Grade 9
Math 1
Scope
Algebra 1 covers all standards for NYS Math Standards for Algebra I. The course builds on work from middle school math and develops and deepens the understanding of both algebra and functions
Unit — Relationships Between Quantities
Essential Questions
How can we model real-world situations with algebraic expressions?
How can we write an equation to model a real-world situation?
Guiding Questions
How do we use properties to simplify algebraic expressions?
How do we use properties to find expressions that are algebraically equivalent?
How do we solve linear equations?
How do we know which solutions are viable for a given real-world problem?
Resources
Algebra 1 published by McGraw Hill © 2014
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
Number and Quantities: AI-N.Q.1, AI-N.Q.3
Algebra: Seeing Structure in Expressions: AI-A.SSE.1a, AI-A.SSE.1b, AI-A.SSE.2
Algebra: Creating Equations: AI-A.CED.1, AI-A.CED.2, AI-A.CED.4
Algebra: Reasoning with Equations and Inequalities: AI-A.REI.1a, AI-A.REI.3, AI-A.REI.10
Functions: Interpreting Functions: AI-F.IF.1, AI-F.IF.2, AI-F.IF.4
Unit — Linear Relationships
Essential Questions
How does the graph of a linear function relate to an equation?
How do the parts of a linear function in slope intercept form relate to a real-world situation?
How does solving a linear inequality differ from solving a linear equation?
What does the solution to a system of equations/inequalities represent?
Guiding Questions
How do we graph a line from standard form?
How does slope relate to average rate of change?
How are the slopes of parallel and perpendicular lines related?
How can we write a system of equations/inequalities to model a real world situation?
Resources
Algebra 1 published by McGraw Hill © 2014
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
Number and Quantities: AI-N.Q.1
Algebra: Creating Equations: AI-A.CED.1, AI-A.CED.2, AI-A.CED.3
Algebra: Reasoning with Equations and Inequalities: AI-A.REI.3, AI-A.REI.6a, AI-A.REI.10, AI-A.REI.11, AI-A.REI.12
Functions: Interpreting Functions: AI-F.IF.2, AI-F.IF.4, AI-F.IF.5, AI-F.IF.6, AI-F.IF.7a
Functions: Building Functions: AI-F.BF.1, AI-F.BF.3a
Functions: Linear, Quadratic, and Exponential Models: AI-F.LE.1a, AI-F.L.E.1b, AI-F.LE.2, AI-F.LE.5
Statistics and Probability: Interpreting Categorical and Quantitative Data: AI-S.ID.6, AI-S.ID.7, AI-S.ID.8, AI-S.ID.9
Unit — Exponential & Quadratic Relationships
Essential Questions
What are the key parts of an exponential function?
What is an equivalent expression and what steps can we use to find equivalent expressions from a given expression?
How are the zeros of a quadratic equation related to the graph of the quadratic function?
How do the different forms of a quadratic function give information about key features of the graph?
What is the difference between a rational and irrational number?
Guiding Questions
How can we model real-world situations using exponential functions?
What is a polynomial?
How can we solve quadratic equations graphically/algebraically?
What is the quadratic formula?
What impact does adding/subtracting inside/outside the function have on the graph?
What is the shape of an absolute value graph?
Resources
Algebra 1 published by McGraw Hill © 2014
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
Algebra: Seeing Structure in Expressions: AI-A.SSE.1a, AI-A.SSE.2, AI-A.SSE.3c
Algebra: Arithmetic and Polynomials and Rational Expressions: AI-A.APR.1, AI.A.APR.3
Algebra: Reasoning with Equations and Inequalities: AI-A.REI.1a, AI-A.REI.4, AI-A.REI.4b, AI-A.REI.7a, AI-A.REI.11
Functions: Interpreting Functions: AI-F.IF.3, AI-F.IF.4, AI-F.IF.6, AI-F.IF.7, AI-F.IF.7a, AI-F.IF.7b, AI-F.IF.8, AI-F.IF.8a, AI-F.IF.9
Functions: Building Functions: AI-F.BF.3a
Functions: Linear, Quadratic, and Exponential Models: AI-F.LE.1c, AI-F.LE.2, AI-F.LE.3, AI-F.LE.5
Statistics and Probability: Interpreting Categorical and Quantitative Data: AI-S.ID.6a
Unit — Advanced Functions and Equations
Essential Questions
What key features are used when graphing each type of function?
What is a radical?
What is a rational expression?
Guiding Questions
How do we graph a square root function?
How do we graph a cube root function?
How do we simplify radicals?
How do we use operations with radicals?
How do we simplify rational expressions?
Resources
Algebra 1 published by McGraw Hill © 2014
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
Number and Quantity: The Real Number System: AI-N.RN.3
Algebra: Creating Equations: AI-A.CED.2
Algebra: Reasoning with Equations and Inequalities: AI-A.REI.4a, AI-A.REI.11
Functions: Interpreting Functions: AI-F.IF.4, AI-F.IF.7b
Unit — Data Analysis
Essential Questions
Which measure of central tendency best describes a given data set?
What are the benefits/limitations for different methods of displaying data?
Guiding Questions
What is the mean/median/mode?
How do we read/create a dot plot?
Resources
Algebra 1 published by McGraw Hill © 2014
Skills
Students will:
make sense of problems and persevere in solving them.
reason abstractly and quantitatively.
construct viable arguments and critique the reasoning of others.
model with mathematics.
use appropriate tools strategically.
attend to precision.
look for and make use of structure.
look for and express regularity in repeated reasoning.
Statistics and Probability: Interpreting Categorical and Quantitative Data: AI-S.ID 1, AI-S.ID.2, AI-S.ID.3, AI-S.ID.5