Curriculum Documents by Quarter - Mathematics - Algebra I

Unit of Study 1: Algebra I Unit 1
Standards
Essential Questions

Learning Objectives

The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. 

 

The student uses the properties and attributes of functions.

 

The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols

To represent situations. 

 

The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

What are different ways of representing numbers?

 

How do patterns and relationships help us understand mathematical situations?

 

How do we represent patterns and relationships in everyday life?

 

How can change be analyzed?

Vocabulary

  • ·        Linear Equation
  • ·        Problem solving strategy
  • ·        Algebraic model
  • ·        Matrix
  • ·        Function form
  • ·        Coordinate Plane
  • ·        Ordered pair
  • ·        Quadrant
  • ·        Scatter plot
  • ·        Slope
  • ·        Direct variation

Learning Objectives

·         Student translates a verbal phrase into algebraic equations to solve real life situations.

·         Student follows a problem solving plan using an algebraical model of the real life situation.

·         Student organizes data in a matrix and performs arithmetic operations among them. 

·         Student applies four arithmetic operations to solve linear equations.  

·         Student solves a real life problem by drawing a diagram or applying tables and graphs to represent a linear equation. 

·         Student rewrites a two-variable equation in function form. 

·         Students plot points and recognize the location of ordered pairs in a coordinate plane.

·         Students predict outcomes using a scatter plot to organize and display the data.

·         Students recognize and apply strategies to graph equations by using tables and slope intercept form.

·         Students recognize and use direct variation to represent linear equations.

Students solve a linear equation and check the solution graphically and algebraically.

Unit of Study 2: Algebra I Unit 2

The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

 

The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

 

How do patterns and relationships help us understand mathematical situations?

How do we represent patterns and relationships in everyday life?

How can mathematical thinking be organized and presented so that it can be         shared with others?

How can we develop a mathematical language that is useful in the real world?

How can we use representations to model and interpret physical, social and          mathematical phenomena?

Vocabulary

  • Slope Intercept form of the equation of a line
  • Linear function
  • Point slope form of a linear equation
  • Standard form of a linear equation
  • Linear Inequality
  • Compound Inequalities
  • Absolute Value equations
  • Absolute Value Inequalities
  • Linear system

Skills

·         Students recognize and write an equation of a line using slope intercept form, point slope form and standard form of a linear equation. 

·         Students solve and graph linear and compound inequalities and absolute value equations and inequalities.

·         Students compare and contrast among absolute value equations and inequalities.

·         Students graph and represent linear inequalities in two variables by separating the coordinate plane and testing points on it.

·         Students apply and choose strategies for solving linear systems by using graphing, substitution, or by linear combinations.  

·         Students identify linear systems as having one solution, no solution or infinitely many solutions.

Unit of Study 3: Algebra I Unit 3

The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

 

The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

 

 
What are different ways of representing, organizing, and relating numbers to mathematical operations?

How do we understand and represent patterns, relationships, and change?

·         What are the characteristics, properties, and applications of multi-dimensional shapes?

·         How do we collect, organize, display, and analyze data?

·         Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?

·         How can mathematical thinking be effectively communicated to different audiences?

·         How are mathematical concepts related to one another, other disciplines, and to the real world?

Vocabulary

  • Zero exponents
  • Negative exponents
  • Exponential functions
  • Exponential growth
  • Exponential Growth Model
  • Exponential decay
  • Exponential decay model
  • Perfect square
  • Irrational Numbers
  • Radical expressions
  • Quadratic equation
  • Parabola
  • Vertex
  • Axis of symmetry
  • Quadratic formula
  • Discriminant

Skills

Students use and apply properties of exponents to perform operations with exponential expressions.

Students evaluate powers, simplify expressions and graph exponential functions.

Students write, model and graph exponential growth and decay. 

Students solve a quadratic equation graphically, using the quadratic formula or using a square root.

Students represent a quadratic equation on a U shaped graph or parabola 

Students apply properties of radicals to simplify radicals. 

Students apply the discriminant to find number of solutions of a quadratic equation.

Unit of Study 4: Algebra I Unit 4

The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

 

The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation

 

·What are different ways of representing, organizing, and relating numbers to mathematical operations?

·         How do we understand and represent patterns, relationships, and change?

·         How do we collect, organize, display, and analyze data?

·         Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?

·         How can mathematical thinking be effectively communicated to different audiences?

·         How are mathematical concepts related to one another, other disciplines, and to the real world?

Vocabulary

  • Polynomial
  • Degree of a polynomial
  • Monomial
  • Binomial
  • Trinomial
  • FOIL pattern
  • Factored form of a polynomial
  • Factor
  • Inverse variation
  • Rational number
  • Rational expression
  • Rational equation
  • Rational Function
  • Hyperbola
  • Center
  • Asymptote

 

Skills

·         Students apply arithmetic operations to polynomials

·         Students apply special product patterns for the product of a sum and a difference, and for the square of a binomial. 

·         Students factor a quadratic expression applying different strategies.

·         Students model and apply inverse variation and contrast it with direct variation.

·         Students simplify and apply arithmetic operations to rational expressions.

·         Students solve and represent the graph of a rational equation.

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