Download Algebra I Pacing Guide

Algebra I Pacing Guide
Days
9
Units
Chapter 1
(1.1-1.4, 1.6-1.7)
8
Chapter 2
(2.1-2.7)
14
Chapter 3
(3.1-3.8)
14
Chapter 4
(4.1-4.7)
14
Chapter 5
(5.1-5.7)
14
Chapter 6
(6.1-6.7)
11
Chapter 7A
(7.1-7.4)
Notes
Expressions, Equations and Functions
Differentiate between and write expressions,
equations and inequalities as well as applying order
of operations. Word problems will be incorporated
in several of the different sections.
Properties of Real Numbers
Add, Subtract, Multiply, Divide and apply the
Square Root function as well as classify and
differentiate between different types of numbers.
Word problems will be incorporated in many of the
different sections.
Solving Linear Equations
Progress through solving equations, including onestep equations, two-step equations, multi-step
equations, equations with variables on both sides of
the equation, ratios and proportions and percents.
Word problems will be incorporated in each
individual section.
Graphing Linear Equations and Functions
Students will learn about graphing points as well as
linear equations (lines). During this time we will
investigate topics like slope, rate of change and
different forms of equations and methods of
graphing. Students will also use the graphing
calculator to estimate what a line would look like
when given specific data.
End of 1st Nine Weeks
Writing Linear Equations
Students will learn how to write equations that will
produce graphs similar to those in the previous
chapter. They will investigate many different ways
of writing equations and determine which method is
most appropriate in certain situations. Also, parallel
and perpendicular lines will be discussed.
Solving and Graphing Linear Inequalities
Students will investigate the graphs of inequalities,
including greater than, less than, greater than or
equal to and less than or equal to. Absolute value
equations and inequalities will also be discussed in
this chapter. Students will also write and solve word
problems in this chapter.
Systems of Equations
Students will explore the different methods for
5
Chapter 7B
(7.5 & 7.6)
12
Chapter 8
(8.1-8.6)
12
Chapter 11
(11.2-11.4)
10
Chapter 9A
(9.1-9.4)
13
Chapter 9B
(9.5-9.8)
12
Chapter 10A
(10.1-10.5)
7
Chapter 10B
(10.6 & 10.7)
solving two equations at the same time. Methods
that will be explored include graphing, substitution
and adding or subtracting.
End of 2nd Nine Weeks
End of 1st Semester
Systems of Inequalities and Special Systems of
Equations
Students will learn about special cases of systems of
equations (no solution and infinite solutions) as well
as discover how to graph systems of inequalities.
Students will also write and solve word problems.
Exponents and Exponential Functions
Students will learn rules for working with exponents
in Algebra. They will also learn several properties,
use scientific notation and explore exponential
growth and decay. Word problems will be used
often in this chapter.
Simplifying and Solving Square Root Expressions
and Equations, Pythagorean Theorem
Students will simplify radical expressions exactly
(rather than estimate), they will learn to solve radical
equations and apply the Pythagorean Theorem.
Word problems will be used in much of this chapter.
Simplifying Polynomials
Students will learn to simplify polynomials through
addition, subtraction and multiplication, as well as
distribution. Students will also begin to learn how to
solve equations involving polynomials with
equations that have already been factored.
Factoring Polynomials
Students will learn to factor polynomials on their
own through many different methods. They will
also learn to solve equations with unfactored
polynomials. Word problems and writing about
their answers can be expected in this and the
previous unit.
End of 3rd Nine Weeks
Graphing Quadratic Equations and Solving by
Factoring
Students will graph quadratic equations and solve
them through interpreting the graphs. Use of
calculators and graphing by hand will both be
implemented.
Solving Quadratic Equations by Quadratic Formula
Students will solve quadratic equations through the
use of the quadratic formula and will be able to find
14
Chapter 13
(13.1-13.8)
the number of real roots by using the discriminant.
Probability and Statistics
Students will begin to investigate the world of
probability and statistics, including an investigation
of permutations and combinations, simple
probability, compound probability and critique of
samples and surveys.
End of 4th Nine Weeks
End of 2nd Semester
Algebra I Learning Targets
Section
1.1
1.3
1.2
1.4
1.6
1.7
Chapter 1: Expressions, Equations and Functions
Section Title
Learning Target(s)
I can…
Evaluate
1. Define a variable and an expression.
Expressions and
2. Translate an expression into a word sentence and
Write Expressions vice versa.
3. Use proper terminology with respect to
exponents, bases and powers.
Order of Operations 1. Correctly use the order of operations to simplify
expressions without a calculator.
2. Check their answers with a calculator and look
for mistakes that may have been made.
Write Equations
1. Differentiate between an expression, equation and
and Inequalities
inequality.
2. Correctly identify inequality symbols (less than,
greater than, less than or equal to, greater than or
equal to).
3. Begin to identify solutions to an equation through
checking possible solutions.
4. Write and solve word problems.
Represent
1. Define function, domain, range, independent
Functions as Rules variable and dependent variable.
and Tables
2. Identify a function.
3. Make a table and a rule for a function, including
real-life applications.
Represent
1. Identify the X and Y axes on a coordinate plane.
Functions as
2. Graph ordered pairs on a coordinate plane.
Graphs
3. Write a rule for a function from a
graph…translate from a graph to a table or rule.
Section
2.1
2.2 & 2.3
2.4
2.5
2.6
2.7
Chapter 2: Properties of Real Numbers
Section Title
Learning Target(s)
I can…
Using Integers and 1. Graph positive and negative numbers on a
Rational Numbers number line.
2. Compare positive and negative numbers.
3. Compare (differentiate between) whole numbers,
integers and rational numbers.
Add and Subtract 1. Add and subtract positive and negative numbers.
Real Numbers
2. Use number sense to solve and write word
problems.
3. Add and subtract decimals and fractions with and
without a calculator.
Multiply Real
1. Multiply real numbers with and without a
Numbers
calculator.
2. Substitute values for variables and simplify
expressions.
Apply Distributive 1. Determine when to apply the distributive
Property
property.
2. Apply the distributive property when appropriate.
3. Use the distributive property to help write and
solve word problems.
Divide Real
1. Divide real numbers with and without a
Numbers
calculator.
2. Divide by fractions and decimals.
3. Understand and correctly use the terminology
associated with division (quotient, reciprocal, etc.).
Find Square Roots 1. Find approximate values of square roots and
and Compare with order them with other numbers.
Real Numbers
2. Classify numbers as real, rational, irrational or
integers.
3. Use square roots to write and solve word
problems.
Section
3.1
3.2
3.3
3.4
3.5 & 3.6
3.7
3.8
Chapter 3: Solving Linear Equations
Section Title
Learning Target(s)
I can…
Solving One-Step 1. Solve one-step equations using addition,
Equations
subtraction, multiplication and division.
2. Solve equations that have decimals and fractions.
3. Solve equations with the variable on either side
of the equation.
Solve Two-Step
1. Solve two-step equations using addition,
Equations
subtraction, multiplication and division.
2. Differentiate a one-step equation from a two-step
equation.
3. Solve equations with the variable(s) on either side
of the equation.
Solve Multi-Step
1. Differentiate between one-step, two-step and
Equations
multi-step equations.
2. Solve multi-step equations with decimals and
fractions.
3. Apply the distributive property and use correctly
to solve multi-step equations.
Solving Equations 1. Differentiate between an equation with variables
with Variables on on both sides and a multi-step equation or two-step
Both Sides
equation.
2. Combine like terms appropriately by moving the
correct variable or number.
3. Apply the distributive property if necessary.
4. Write and solve real-world word problems.
Write Ratios and
1. Differentiate between a ratio and a proportion.
Proportions
2. Set up ratios and proportions.
3. Solve proportions using the cross multiply
method. Correctly apply distribution if necessary.
4. Write and solve word problems.
Solve Percent
1. Apply number sense to remember that a percent
Problems
is a number out of 100.
2. Solve percent problems by writing a proportion
or using the percent equation.
3. Write and solve real-world word problems
involving percents.
Rewrite Equations 1. Successfully manipulate equations to solve for a
and Formulas
variable instead of a number.
2. Solve problems using the manipulation of an
equation.
Section
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Chapter 4: Graphing Linear Equations and Functions
Section Title
Learning Target(s)
I can…
Plot Points in a
1. Plot points when given coordinates.
Coordinate Plane
2. Give coordinates when points have been plotted.
Graph Linear
1. Recognize a vertical and horizontal line by their
Equations
equation.
2. Write an equation in standard form.
3. Graph an equation by using a table.
Graph Using
1. Understand the concept of X- and Y-Intercepts.
Intercepts
2. Use the intercepts to find an equation.
3. Use a graph to find the intercepts.
Find Slope and
1. Differentiate between positive, negative, 0 and no
Rate of Change
slopes.
2. Use the formula to find slope of lines.
3. Relate Rate of Change to Slope.
Graph Using Slope 1. Recognize Slope-Intercept Form (in equation
Intercept Form
form).
2. Identify different parts of the equation (Slope &
Intercept).
3. Graph using slope intercept form.
Model Direct
1. Graph direct variation equations.
Variation
2. Write direct variation equations.
Graph Linear
1. Apply earlier knowledge of Standard and SlopeFunctions
Intercept Forms to graph functions.
2. Find values when given a function.
Section
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Chapter 5: Writing Linear Equations
Section Title
Learning Target(s)
I can…
Write Linear
1. Write an equation of a line when given two
Equations in Slope- points.
Intercept form
2. Use slope and y-intercept to write an equation.
Use Linear
1. Write equations when given the slope and yEquations in Slope- intercept.
Intercept Form
2. Recall information from section 5.1 and apply it
to real world situations.
Write Linear
1. Recognize difference between slope-intercept,
Equations in Point- standard and point-slope forms.
Slope Form
2. Write equations using point-slope forms.
Write Linear
1. Transfer between slope-intercept, standard and
Equations in
point-slope forms.
Standard Form
Write Equations of 1. Differentiate between parallel and perpendicular
Parallel and
lines.
Perpendicular Lines 2. Recognize parallel and perpendicular lines based
on their slopes.
3. Determine whether lines are parallel or
perpendicular.
Fit a Line to Data 1. Discuss correlation and differentiate between
positive, negative and no correlation.
2. Sketch a line of best fit.
Predict with Linear 1. Find a linear equation that represents the data
Models
well.
2. Make an estimate for given values.
Section
6.1
6.2
6.3
6.4
6.5
6.6
6.7
Chapter 6: Solving and Graphing Linear Inequalities
Section Title
Learning Target(s)
I can…
Solve Inequalities 1. Write and graph basic inequalities.
using Addition and 2. Solve and graph an inequality using addition or
Subtraction
subtraction.
3. Differentiate between inequality signs.
Solve Inequalities 1. Solve and graph inequalities using multiplication
using
and division.
Multiplication and 2. Differentiate between dividing by and negative
Division
number and simply dividing a negative number.
Solve Multi-Step
1. Solve and graph inequalities that require more
Inequalities
than one step.
2. Recognize both “no solution” and “infinite
solution” inequalities.
1. Differentiate between compound inequalities
Solving Compound from simple inequalities.
Inequalities
2. Differentiate between or and and compound
inequalities.
3. Write and graph both types of compound
inequalities.
Solve Absolute
1. Understand and apply the absolute value concept.
Value Equations
2. Solve one-, two- and multi-step equations with
absolute values.
3. Graph absolute value equations.
Solve Absolute
1. Understand the difference between or and and
Value Inequalities inequalities.
2. Solve and graph absolute value inequalities.
Graph Linear
1. Manipulate inequalities to graph them more
Inequalities in Two easily (slope-intercept form).
Variables
2. Graph two variable inequalities with proper
shading and line type.
Section
7.1
7.2
7.3
7.4
Chapter 7A: Solving Systems of Equations
Section Title
Learning Target(s)
I can…
Solving Linear
1. Identify a linear system of equations.
Systems by
2. Graph two linear equations on the same
Graphing
coordinate plane.
3. Estimate and identify exactly the solution of a
linear system.
Solve Linear
1. Solve an equation for an identified variable.
Systems by
2. Substitute and solve an equation for a variable.
Substitution
3. Solve word problems by using substitution.
Solve Linear
1. Re-order equations to place variables in the same
Systems by
order.
Elimination
2. Determine whether to use addition or subtraction
(Adding and
to eliminate a variable.
Subtracting)
3. Solve word problems using elimination.
Solve Linear
1. Determine when multiplication is necessary.
Systems by
2. Decide whether one or both equations must be
Multiplying First
multiplied.
3. Solve using elimination as in section 7.3
Section
7.5
7.6
Chapter 7B: Solving Systems of Inequalities
Section Title
Learning Target(s)
I can…
Solve Special
1. Solve systems of equations through graphing,
Types of Linear
elimination or substitution, whichever is easiest.
Systems
2. Recognize a system of equations with one
solution, infinite solutions or no solution
Solving Systems of 1. Solve and graph multiple (2 or 3) linear
Linear Inequalities inequalities on the same coordinate plane.
2. Shade appropriately for each individual
inequality and for the overall system of inequalities.
3. Identify systems with no solution as well as
limited solutions.
Section
8.1
8.2
8.3
8.4
8.5
8.6
Chapter 8: Exponents and Exponential Functions
Section Title
Learning Target(s)
I can…
Apply Exponent
1. Understand and apply the Product of Powers
Properties
Property, the Power of a Power Property and the
Involving Products Power of a Product Property.
2. Differentiate between all three properties.
3. Write and solve word problems.
Apply Exponent
1. Understand and apply the Quotient of Powers
Properties
Property and the Power of a Quotient Property.
Involving Quotients 2. Combine knowledge of section 8.1 properties
with section 8.2 properties.
Define and Use
1. Understand and apply the Zero Exponent and
Zero and Negative Negative Exponent Properties.
Exponents
2. Combine knowledge of section 8.1 and 8.2
properties with section 8.3 properties.
Using Scientific
1. Recognize and differentiate between standard
Notation
form and scientific notation.
2. Move between standard form and scientific
notation in both directions.
3. Order numbers from least to greatest in both
standard form and scientific notation.
4. Compute with numbers in scientific notation.
Write and Graph
1. Recognize an exponential function as compared
Exponential
to a linear function.
Growth Functions 2. Graph an exponential function.
3. Use formulas to solve exponential growth word
problems.
Write and Graph
1. Recognize and write a rule for an exponential
Exponential Decay function.
Functions
2. Graph exponential functions.
3. Differentiate between exponential growth and
exponential decay.
Section
11.2
11.3
11.4
Chapter 11: Square Roots Continued
Section Title
Learning Target(s)
I can…
Simplifying Radical 1. Multiply radicals.
Expressions
2. Divide radicals
3. Add and subtract radicals
4. Rationalize the denominator of a fraction.
Solve Radical
1. Recognize a radical equation.
Equations
2. Simplify radical equations.
3. Solve radical equations by squaring both sides.
Apply the
1. Plug numbers into the Pythagorean Theorem and
Pythagorean
determine whether they are in fact a Pythagorean
Theorem and Its
Triple or not.
Converse
2. Solve for missing sides of right triangles.
3. Use the Pythagorean Theorem to solve word
problems.
Section
9.1
9.2
9.3
9.4
Chapter 9A: Simplifying Polynomials
Section Title
Learning Target(s)
I can…
Add and Subtract 1. Determine the degree of a monomial.
Polynomials
2. Determine the degree of a polynomial.
3. Differentiate between monomials, binomials,
trinomials and polynomials.
4. Simplify polynomials by adding and subtracting.
Multiply
1. Multiply a polynomial by a monomial.
Polynomials
2. Multiply a binomial by a binomial.
3. Multiply a polynomial by a polynomial.
4. Simplify after multiplication using skills from
section 9.1.
Find Special
1. Recognize special products.
Products of
2. Simplify special products with and without using
Polynomials
the FOIL method.
Solve Polynomial 1. Find the solutions (roots) of a polynomial
Equations in
equation.
Factored Form
2. Solve equations by factoring out a Greatest
Common Factor (GCF).
3. Solve word problems using factoring.
Section
9.5
9.6
9.7
9.8
Chapter 9B: Factoring Polynomials
Section Title
Learning Target(s)
I can…
Factor Trinomials 1. Understand and apply the pattern of signs.
2. Determine whether the solutions will be positive
or negative without solving problems.
3. Factor a trinomial into two binomials and solve
for roots.
Factor Trinomials 1. Recognize differences between problems in
with Leading
section 9.5 and in this section.
Coefficients
2. Solve problems using guess and check method.
Factoring Special 1. Recognize perfect square trinomials.
Products
2. Factor a difference of two squares both before
and after factoring out a greatest common factor.
Factor Polynomials 1. Factor out a GCF or common binomial.
Completely
2. Factor by grouping.
3. Find all solutions to a polynomial with a degree
of 2 or higher.
Section
10.1
10.2
10.3
10.4
10.5
Chapter 10A: Solving and Graphing Quadratics
Section Title
Learning Target(s)
I can…
Graphing Quadratic 1. Find the vertex and axis of symmetry of a
Equations
parabola.
2. Use the vertex and axis of symmetry to graph
parabolas.
3. Graph using a table of values.
Graph Quadratic
1. Find the vertex and axis of symmetry of a
Equations
parabola that is not at the origin.
2. Use the vertex and axis of symmetry to graph
parabolas not at the center of the coordinate plane.
3. Graph using a table of values.
Solving Quadratic 1. Find whole number solutions for quadratic
Equations by
equations by graphing.
Graphing
2. Recognize when a graph will have two solutions,
one solution and no solution.
Use Square Roots 1. Solve quadratic equations algebraically through
to Solve Quadratic manipulation of numbers and variables.
Equations
2. Use the square root in order to remove squared
terms.
Solve Quadratic
1. Understand and apply the steps of forming a
Equations by
perfect square trinomial using guided notes and
Completing the
example problems.
Square
Chapter 10B: Solving Quadratics using the Quadratic Formula
Section
Section Title
Learning Target(s)
I can…
10.6
Solve Quadratic
1. Recognize different portions of a quadratic
Equations by the
equation (a, b and c).
Quadratic Formula 2. Memorize and recall the quadratic formula.
3. Successfully substitute numbers for letters in the
formula and solve to find solutions.
10.7
Interpret the
1. Memorize and recall the formula necessary to use
Discriminant
the discriminant.
2. Find the number of solutions without actually
finding the actual solutions.
3. Recognize no solution problems by using the
discriminant.
Section
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
Chapter 13: Probability and Statistics
Section Title
Learning Target(s)
I can…
Find Probabilities 1. Define terms often used in probability (event,
and Odds
outcome, sample space, etc.).
2. Use simple division to find the probability of
events.
Find Probabilities 1. Recognize and define permutations.
Using Permutations 2. Memorize, recall and substitute into permutation
formula.
Find Probabilities 1. Recognize and define combinations.
Using
2. Memorize, recall and substitute into combination
Combinations
formula.
Find Probabilities 1. Recognize differences between simple and
of Compound
compound events.
Events
2. Define independent and dependent events.
3. Define mutually exclusive events and understand
events that are counted twice.
Analyze Surveys
1. Define different types of samples and classify
and Samples
examples of different types as one of the methods.
2. Identify biased samples and suggest potentially
more appropriate samples.
Use Measures of
1. Define measures of center (measures of central
Central Tendency tendency), including mean, median and mode.
2. Use appropriate skills to find the measures of
center.
3. Compare measures of center and determine which
is best.
Interpret Stem and 1. Understand construction of both types of graphs
Leaf Plots and
and interpret their meaning.
Histograms
2. Determine which type of plot may be most
appropriate for different types of data.
3. Construct a stem and leaf plot and histogram.
Interpret Box and 1. Understand construction of and interpret meaning
Whisker Plots
of a box and whisker plot.
2. Define key terms, including quartiles, median,
minimum and maximum.
3. Construct a box and whisker plot.