Curriculum Map: Algebra 1

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