Recognize equations with no solution when 4 = 8 or any a = b
Solving Equations with Matrices on Both Sides / Solve equations made from corresponding elements from each matrix
Equations and Problem Solving / Defining One Variable in Terms of Another / Define a variable and use it to write other algebra expressions for parts in the problem
Write and solve equations using several terms and only one variable
Consecutive Number Problems / Define a variable and increase it for consecutive integers, consecutive odd or even integers, consecutive multiples
Distance-Rate-Time Problems (Uniform Motion) / Make a table to organize data for rate, time and distance and use the table to write an equation
Formulas / Transforming Literal Equations / Use properties of equality to rewrite a literal equation in terms of a different variable
Measures of Central Tendency / Mean, Median, Mode and Range / Differentiate between mean, median and mode
Calculate the mean, median, mode and range
Stem and Leaf Plots / Create a one or two-sided stem and leaf plot from a set of data
Determine the mean, median, mode and range from a stem and leaf plot
Major Concepts / Topics / Student Expectations
Solving Inequalities - Chapter 3
Inequalities and their Graphs / Finding Solutions / Determine a solution to an inequality by inspection or evaluation
Graph the solution to an inequality on a number line with open/closed circles and arrows
Solving Inequalities Using Addition and Subtraction / Addition Property of Inequality / Use the Addition Property of Inequality to solve inequalities
Subtraction Property of Inequality / Use the Subtraction Property of Inequality to solve inequalities
Solving Inequalities Using Multiplication and Division / Multiplication Property of Inequality for c>0 / Apply the Multiplication Property of Inequality for c>0 by multiplying both sides of the inequality by a positive number
Multiplication Property of Inequality for c<0 / Apply the Multiplication Property of Inequality for c<0 by multiplying both sides of the inequality by a negative number and reversing the inequality sign
Division Property of Inequality / Apply the Division Property of Inequality for c>0 and c<0 by dividing both sides of the inequality by c and leaving the inequality alone or reversing it respectively.
Solving Multi-Step Inequalities / Simplifying before Solving / Combine like terms before solving the equation
Use the Distributive Property to eliminate grouping symbols before solving
Collect variables on one side of the inequality and numbers on the other before solving
Compound Inequalities / Writing a Compound Inequality / Write a compound inequality from a number line graph of one segment with two endpoints or two sections with arrows heading in opposite directions
Compound Inequalities Joined by "and" / Know that solutions to the inequality must make both inequalities true
Know that the solution on the graph will be one segment
Compound Inequalities Joined by "or" / Know that solutions to the inequality can make either inequality true
Know that the solution on the graph will be two rays heading in opposite directions
Absolute Value Equations and Inequalities / Solving Absolute Value Equations / Calculate two correct answers to an absolute value equation (|a| = b) by creating two equations joined by "or" ( a = b or a = -b )
Solving Absolute Value Inequalities / Rewrite and absolute value inequality using "and" with < or ≤ and using "or" with > and ≥
Calculate two correct answers to an absolute value inequality by creating two equations joined by "or" or "and"
Given |a| > b use a > b or a < -b
Given |a| < b use a < b and a > -b leading to -b < a < b
Applying Absolute Value in Quality Control situations / Write an absolute value inequality to describe an acceptable tolerance
Major Concepts / Topics / Student Expectations
Solving and Applying Proportions - Chapter 4
Ratio and Proportion / Definitions / Define terms such as: ratio, proportion, unit analysis, unit rate, means and extremes of a proportion, cross products
Find the unit rate
Unit Analysis / Convert from one set of units to another by multiplying by conversion factors
Solving Proportions / Solve a proportion by cross multiplying and setting cross products equal
Solve a proportion by multiplying a binomial by a monomial
Proportions and Similar Figures / Similar Figures / Define similar figures as those with the same shape but different size, the angle measures are equal and the sides are proportional
Use the ~ symbol for similar figures ex: Δ ABC ~ Δ DEF
Use similar figures to determine indirect measurement
Use scale and a drawing to determine actual size
Proportions and Percent Equations / Applying Proportions to Percent Problems / Use part/whole = n/100 to solve percent problems
Change the % to a #/100 to solve part/whole problems
Writing Percent Equations / Translate verbal descriptions to algebraic percent equations and solve
Solve percent equations with percents greater than 100% or less than 1%
Estimating with Percents / Use fractional quantities to estimate percents ex: 32% ≈ ⅓ 32% of 18 ≈ 6
Percent of Change / Percent of Change / Calculate the percent increase
Calculate the percent decrease
Determine the greatest possible error or a measuring unit
Calculate the percent error
Applying Ratios to Probability / Definitions / Define: probability, outcome, sample space, event, theoretical probability, complement of an event, experimental probability, P(A), P(not A)
Change decimal results to percentage results when calculating probability
Theoretical Probability / Determine the theoretical probability by finding the number of possible favorable outcomes / the sample space
Determine the complement of an event ex: P(not event) = 1 - P(event)
Experimental Probability / Determine the experimental probability by counting the number of times a favorable event happens / the number of times the experiment was done
Law of Large Numbers / Explain that experimental probability will be closer to theoretical probability when the amount of data is large
Probability of Compound Events / Independent Events / Define independent events as events that do not influence one another ex: drawing cards with replacement
Apply P(A and B) = P(A) • P(B) to determine probability
Dependent Events / Define dependent events as events that influence one another because the occurrence of one event affects the probability of the other ex: drawing cards without replacement
Apply P(A then B) = P(A) • P(B after A) to determine probability
Part B Major Concepts / Topics / Student Expectations
Graphs and Functions - Chapter 5
Relating Graphs to Events / Story Graphs / Using labels and the horizontal and vertical scale, describe the changes in a graph with a story
Given a story, sketch a graph with appropriate changes for each part of the story
Relations and Functions / Definitions / Define relation, domain, range, function, function rule, function notation, vertical line test
Functions / Determine whether a relation is a function by the vertical line test
Determine whether a relation is a function by examining tables and mapping diagrams
Evaluate a function by substituting and solving for f(n)
Find the range given the domain
Function Rules, Tables and Graphs / Independent vs. Dependent Variables / Differentiate between independent and dependent variables as input and output
Differentiate between independent and dependent variables as x and y values
Differentiate between independent and dependent variables on the horizontal and vertical axes
The Rule of Four / Show an algebraic, graphic, numeric and verbal display of a function ex: f(x) = 2x + 4, a linear graph, a table of values and a verbal description for each function
Writing a Function Rule / Writing a Rule from a Table / Write a rule from a table that is a linear or a simple quadratic (f(x) = x^2 + c)
Writing a Rule from a Verbal Description / Write a rule from a verbal description that is a linear or a simple quadratic (f(x) = x^2 + c)
Writing a Rule from a Graph / Write a rule from a graph that is a linear or simple quadratic (f(x) = x^2 + c)
Direct Variation / Definitions / Define direct variation, constant of variation
Direct Variation Equation / Determine if an equation is a direct variation in the form y = kx
Find the constant of variation (k)
Write the equation of direct variation given a point
Use a table to determine the constant of variation k = y/x
Describing Number Patterns / Definitions / Define inductive reasoning, conjecture, sequence, term, arithmetic sequence, common difference, input, output
Extend Number Patterns / Use inductive reasoning to extend number patterns to the next 4 terms
Arithmetic Sequences / Use the common difference in A(n) = a + (n - 1) d to extend the pattern to the nth term of an arithmetic sequence
Major Concepts / Topics / Student Expectations
Linear Equations and Their Graphs - Chapter 6
Rate of Change and Slope / Definitions / Define rate of change, slope, positive slope, negative slope, zero slope, undefined slope
Calculating Slope / Find the rate of change using a table
Find the rate of change using two points on a graph
Find the slope using two given points or two points on a graph
Find the slope of a horizontal line using two points or memorization
State the slope of a vertical line is undefined
Slope-Intercept Form / Definitions / Define y-intercept, slope-intercept form
y-intercept / Find the y-intercept by looking at a graph
Slope-Intercept Form / Find the slope and y-intercept by looking at the equation y = mx + b
Write an equation in slope-intercept form given the slope and the y-intercept
Write an equation in slope-intercept form from a graph
Graph an equation in slope-intercept form
Standard Form / Definitions / Define standard form of a linear equation, x-intercept
x and y-intercepts / Find x-intercept by making y=0 and solving for x
Find y-intercept by making x=0 and solving for y
Graph a line using the x and y-intercepts
Graph a horizontal line by keeping the y value constant
Graph a vertical line by keeping the x value constant
Transform an equation in slope-intercept form to standard form through algebra
Point-Slope From and Writing Linear Equations / Definitions / Define point-slope form
Point-Slope Form / Graph a line in point-slope form
Write the equation of a line in point-slope form given a point and a slope
Write the equation of a line in point-slope form given two points
Write the equation of a line in point-slope form given a table of data
Parallel & Perpendicular Lines / Definitions / Define parallel lines, perpendicular lines, negative reciprocal slope, right angle
Parallel Lines / Determine whether two lines are parallel given any form of the linear equations
Write the equation of a line through a given point, parallel to another line
Perpendicular Lines / Find the slope of a line perpendicular to a given line
Write the equation of a line through a given point, perpendicular to a given line
Scatter Plots & Equations of Lines / Definitions / Define line of best fit, correlation coefficient
Trend Lines or Lines of Best Fit / Draw a trend line (line of best fit) from a scatter plot
Use points on the trend line to estimate the equation of the line
Use a graphing calculator to find the equation of a line of best fit
Use a graphing calculator to find the correlation coefficient, r
Absolute Value Equations / Definitions / Define absolute value equation, translation
Absolute Value Equations / Graph the absolute value equation with a vertical translation
Graph the absolute value equation with a horizontal translation
Write the equation of an absolute value function using horizontal and/or vertical translations to y = |x|
Major Concepts / Topics / Student Expectations
Systems of Equations and Inequalities - Chapter 7
Solving Systems by Graphing / Definitions / Define system of equations, solution of a system of equations
Solving Systems by Graphing / Manually graph two lines and find any points of intersection
Use Technology to graph two lines and find any points of intersection
Identify a system with one solution
Identify a system with no solution
Identify a system with an infinite number of solutions
Solving Systems Using Substitution / Substitution Method / Use the Substitution Method to find any solutions when the coefficient where you substitute is 1
Use the Substitution Method to find any solutions when the coefficient where you substitute is not 1
Solving Systems Using Elimination / Elimination Method / Use the Elimination Method and addition to solve a system where one pair of like terms are opposites.
Use the Elimination Method and subtraction to solve a system where one pair of like terms are the same.
Use the Elimination Method after multiplying one equation to get a pair of opposites.
Use the Elimination Method after multiplying two equations to get a pair of opposites.
Applications of Linear Systems / Writing Systems of Linear Equations / Write a system of linear equations from a verbal description and solve
Linear Inequalities / Definitions / Define linear inequality, solutions of an inequality
Graphing Linear Inequalities / Use dotted or solid lines and shading to represent the solution to a linear inequality
Transform the given inequality if necessary to facilitate graphing
Check a point on the graph to verify the solution
Systems of Linear Inequalities / Solving by Graphing / Graph the linear inequalities on the same coordinate plane and indicate any solution
Writing Systems of Linear Inequalities / Write a system of linear inequalities from a verbal description and solve by graphing
Part C Major Concepts / Topics / Student Expectations
Exponents and Exponential Functions - Chapter 8
Types of Exponents / Zero Exponent / Know that every nonzero number raised to the zero power is one ex: a0 = 1
Negative Exponent / Know that every nonzero number raised to a negative exponent is one over that number raised to the positive of that exponent ex: a-n = (1/an)
Simplify expressions involving exponents
Scientific Notation / Recognize scientific notation
Manually Convert between scientific notation and standard notation
Order numbers written in scientific notation
Properties of Exponents / Multiplication Properties of Exponents / Multiply two numbers with the same base ex: am • an = an+m
Raise a number with an exponent to a power ex: (am)n = am•n
Raise a product to a power ex: (ab)m = am • bm
Division Properties of Exponents / Divide powers with the same base ex: (am/an) = am-n
Raise a quotient to a power ex: (a/b)m = (am/bm)
Geometric Sequences / Definition / Calculate the common ratio of a geometric sequence
Determine whether a sequence is arithmetic, geometric or neither
Rules / Determine the first term, common ratio, and term number of a rule
Create a rule given a geometric sequence: A(n) = a • r n-1
Exponential Functions / Definition / Identify that an exponential function is in the form y = a • bx
Graphing / Generate tabular data from exponential functions
Graph exponential functions utilizing tabular data
Exponential Growth / Identify exponential growth functions in the form y = a • bx when a>0 and b>1
Identify the growth factor from the function (b)
Use functions to reflect compound interest with varying interest periods
Exponential Decay / Identify exponential decay functions in the form y = a • bx when a>0 and 0<b<1
Identify the decay factor from the function (b)
Major Concepts / Topics / Student Expectations
Polynomials and Factoring - Chapter 9
Adding/Subtracting Polynomials / Definitions / Identify and differentiate between a mono-, bi-, tri-, and poly-nomials
Determine degrees of polynomials
Write polynomials in Standard Form
Adding and Subtracting Polynomials / Simplify polynomials by combining like terms
Multiplying Polynomials / Multiplying a Monomial and a Trinomial / Multiply polynomials using the Distributive Property
Multiplying a Binomial and a Trinomial / Multiply polynomials using the vertical or horizontal method
Multiplying a Binomial and a Binomial / Multiply using the Distributive Property
Multiply using First Outside Inside Last (FOIL) method
Identifying special cases with squares and differences of squares
Alternative Methods of Multiplying Polynomials / Multiply polynomials using the area model
Multiply polynomials using algebra tiles
Factoring Polynomials / Finding the Greatest Common Factor (GCF) / Find GCF using prime factorization or common factors
Factoring out a Monomial / Use the GCF to factor out a monomial from a polynomial
Factoring ax2 + bx + c where a = 1 / Factor a trinomial into two binomials
Factoring ax2 + bx + c where a ≠ 1 / Factor a trinomial into two binomials
Identify perfect square polynomials and factor them
ex: a2 + 2ab + b2 = (a + b)2 and a2 − 2ab + b2 = (a − b)2
3rd Degree Polynomials with Four Terms / Factor four term polynomials by grouping
Major Concepts / Topics / Student Expectations
Quadratic Equations and Functions - Chapter 10
Square Roots / Working with Square Roots / State the square root of a number (and whether it is rational or irrational)
Know the perfect squares from 0-400
Standard Form / Quadratic Function / Convert quadratic functions into Standard Form ex: y = ax2 + bx + c
Quadratic Equation / Convert quadratic equations into Standard Form ex: ax2 + bx + c = 0
Graphing Quadratic Equations / Definitions / Define and label a parabola, axis of symmetry, vertex, and the maximum or minimum point of a parabola
Creating Coordinate Tables / Create a table of values to graph a parabola from a quadratic equation
Finding the Axis of Symmetry / Use x= −b/2a to find the axis of symmetry of a parabola
Solving Quadratic Equations / Various Methods to Solve Quadratic Equations / Solve quadratic equations by graphing (creating parabolas)
Solve quadratic equations by using algebra and square roots
Solve quadratic equations by factoring polynomials
Solve quadratic equations by completing the square
Solve quadratic equations by using the Quadratic Formula
Utilize the discriminant to determine whether there are two, one or no solutions to a quadratic equation
Linear, Quadratic and Exponential Models / Choosing a Model from Graphs, Data and Verbal Descriptions / Identify and differentiate between the following types of functions:
Linear, Quadratic and Exponential
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