Math-Algebra 1 Core Map Quarter 2
| Subject/Grade Level/Unit Title | Timeframe/Grading Period | Big Idea/Themes/Understandings | Essential Questions | Standards | Essential Skills | Vocabulary | Assessment Tasks | Resources | |||||||||||||||||||||||||||||||||||||||||||||||||||
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Linear Functions Function tables and notation Domain and Range Discrete and Contiuous Linear Function Pattern Special Functions Comparing Linear and Nonlinear Arithmetic Sequences Solving Inequalities using addition and Subtraction Solving inequalities using multiplication and division Solving multi-step inequalities Graphing linear inequalities with two variable with two variables Solving Geometric problems using inequalities Solving system of inequalities Absolute value inequalities and graphing on the number line Graphing absolute value functions Key features Transformation of graph Polynomials Operations with polynomials Adding and subtract poynomials Multiplying a monomial by a monomial Multiplying a polynomial by a monomial Factoring Factoring polynomials Factoring greatest common factor Factoring the difference of two perfect squares Factoring trinomials With lead coefficients one one With lead coefficients other than one Factoring Special Products Perfect Square Trinomials Product of the sum and difference Factoring Completely Factoring by grouping
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Quarter 2 |
Linear Functions Discrete and Continuous Domains Linear Function Patterns Special Functions-Piecewise, absolute value and step functions Function Notation Comparing Linear and Nonlinear Functions Arithemetic Sequences Writing and Graphing Inequalities Solving Inequalities Using Addition or Subtraction Solving Inequalities Using Mulitplication and Division Solving Multi-step Inequalities Solving Compound Inequalities Graphing Linear Inequalities in two variables Solving Systems of Inequalities Polynomials Adding and Subtracting Polynomials Multiplying Polynomials Special Products of Polynomials Solving Polynomial Equations in Factored Form Factoring Factoring Polynomials using GCF Factoring trinomials with lead coefficient on 1 Factoring trinomials with lead coefficient other than 1 Factoring special products Factoring by grouping Factoring completely
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Linear Functions How can we determine if a relation is a function? How can you find the domain and range of a function? How are independent variables and dependent variables different? Why does the vertical line test help determine if a relation is a function? How can we determine if a function is discrete or continuous? How can you use a linear function to describe a linear pattern? Why is a linear function a graph of a non-linear line? How can you use function notation to represent a function? How can you recognize when a pettern in real life is linear or nonlinear? How do graph a piecewise function? What real life situations can be modeled by piecewise functions? How do we graph step functions? What real life situations can be modeled by step functions? How do we graph absolute value functions? What real life situations can be modeled by absolute value functions? Does a non-linear function have a constant rate of change? How are arithmetic sequences used to describe a pattern? How does an inequalitiy statement differ from an equation? How can we determine the solutions to the inequality? How can we graph (display) the solutions to an inequaltiy? What are alternate ways we can describe solution sets? When do we include the stated value and when do we exclude it? What are real life situations that can be modeled by inequalities? What properties hold true when solving inequalities? Can you explain why those that do not, do not? Can can you use an inequalitiy to describe the area and perimeter of a composite figure? What does a compound inequality represent? How does an absolute value inequality look on a graph? How can we represent solutions to inequalities with two variables on a coordinate plane? How can we know exclusivity or inclusivity on the boundry lines? Polynomials How can you use algebra tilles to model and classify polynomials? How can you determine the degree of a polynomial? How can we find a sum of polynomials? How can we determine the difference of polynomials? Can you describe the difference in finding a sum and difference of polynomials? What methods can be used to find the product of two binomials? Can you determine the patterns of special products? How can you solve an equation that is written in factored form? What is the connection between the roots, solutions and zeros of a polynomial equation? Factoring How can we rewrite a polynomial as the product of factors? What is the only type of binomial that factors into two binnomials? Why? What do the signs in the binomal factors tell you about the polynomial in standard form? Can you recgonize and factor special products? How does using commutative and associative properties help us to factor by grouping? What do like terms physically look like?
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Linear Functions Use the vertical line test to determine if a given relation is a function Determine the domain and range of a function Write the domain and range in multiple forms Determine restrictions of domain and range Determine if a domain is discrete or continuous Write functions and graph functions based on real life situations Examine patterns in functions Use patterns to write functions Determine the common differences in linear functions Graph and state domain and ranges of piecewise, absolute value and step functions Examine the translations of the functions Solve multi-step inequalties in one variable Graph solutions to inequalities on number line Solve compound inequalities and graph on the number line Solve absolute value inequalities and graph on the number line Solve multi-step absolute value inequalities and graph on the number line Solving and graphing inequalities with two variables and graph on the coordinate plane Solve geometric problems with inequalities Polynomials Determine if a term is a monomial Determine the number of terms and degree of a given polynomial Add, subtract, mulitply and divide polynomials (by monomials only) Factoring Factoring polynomials using GCF Factoring binomials Factoring trinomials Factoring completely Factoring by grouping
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Functions relations function function notation discrete function continuous function vertical line test function notation intercepts positive, negative, increasing, decreasing, extrema and end behavior relative minimum relative maximum constant function constant of variation dependent variable dependent axis direct variation domain indentity function independent axis independent variable intercept linear function parallel perpendicular range rate of change compound inequalities inclusive exclusive inverses functions modeling with linear functions non-linear functions absolute value functions absolute value inequalities sequence arithmetic sequene common difference Polynomials term monomial polynomial degree of monomial degree of polynomial binomial trinomial special products distribute double distribute Factoring factoring standard non-standard form factored form zero-property roots greatest common factor differene of two perfect squares factoring by grouping prime polynomial factored completely |
Pass the paper Pair share Exit Notes Classroom Assessments Writing prompt Dailly spiral review Weekly spiral review Benchmarks Self-Correcting Lab Assessment Algebra I Core Assessment STARS Assessment |
Algebra 1 - McGraw Hill Education Algebra 1- Amsco School Publications Big Ideas Algebra 1- Big Ideas Learning NYS Modules |
