Curriculum Map: Algebra Enrichment (2014)
(12 Week Trimester) Total Estimated 54/60 days
I.
Algebra Tools (9 days)
Day 1
Variables and Expressions
i. Introduce Vocabulary
ii. Model Expressions
Day 2
Properties of Real Numbers
i. Introduce Vocabulary
ii. Classifying Number Sets
iii. Comparing Values
Day 3
Properties of Real Numbers
i. Absolute Values
ii. Properties of Real Numbers
Day 4
Real Numbers
i. Introduce Vocabulary
ii. Add/Subtract Integers, Fractions, Decimals, Irrationals
iii. Multiply/Divide Integers, Fractions, Decimals, Irrationals
Day 5
Order of Operations and Evaluation Expressions
i. Introduce Vocabulary
ii. Order of Operations
iii. Simplify Multi-Step Expressions
iv. Evaluate Variable Expressions and Simplify
Day 6
Distributive Property
i. Introduce Vocabulary
ii. Simplifying -1 Coefficients
iii. Rewriting Expressions Using Distribution
iv. Combining Like Terms
Day 7
Applications
i. Writing Expressions from Written Models
ii. Simplifying Written Expressions
iii. Classifying Sets from Written Models
iv. Using Real Numbers in Written Models
Day 8
Review
Day 9
TEST
II.
Exponents and Square Roots (9 days)
Day 1
Using Square Roots
i. Introduce Vocabulary
ii. Perfect Squares
iii. Simplifying Non-Perfect Squares using Perfect Squares
Day 2
Operations with Square Roots
i. Add/Subtract
ii. Multiply/Divide
iii. Rationalize Denominator
Day 3
Properties of Exponents
i. Zero Exponent
ii. Negative Exponents
Day 4
Properties of Exponents
i. Products of Powers with Same Base
ii. Quotients of Powers with Same Base
Day 5
Properties of Exponents
i. Powers of Powers
ii. Powers of Products
iii. Powers of Quotients
Day 6
Rational Exponents and Power Tables
i. The nth Root of Numbers Resulting in Integers
ii. Generating Power Tables
iii. Rational Exponents using Power Table
Day 7
Applications
i. Finding Square Roots from Written Models
ii. Simplifying Roots using Properties of Exponents from Written Models.
iii. Identifying Properties of Exponents from Written Models
Day 8
Review
Day 9
TEST
III.
Polynomials (9 days)
Day 1
Classifying Polynomials
i. Introduce Vocabulary
ii. Understanding Degree of Polynomials
Day 2
Writing Polynomials
i. Standard Form of Polynomials
ii. Naming Polynomials by Degree and Number of Terms
Day 3
Adding Polynomials
i. Combining Like Terms
ii. Writing in Standard Form
Day 4
Subtracting Polynomials
i. Using -1 to Distribute
ii. Combine Like Terms
iii. Writing in Standard Form
Day 5
Multiplying/Distributing Polynomials
i. Monomial with a Polynomial
ii. Binomial with a Polynomial
iii. Trinomial with a Polynomial
Day 6
Factor Monomials
i. Divide Polynomial by Monomials
ii. Identify GCF
iii. Factor out GCF and Write using Distributive
Day 7
Applications
i. Write Polynomials in Standard Form using Written Models
ii. Add/Subtract/Multiply/Divide Polynomials using Written Models
Day 8
Review
Day 9
TEST
IV.
Equations and Inequalities (9 days)
Day 1
Writing and Graphing Equations and Inequalities on a Number Line
i. Understanding Solutions to Equations
1. i.e. x = 3 as a point on a number line
2. true vs. false solutions
ii. Understanding Solutions to Inequalities
1. i.e. x < 3 as a set of points on a number line
2. true vs. false solution sets
3. Discrete vs. Continuous using Number Sets
iii. Finding solution sets
Day 2
Solving and Graphing Simple Equations and Inequalities Mentally
i. What Makes Equations True or False
1. i.e. What solution make x + 7 = 10 true?
2. i.e. What solution(s) make x + 7 = 10 false?
ii. What Makes Inequalities True or False
3. i.e. What solution(s) make x + 7 < 10 true?
4. i.e. What solution(s) make x + 7 < 10 false?
iii. Infinite Solutions vs. 1 Solution
iv. Discrete vs. Continuous Number Sets
Day 3
Solving and Graphing One-Step and Two-Step Equations and Inequalities on a number line
i. Properties of Equality and Inequality to Solve
1. Addition Property
2. Subtraction Property
3. Multiplication Property
4. Division Property
ii. Non-Negative Coefficients
Day 4
Solving and Graphing Equations and Inequalities with Negative Coefficients on a Number Line
i. Identify Negative Coefficients and Solutions to Equations
1. i.e. if –x = 3, then x = -3
2. Using the Property of Multiplication by -1
ii. Identify Negative Coefficients and Solutions to Inequalities
1. i.e. if –x < 3, then x > -3
2. Using the Property of Multiplication by -1
iii. Introduce this Concept when Solving One and Two-Step Equations or Inequalities
1. i.e. if -2x + 5 = 9, then 2x – 5 = -9
2. i.e. if -2x + 5 > 9, then 2x – 5 < -9
Day 5
Solving and Graphing Multi-Step Equations and Inequalities on a number line
i. Right Side of Equation or Inequality is a Constant, Left Side has the Expression
ii. Use Distribution and Combine Like Terms to Simplify One Side Only
1. Set One Side to a Two-Step Equation or Inequality.
2. If Coefficient is Negative then Make Coefficient Positive
Day 6
Solving and Graphing One-Step and Two-Step Absolute Value Equations
i. Two Solutions from Two Equations
1. i.e. if | x – 5 | = 2, then x – 5 = 2 or x – 5 = -2
2. Plot two points on number line
ii. Identify any number of solutions.
Day 7
Applications
Day 8
Review
Day 9
TEST
V.
Intro to Functions (9 days)
Day 1
Dependent vs. Independent variables
i. Identify Independent and Dependent Variables from Tables, Word Phrases and Graphs
ii. Title Graph and Label Quad I Axes
iii. Plot Variables on Quad I only
iv. Discrete vs. Continuous
v. Correlations
Day 2
Expand Graphing Variables to Entire Coordinate Plane
i. Quad I,II, III, IV
ii. Label Coordinate Axes
iii. Reinforce Independent and Dependent Variables
iv. Reinforce Plotting Points Using Tables and Word Phrases
v. Relate Coordinate Pairs to Independent and Dependent Variables
Day 3
Introduce Functions
i. Generate Tables from Functions as “y =”
1. Create tables and plot points from generated tables
2. Reinforce the independent and dependent variables in table
ii. Show (x, y) as an infinite number of points from table as the independent variable determines the
dependent variable
Day 4
Introduce Function Notation
i. From “y =” , introduce ”f(x) =” as function notation
1. Create tables and plot points from generated tables
2. Reinforce the independent and dependent variables in table
3. Show (x, f(x)) as an infinite number of points from table as the independent variable
determines the dependent variable
ii. Generate tables for all families of functions and discuss the naming of each family
1. Linear Function
2. Absolute Value Function
3. Quadratic Function
4. Root Function
Day 5
Identify the Patterns of Each Family to Graph Parent Functions
i. Point to Point Pattern for each Parent Starting at the Origin
ii. Identify Parents from Given Transformed Graphs
1. Discuss what happened to the function to be transformed
2. Discuss translation, stretch and reflections from parent function
Day 6
Properties of Parent Functions
i. Identify the Major Properties of each Parent Function
1. Vertex
2. Domain/Range
3. Max/Min
4. Roots
ii. Match Graphs to Parent Functions
1. Given function notation
2. Given “graphs” of transformed functions
iii. Identify Any Major Properties of Transformed Parent Functions
Day 7
Applications
Day 8
Review
Day 9
TEST
VI.
Pairs of Linear Equations (9 days)
Day 1
Graphical Solutions
i. Given a Graph of Two Lines
1. Identify number of solutions
2. Write solution as a coordinate pair
ii. Given a Table of Points
1. Plot points as 2 lines
2. Write solution as a coordinate pair
Day 2
Types of Solutions
i. Parallel Lines (No Solution)
ii. Collinear Lines (Infinite Solutions)
iii. Intersecting Lines (One Solution)
Day 3
Simple Substitution
i. First Equation in Standard Form, Second Equation has Variable as Constant
1. i.e. if 3x + 4y = 10 and x = 2, then find x and y
2. i.e. if x + y = 10 and y = 2x – 2, then find x and y
3. Write solution as a coordinate pair
ii. First Equation Variable is Constant, Second Equation Variable is an Expression
1. i.e. if y = 4 and y = 2x – 6, then find x and y
2. i.e. if 2x = 8 and x = y – 10, then find x and y
3. Write solution as a coordinate pair
Day 4
Equivalent Equations for Substitution
i. Find Equivalent Sets of Equations
1. i.e. if y = x + 4, then 2y = 2x + 8
2. Discuss multiplication and division factors that make equivalent equations
ii. Use Equivalent Equations for Substitution
1. i.e. if 4x + 3y = 15 and y = x – 2, then use 3y = 3x – 6 to substitute 3y
2. i.e. if 2x – 4y = 12 and y = 2x, then use -4y = -8x to substitute -4y
iii. Show Multiplication of Equations is the Same as Adding or Subtracting Equations
1. i.e. if x + y = 10, then 2x + 2y = 20 or 3x + 3y = 30 by multiplication
2. i.e. x + y = 10 added to 2x + 2y = 20 equals 3x + 3y = 30
Day 5
Simple Elimination
i. Adding Equations to Eliminate
ii. Multiply One Equation to Eliminate
Day 6
Complex Elimination
i. Multiply Both Equations to Eliminate
a. Find LCM for each variable in both equations
b. Choose variable to eliminate
Day 7
Applications
Day 8
Review
Day 9
TEST