Algebra I Curriculum Map
Modified: July, 2013
Timeline:1stTrimester
4 weeks
Vocabulary:
Quantity
Variable
Algebraic Expression
Numerical Expression
Power
Exponent
Base
Simplify
Evaluate
Square Root
Radicand
Radical
Perfect Square
Set
Element of a Set
Subset
Rational Numbers
Natural Numbers
Whole Numbers
Integers
Irrational Numbers
Real Numbers
Inequality
Absolute Value
Opposites
Additive Inverses
Multiplicative Inverse
Reciprocal
Distributive Property
Term
Constant
Coefficient
Like Terms
Decompose / Unit 1: Foundations for Algebra
(Designed for building a stronger skill base in arithmetic, measurements, and number sense.)
New State Standards:
Number and Quantity
(The Real Number System)
HSN-RN.B
Use properties of rational and irrational numbers.
3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Number and Quantity
(Quantities)
HSN-Q.A
Reason quantitatively and use units to solve problems.
2. Define appropriate quantities for the purpose of descriptive modeling.
3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
College Readiness:
(Range 13-15) Basic Operations and Applications: Perform one-operation computation with whole numbers
(Range 16-19) Basic Operations and Applications: Solve some routine two-step arithmetic problems (Range 13-15) Numbers: Concepts and Properties: Recognize equivalent fractions and fractions in lowest terms (Range 16-19) Expressions, Equations, and Inequalities: Substitute whole numbers for unknown quantities to evaluate expressions.
(Range 16-19)Expressions, Equations, and Inequalities: Combine like terms
NCTM:
Number and Operations:
- Develop a deeper understanding of very large and very small numbers and of various representations of them;
- Compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions;
- Use number-theory arguments to justify relationships involving whole numbers.
- Understand the meaning of equivalent forms of expressions
- Use symbolic algebra to represent and explain mathematical relationships
- Draw reasonable conclusions about a situation being modeled
A1A: Set up and solve problems following the correct order of operations (including proportions, percent, and absolutevalue) with rational numbers (integers, fractions, decimals)
A1B: Find the greatest common factor and least common multiple of a set of whole numbers
A1C: Use rational numbers to demonstrate knowledge of additive and multiplicative inverses
A1F: Add, subtract, multiply, and divide rational numbers, including integers, fractions, and decimals, without calculators
B1: Mathematical processes learned in the context of increasingly complex mathematical and real-world problems
C1A: Evaluate and simplify expressions requiring addition, subtraction, multiplication, and division with and withoutgrouping symbols
C1B: Translate real-world problems into expressions using variables to represent values
C1C: Apply algebraic properties (e.g., commutative, associative, distributive, identity, inverse, substitution) to simplifyalgebraic expressions
D1A: Solve single-step and multistep equations and inequalities in one variable
F1A: Use properties of exponents (including zero and negative exponents) to evaluate and simplify expressions
F1D: Find rational number square roots (without calculators) and approximate irrational square roots (with and withoutcalculators) / Activities:
FAL Activities
Making Math Magic
Student-driven instruction
Small group instruction
Modeling
Problem-solving
Bell Ringer
Concepts and Skills:
Students will:
- Perform operations with integers and fractions
- Convert between decimals and fractions
- Write algebraic expressions
- Simplify expressions involving exponents
- Use the order of operations to evaluate expressions
- To classify, graph, and compare real numbers
- Find and estimate square roots
- Find sum and differences of real numbers
- Find products and quotients of real numbers
- Use the distributive property to simplify expressions
1) Make sense of problems and persevere in solving them.
2) Reason abstractly and quantitatively.
3) Construct viable arguments and critique the reasoning of others.
4) Model with mathematics.
5) Use appropriate tools strategically.
6) Attend to precision.
7) Look for and make use of structure.
8) Look for and express regularity in repeated reasoning.
Resources:
- Algebra Tiles
- Making Math Magic
- Infinite Algebra
- McDougal Littlell Algebra 1 Textbook
Timeline:
1st Trimester
2 weeks
Vocabulary:
Equivalent Equations
Addition Property of
Equality
Subtraction Property of
Equality
Isolate
Inverse Operations
Multiplication Property
of Equality
Division Property of
Equality
Identity
Literal Equation
Formula
Proportion
Cross Products
Cross Products Property / Unit 2: Solving Equations
New State Standards:
Algebra
(Creating Equations)
HSA-CED.A
Create equations that describe numbers or relationships.
- Create equations and inequalities in one variable and use them to solve problems.Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
College Readiness:
(Range 13-15) Basic Operations and Applications: Solve problems in one or two steps using whole numbers
(Range 13-15) Expressions, Equations, and Inequalities: Exhibit knowledge of basic expressions
(Range 13-15) Expressions, Equations, and Inequalities: Solve equations in the form x + a = b, where a and b are whole numbers or decimals
(Range 16-19) Expressions, Equations, and Inequalities: Solve one step equations having integer or decimal answers.
(Range 20-23) Expressions, Equations, and Inequalities: Solve routine first-degree equations
NCTM:
Number and Operations:
- Judge the reasonableness of numerical computations and their results.
- Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations
- Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases
- Use symbolic algebra to represent and explain mathematical relationships
- Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.
A1A: Set up and solve problems following the correct order of operations (including proportions, percent, and absolute value) with rational numbers (integers, fractions, decimals)
A1C: Use rational numbers to demonstrate knowledge of additive and multiplicative inverses
A1D: Simplify ratios
A1F: Add, subtract, multiply, and divide rational numbers, including integers, fractions, and decimals, without calculators
B1: Mathematical processes learned in the context of increasingly complex mathematical and real-world problems
C1A: Evaluate and simplify expressions requiring addition, subtraction, multiplication, and division with and without grouping symbols
C1B: Translate real-world problems into expressions using variables to represent values
C1C: Apply algebraic properties (e.g., commutative, associative, distributive, identity, inverse, substitution) to simplify algebraic expressions
D1A: Solve single-step and multistep equations and inequalities in one variable
D1C: Solve formulas for a specified variable
D1F: Write and graph linear equations and inequalities from real-world situations (e.g., a constant-rate distance/timeproblem) / Activities:
FAL Activities
Making Math Magic
Student-driven instruction
Small group instruction
Modeling
Problem-solving
Bell Ringer
Concepts and Skills:
Students will:
- Solve one-step equations in one variable
- Solve two-step equations in one variable
- Solve equations with variables on both sides
- Identify equations that are identities or have no solution
- To rewrite and use literal equations and formulas
- To solve and apply proportions
- Algebra Tiles
- Making Math Magic
- Infinite Algebra
- McDougal Littlell Algebra 1 Textbook
Timeline:
1st Trimester
2 weeks
Vocabulary:
Cartesian Plane
Dependent variable
Direct Variation
Domain
Function
Function Notation
Input
Independent Variable
Inverse Variation
Linear Function
Nonlinear Function
Output
Range
Relation
Vertical Line Test
x-axis
y-axis / Unit 3: An Introduction to Functions
New State Standards:
Expressions and Equations
8.EE.C
Analyze and solve linear equations and pairs of simultaneous linear equations.
7. Solve linear equations in one variable.
Functions
(Interpreting Functions)
HSF-IF.A
Understand the concept of a function and use function notation.
- Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. Iffis a function andxis an element of its domain, thenf(x) denotes the output off corresponding to the inputx. The graph offis the graph of the equationy=f(x).
(Range 24-27) Graphical Representations: Match linear graphs with their equations*
NCTM:
Algebra:
- Understand relations and functions and select, convert flexibly among, and use various representations for them
- Generalize patterns using explicitly defined and recursively defined functions
- Use symbolic algebra to represent and explain mathematical relationships
- Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology
B1: Mathematical processes learned in the context of increasingly complex mathematical and real-world problems
D1F: Identify, formulate, and obtain solutions to problems involving direct and inverse variation
D2A: Graph linear inequalities in one variable on the real number line to solve problems
D2B: Give the domain and range of relations and functions
D2C: Evaluate functions at given values
D2D: Identify graphs of relations and functions and analyze them to determine whether a relation is a function (e.g.,vertical line test)
D2F: Use the terminology associated with the Cartesian plane in describing points and lines
F1B: Evaluate and simplify rational expressions / Activities:
FAL Activities
Making Math Magic
Student-driven instruction
Small group instruction
Modeling
Problem-solving
Bell Ringer
Concepts and Skills:
Students will:
- Connect function notation and ordered pairs
- Find the composition of functions (solving when x = value)
- Identify patterns that describe linear function.
- Identify and represent patterns that describe nonlinear functions using shape language (curved etc).
- Identify and represent patterns that describe functions with direct and inverse variation.
- Solve basic real world problems using direct and indirect variation
- Graph equations that represent functions by plotting points.
- Match equations to sets of points.
- Use a graph to find function values.
- Determine whether a relation is a function (graph or points).
- Find the domain and range (graph or points) and use interval or set notation.
- Evaluate rational expressions given specific values
- Algebra Tiles
- Making Math Magic
- Infinite Algebra
- McDougal Littlell Algebra 1 Textbook
Timeline:
1st Trimester
4 weeks
Vocabulary:
Linear Equations
Line of Best Fit Correlation
Opposite Reciprocals
Parallel Lines
Perpendicular Lines
Rate of Change
Slope
Slope-Intercept Form
Intercept / Unit 4:Linear Functions
New State Standards:
Geometry
(Expressing Geometric Properties with Equations)
HSG-GPE.B
Use coordinates to prove simple geometric theorems algebraically.
5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
College Readiness:
(Range 20-23) Graphical Representations: Exhibit knowledge of slope*
(Range 24-27) Graphical Representations: Determine the slope of a line from points or equations*
(Range 24-27) Graphical Representations: Match linear graphs with their equations*
NCTM:
Algebra:
- Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior
- Use symbolic algebra to represent and explain mathematical relationships
- Understand relations and functions and select, convert flexibly among, and use various representations for them
- Generalize patterns using explicitly defined and recursively defined functions
- Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations
- Use symbolic algebra to represent and explain mathematical relationships
- Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology
B1: Mathematical processes learned in the context of increasingly complex mathematical and real-world problems
D1E: Write linear equations in standard form and slope-intercept form when given two points, a point and the slope, or thegraph of the equation
D2F: Use the terminology associated with the Cartesian plane in describing points and lines
D2G: Recognize the concept of slope as a rate of change and determine the slope when given the equation of a line instandard form or slope-intercept form, the graph of a line, two points, or a verbal description
D2H: Graph a linear equation using a table of values, x- and y-intercepts, slope-intercept form, and technology
D2I: Translate between different representations of relations and functions: graphs, equations, sets of ordered pairs,verbal descriptions, and tables
G1G: Identify an approximate line of best fit to model data and make predictions / Activities:
FAL Activities
Making Math Magic
Student-driven instruction
Small group instruction
Modeling
Problem-solving
Bell Ringer
Concepts and Skills:
Students will:
- Find rates of change and slope from table, graph, and algebraic manipulation for the same problem.
- Write and graph linear equations using slope-intercept or point slope form.
- Find an equation of a line given two points.
- Graph using intercepts.
- Determine whether lines are parallel, perpendicular, or neither.
- Write equations of parallel and perpendicular lines.
- Write an equation of a trend line and of a line of best fit and make predictions based on them (point of emphasis of difference between source data points and prediction points).
- Graph absolute value functions.
- Translate information from graphs of absolute value functions.
- Graph absolute value of nonlinear function (given a graph reflect the negative portion.)
- Draw the tangent line to a graph and find its equation (Calculus tie-in)
- Discuss strength of fit qualitatively (statistical tie-in) optional: draw a rectangle around the core of the data cloud and estimate the correlation and the line of best fit.
- Algebra Tiles
- Making Math Magic
- Infinite Algebra
- McDougal Littlell Algebra 1 Textbook
Timeline:
2nd Trimester
2 weeks
Vocabulary:
Compound Inequality
Equivalent Inequalities
Interval Notation
Set-Builder Notation
Solution of an Inequality
Absolute Value Inequality / Unit 5: Solving and Graphing Linear Inequalities
New State Standards:
Algebra
(Seeing Structure in Expressions)
HSA-SSE.A
Interpret the structure of expressions.
- Interpret expressions that represent a quantity in terms of its context.*
6.EE.B
Reason about and solve one-variable equations and inequalities.
8. Write an inequality of the form xc or xc to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form xc or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
College Readiness:
(Range 20-23) Number Concepts and Properties: Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor
(Range 28-32) Expressions, Equations, and Inequalities: Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions)
(Range 24-27) Expressions, Equations, and Inequalities: Solve first-degree inequalities that do not require reversing the inequality sign
(Range 28-32) Expressions, Equations, and Inequalities: Solve linear inequalities that require reversing the inequality sign
NCTM:
Algebra:
- Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations
- Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases
- Use symbolic algebra to represent and explain mathematical relationships
- Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology
B1: Mathematical processes learned in the context of increasingly complex mathematical and real-world problems
D1A: Solve single-step and multistep equations and inequalities in one variable
D1B: Solve equations that contain absolute value
D1C: Solve formulas for a specified variable
D2A: Graph linear inequalities in one variable on the real number line to solve problems / Activities:
Concepts and Skills:
Students will:
- Solve inequalities using addition, subtraction, multiplication, and division.
- Solve multi-step inequalities.
- Solve equations and inequalities involving absolute value.
- Solve compound inequalities
- Algebra Tiles
- Making Math Magic
- Infinite Algebra
- McDougal Littlell Algebra 1 Textbook
Timeline:
2nd Trimester
4 weeks
Vocabulary:
Consistent
Dependent
Inconsistent
Independent
Linear Inequality
Solution of an Inequality Solution of a System of
Linear Equations
Substitution Method
Elimination Method
Graphing Method / Unit 6: Systems of Equations & Inequalities
New State Standards:
Algebra
(Reasoning with Equations and Inequalities)
HSA-REI.B
Solve equations and inequalities in one variable.
- Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
(Reasoning with Equations and Inequalities)
HSA-REI.C
Solve systems of equations.
- Solve systems of linear equations exactly and approximately focusing on pairs of linear equations in two variables
(Creating Equations)
HSA-CED.A
Create equations that describe numbers and relationships.
- Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axis with labels and scales