|
Topic EI: Essentials — Preparing for Algebra |
EI.A Fractions
(reviews F2.1, F2.2) |
Multiplying and Dividing |
a) Equivalent fractions
b) Prime factorization
c) Reducing to lowest terms
d) The greatest common factor (GCF)
e) Multiplying fractions
f) Finding reciprocals
g) Dividing fractions |
2 hours |
Adding and
Subtracting |
a) Fractions with the same denominators
b) The least common multiple (LCM)
c) The least common denominator (LCD)
d) Fractions with different denominators |
2 hours |
| |
|
Lesson Total |
4 hour |
EI.B Signed Numbers
(reviews F4.1, F4.2) |
Adding and
Subtracting |
a) Adding signed numbers
b) Subtracting signed numbers |
2 hours |
Multiplying and
Dividing |
a) Multiplying and dividing signed numbers
b) Exponential notation
c) Distributive property and other properties of real numbers
d) Order of operations |
2 hours |
| |
|
Lesson Total |
4 hour |
|
Topic 1: Real Numbers |
| 1.1 The Real Numbers |
Number Line and
Notation |
a) Sets
b) Subsets of real numbers: natural numbers, integers, rational,
irrational
c) Graphing real numbers on a number line
d) Ordering symbols : =, <, >, ≤, ≥
e) The absolute value of a real number
f) Grouping symbols
g) Exponents |
2 hours |
| |
|
Lesson Total |
2 hours |
1.2 Factoring and
Fractions |
The GCF and LCM |
a) Prime factors
b) Greatest common factor
c) Least common multiple |
1 hour |
| Fractions |
a) Reducing to lowest terms
b) Multiplication and division
c) Addition and subtraction |
1 hour |
| Explore |
a) Exploring Greatest Common Factor |
1 hour |
| |
|
Lesson Total |
3 hour |
1.3 Arithmetic of
Numbers |
Operations on
Numbers |
a) Addition
b) Subtraction
c) Multiplication
d) Division
e) Order of operations
f) Commutative law
g) Associative law
h) Distributive law
i) Additive and multiplicative identities
j) Inverses |
1 hour |
| Explore |
a) Exploring Operations on Numbers |
1 hour |
| |
|
Lesson Total |
2 hour |
|
Topic 2: Solving Linear Equations and Inequalities |
| 2.1 Algebraic Expressions |
Simplifying
Expressions |
a) Constants and variables
b) Terms and coefficients
c) Combining like or similar terms
d) Parentheses
e) Evaluating expressions
f) Formulas: Substitution |
2 hours |
| |
|
Lesson Total |
2 hour |
2.2 Solving Linear
Equations |
Solving Equations I |
a) Recognizing a linear equation
b) The addition and subtraction principles for solving a
linear equation
c) The multiplication and division principles for solving a
linear equation
d) Combining the principles |
2 hours |
| Solving Equations II |
a) Equations with fractions as coefficients
b) Equations with no solutions or infinitely many solutions
c) Formulas: Solving for a particular unknown |
1 hour |
| |
|
Lesson Total |
3 hour |
| 2.3 Problem Solving |
Number and Age |
a) Translating words into algebraic expressions
b) Number problems
c) Age problems |
2 hours |
| Geometry |
a) Geometry problems |
2 hours |
| |
|
Lesson Total |
4 hour |
| 2.4 Linear Inequalities |
Solving Inequalities |
a) Recognizing solutions of linear inequalities
b) Graphing solutions of inequalities in one variable
c) The addition and subtraction principles for solving a
linear inequality
d) The multiplication and division principles for solving a
linear inequality
e) Combining the addition, subtraction, multiplication, and
division principles
f) Solving problems using inequalities |
2 hours |
| |
|
Lesson Total |
2 hour |
|
Topic 3: Introduction to Graphing |
3.1 Introduction to
Graphing |
Plotting Points |
a) The xy-plane
b) The x-axis and y-axis
c) The origin
d) Ordered pairs
e) The x-coordinate (abscissa), the y-coordinate (ordinate)
f) Plotting ordered pairs of numbers
g) Labeling the four quadrants
h) Determining the quadrant in which a point lies
i) The signs of the coordinates in each quadrant |
1 hour |
| Rise and Run |
a) Subscript notation
b) Geometric interpretation of rise and run
c) Algebraic definition of rise and run |
1 hour |
| The Distance Formula |
a) Pythagorean Theorem
b) The distance formula
c) The equation of a circle |
0.5 hours |
| Explore |
a) Plotting Points |
0.5 hours |
| |
|
Lesson Total |
3 hour |
|
Topic 4: Graphing Linear Equations and Inequalities |
| 4.1 Graphing Equations |
Graphing Lines I |
a) Definition of a linear equation in two variables
b) Recognizing linear equations in two variables
c) Solutions of linear equations
d) Graphing a linear equation by plotting ordered pairs |
2 hours |
| Graphing Lines II |
a) Equations and graphs of horizontal and vertical
lines
b) The intercepts of a line
c) Graphing a linear equation by finding the intercepts |
1 hour |
| Slope of a Line |
a) Definition of the slope of a line
b) Positive slope, negative slope , zero slope , undefined
slope
c) Graphing a line given a point and the slope
d) Parallel and perpendicular lines |
2 hours |
| |
|
Lesson Total |
5 hour |
| 4.2 The Equation of a Line |
Finding the Equation I |
a) Finding the equation of a line given a point on the
line and the slope of the line
b) The point-slope form of the equation of a line
c) Finding the equation of a line given two points on the line |
1 hour |
| Finding the Equation II |
a) The slope-intercept form of the equation of a line
b) Finding the equation of a horizontal line
c) Finding the equation of a vertical line
d) Finding the equation of a line parallel or perpendicular to
a given line |
2 hours |
| |
|
Lesson Total |
3 hour |
| 4.3 Graphing Inequalities |
Linear Inequalities |
a) Ordered pairs as solutions of linear
inequalities
b) Graphing inequalities |
2 hours |
| |
|
Lesson Total |
2 hour |
|
Topic 5: Solving Linear Systems |
5.1 Solving Linear
Systems |
Solution by Graphing |
a) The solution of a linear system
b) Graphing linear systems
c) Systems with a unique solution
d) Systems with no solutions
e) Systems with an infinite number of solutions |
1 hour |
| Solution by Algebra |
a) Solving linear systems by the substitution method:
one
solution, no solution, and an infinite number of solutions
b) Solving linear systems by the elimination method: one solution,
no solution, and an infinite number of solutions |
1.5 hours |
| Explore |
a) Exploring Graphing Linear Systems |
0.5 hours |
| |
|
Lesson Total |
3 hour |
| 5.2 Problem Solving |
Using Linear Systems |
a) Number problems
b) Interest problems
c) Coin problems
d) Mixture problems |
2 hours |
| |
|
Lesson Total |
2 hour |
| 5.3 Systems of Inequalities |
Solving Linear Systems |
a) Solving systems of linear inequalities by graphing |
1 hour |
| Explore |
a) Exploring Solving Linear Systems |
1 hour |
| |
|
Lesson Total |
2 hour |
|
Topic 6: Exponents and Polynomials |
| 6.1 Exponents |
Properties of
Exponents |
a) Definition of exponent, power, and base
b) Multiplication property
c) Division property
d) Powers raised to powers
e) Products raised to powers
f) Quotients raised to powers
g) The zero exponent |
2 hours |
6.2 Polynomial
Operations I |
Adding and
Subtracting |
a) Definition of polynomial, term, and coefficient
b) Evaluating a polynomial
c) The degree of a term and a polynomial
d) Writing the terms of a polynomial in descending order
e) Definition of a monomial, binomial, and trinomial
f) Recognizing like or similar terms
g) Combining like or similar terms
h) Polynomial addition
i) Polynomial subtraction |
2 hours |
Multiplying and
Dividing |
a) Multiplying a monomial by a monomial
b) Multiplying a polynomial by a monomial
c) Dividing a monomial by a monomial
d) Dividing a polynomial by a monomial |
2 hours |
| |
|
Lesson Total |
4 hour |
6.3 Polynomial
Operations II |
Multiplying Binomials |
a) Multiplying binomials by the "FOIL" method
b) Perfect squares, product of the sum and difference of two terms |
1.5 hours |
Multiplying and
Dividing |
a) Multiplying a polynomial by a polynomial
b) Dividing a polynomial by a polynomial |
1.5 hours |
| Explore |
a) Multiplying Binomials |
1 hour |
| |
|
Lesson Total |
4 hour |
|
Topic 7: Factoring |
7.1 Factoring
Polynomials I |
Greatest Common Factor |
a) Finding the greatest common factor (GCF) of a set of
monomials
b) Factoring a polynomial by finding the GCF when the GCF is a
monomial |
2 hours |
| Grouping |
a) Factoring a polynomial by finding the GCF when the
GCF is a
binomial
b) Factoring a polynomial with four terms by grouping |
2 hours |
| |
|
Lesson Total |
4 hour |
7.2 Factoring
Polynomials II |
Trinomials I |
a) Factoring trinomials of the form x^2 + bx+ c;
x^2 + bxy+ cy^2; |
1 hour |
| Trinomials II |
a) Factoring trinomials of the form ax^2 + bx + c, a ≠
1, by trialand-error
b) Factoring trinomials of the form ax^2 + bx + c, a ≠ 1, by grouping
c) Solving quadratic equations by factoring |
2 hours |
| |
Explore |
a) Exploring Factoring |
1 hour |
| |
|
Lesson Total |
4 hour |
| 7.3 Factoring by Patterns |
Recognizing Patterns |
a) Factoring a perfect square trinomial
b) Factoring a difference of two squares
c) Factoring a sum and difference of two cubes
d) Factoring using a combination of methods |
2 hours |
| |
|
Lesson Total |
2 hour |
|
Topic 8: Rational Expressions |
| 8.1 Rational Expressions I |
Multiplying and Dividing |
a) Determining when a rational expression is undefined
b) Writing a rational expression in lowest terms
c) Multiplying rational expressions
d) Dividing rational expressions
e) Simplifying a complex fraction |
1 hour |
| Adding and Subtracting |
a) Adding rational expressions with the same
denominator
b) Subtracting rational expressions with the same
denominator |
1 hour |
| |
|
Lesson Total |
2 hour |
8.2 Rational
Expressions II |
Negative Exponents |
a) Notation
b) Scientific notation |
1 hour |
| Multiplying and Dividing |
a) Reducing a rational expression of the form
(a -b)/(b-a)
b) Multiplying rational expressions
c) Dividing rational expressions
d) Simplifying a complex fraction |
1 hour |
| Adding and Subtracting |
a) Finding the least common denominator of two or more
rational expressions
b) Adding rational expressions with different denominators
c) Subtracting rational expressions with different
denominators
d) Simplifying a complex fraction |
1 hour |
| |
|
Lesson Total |
3 hour |
8.3 Equations with
Fractions |
Solving Equations |
a) Solving equations with rational expressions
b) Solving for an unknown in a formula involving a rational
expression |
2 hour |
| |
|
Lesson Total |
2 hour |
| 8.4 Problem Solving |
Rational Expressions |
a) Ratio and proportion
b) Distance problems
c) Work problems
d) Variation |
2 hours |
| |
|
Lesson Total |
2 hour |
| Topic 9: Rational
Exponents and Radicals |
| 9.1 Roots and Radicals |
Square Roots and
Cube Roots |
a) Definition of square root and cube root
b) Radicand, radical
c) Principal square root
d) Multiplication and division properties
e) Simplifying a square root or a cube root of a
whole number
f) Simplifying a square root or a cube root of simple
monomial expression |
1 hour |
| Radical Expressions |
a) Simplifying radical expressions
b) Like radical terms
c) Simplifying a sum or difference of radical expressions
d) Multiplying radical expressions
e) Conjugates
f) Rationalizing the denominator
g) Solving radical equations |
2 hours |
| |
|
Lesson Total |
3 hour |
| 9.2 Rational Exponents |
Roots and Exponents |
a) The nth root of a number
b) Definition of a1/n and am/n
c) Properties of rational exponents |
1 hour |
| Simplifying Radicals |
a) Simplifying radicals |
1 hour |
Operations on
Radicals |
a) Multiplying radical
expressions
b) Dividing radical expressions
c) Adding and subtracting radical expressions |
2 hours |
| |
|
Lesson Total |
4 hour |
|
Topic 10: Quadratic Equations |
| 10.1
Quadratic Equations I |
Solving by Factoring |
a) The standard form of
a quadratic equation
b) Putting a quadratic equation into standard form
ax^2 + bx + c = 0; a ≠ 0
c) Solving quadratic equations of the form
ax^2 + bx = 0 by factoring
d) Solving quadratic equations of the form
ax^2 + bx + c = 0 by factoring |
1 hour |
Solving by Square
Roots |
a) Finding square roots
Roots b) Solving quadratic equations of the form ax^2 = b
c) Solving quadratic equations of the form (ax + b)^2 = c |
1 hour |
| |
|
Lesson Total |
2 hour |
| 10.2
Quadratic Equations II |
Completing the Square |
a) Solving quadratic
equations of the form
x^2 + bx + c = 0 by completing the square
b) Solving quadratic equations of the form
ax^2 + bx + c = 0, a ≠ 1, by completing the square |
1 hour |
The
Quadratic
Formula |
a)
Introducing the quadratic formula
b) Using the quadratic formula to solve
quadratic equations of the form ax^2 + bx + c = 0
c) Using the discriminant of a quadratic equation to
determine the nature of the solutions of the equation |
1 hour |
| Explore |
a) Solving Equations |
1 hour |
| |
|
Lesson Total |
3 hour |
| 10.3 Complex Numbers |
Complex Number
System |
a) Definition of complex
numbers
b) Powers of i
c) Operations on complex numbers |
2 hours |
| |
|
Lesson Total |
2 hour |
|
Topic 11: Functions and Graphing |
| 11.1
Functions |
Functions and Graphs |
a) Definition of a
function
b) Function as an ordered pair of numbers
c) Finding function values given a formula
d) Function notation: y = f(x)
e) Graphing simple functions
f) Domain and range of a function
g) The vertical line test |
1 hour |
| Linear Functions |
a) Graphs of linear
functions
b) Graphs of absolute value functions |
1 hour |
| Quadratic Functions |
a) Graphs of quadratic
functions
b) Intercepts of quadratic functions |
1 hour |
| Explore |
a) Functions and Graphs |
1 hour |
| |
|
Lesson Total |
4 hour |
11.2 The Algebra of
Functions |
The Algebra of
Functions |
a) The sum and
difference of functions
b) The product and quotient of functions
c) The composition of functions |
2 hours |
| |
Inverse
Functions |
a) Finding
the inverse and the equation of the inverse
b) Defining one-to-one and checking whether a function has
an inverse that is a function
c) Graphing inverse functions |
2 hours |
| |
|
Lesson Total |
4 hour |
|
Topic F3: Proportional Reasoning
II |
| F3.1 Ratio
and Proportion |
Ratios |
a) Notation
b) Equivalent ratios
c) Rates
d) Applications |
2 hours |
| Proportions |
a) Setting up a
proportion
b) Solving a proportion
c) Similar triangles
d) Applications |
3 hours |
| Explore |
a) Inverting Ratios
b) Similar Figures |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F3.2 Percent |
Definition |
a) Percent as a fraction
b) Percent as a decimal
c) “Benchmark” percents
d) Applications |
2 hours |
| Converting |
a) Converting among
fractions, decimals and percents
b) Percent increase and decrease
c) Applications |
3 hours |
Solving Percent
Problems |
a) Setting up and
solving proportions
b) Setting up and solving other equations
c) Applications |
3 hours |
| Explore |
a) A Survey
b) Computing Tips
c) A Percent Question |
1 hour |
| |
|
Lesson Total |
6-8 hours |
|
Topic F5: Geometry |
| F5.1
Geometry I |
Geometric Figures |
a) Point, line, line
segment, ray
b) Polygons
c) Measuring angles
d) Angles: acute, right, obtuse, straight
e) Relationships between angles: complementary,
supplementary, adjacent, vertical
f) Applications |
3 hours |
| Explore |
a) Tiling with Polygons
b) What’s the Sum? |
1 hour |
| |
|
Lesson Total |
4hours |
| F5.2
Geometry II |
Perimeter and Area |
a) Perimeter of a
polygon
b) Area of a polygon
c) Area of a rectangle, square, parallelogram, triangle,
trapezoid
d) Circumference of a circle
e) Area of a circle
f) Perimeter and area of composite figures
g) Applications |
2 hours |
Surface Area and
Volume |
a) Surface area of a
solid
b) Volume of a solid
c) Surface area and volume of a rectangular prism
d) Surface area and volume of a cylinder
e) Volume of a cone
f) Volume of a sphere
g) Composite figures
h) Applications |
3 hours |
| Explore |
a) Don’t Fence Me In
b) Why π?
c) Packaging Products |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F5.3 Geometry III |
Triangles and
Parallelograms |
a) Angle sum of a triangle
b) Congruent triangles
c) Isosceles and equilateral triangles
d) Right triangles
e) The Pythagorean Theorem
f) Parallel lines and transversals
g) Properties of parallelograms
h) Applications |
2 hours |
| Similar Polygons |
a) Similar polygons
b) Similar triangles
c) Applications |
3 hours |
| Explore |
a) Congruent Triangles
b) Door to Door |
1 hour |
| |
|
Lesson Total |
4-6 hours |
|
Topic F6: Interpreting Data |
| F6.1 Units of Measurement |
US/English Units |
a) Measures: length, weight, time, volume
b) Converting from one unit to another
c) Adding and subtracting measurements
d) Applications |
2 hours |
| The Metric System |
a) The metric system: length, mass, volume
b) Fahrenheit and Celsius scales
c) Converting between US and metric units
d) Applications |
3 hours |
| Explore |
a) Sizing it Up
b) Choosing Units |
1 hour |
| |
|
Lesson Total |
4-6 hours |
| F6.2 Interpreting Graphs |
Data and Graphs |
a) Reading data from graphs
b) Graphing data
c) Pictographs
d) Bar graphs
e) Circle graphs
f) Line graphs
g) Applications |
2 hours |
| Explore |
a) Collecting and Picturing Data
b) Graphs in the News |
1 hour |
| |
|
Lesson Total |
2-3 hours |
F6.3 Introduction to
Statistics |
Statistical Measures |
a) Mean
b) Median
c) Mode
d) Box-and-whisker plots
e) Applications |
2 hours |
| Explore |
a) Collecting Data
b) Where’s the Middle? |
1 hour |
| |
|
Lesson Total |
2-3 hours |
