Grade 11
Math 3
Scope
Students work with many function types both algebraically and graphically and apply them to real world applications. Function types include linear, quadratic, square root, cube root, piecewise-defined, polynomial, exponential, logarithmic and trigonometric. In addition, probability and inferential statistics concepts are explored.
Unit — Linear Relationships and Functions
Essential Questions
How can functions apply to real-world situations?
When solving a 2-variable system algebraically, which method is the most efficient?
What is the best way to model a given bivariate data set?
Guiding Questions
How can we evaluate functions at certain values?
How can we solve a 2-variable system both graphically and algebraically?
How can we solve systems with 3 equations and 3 unknowns?
How can we use the calculator to come up with the best model for a given bivariate data set?
Resources
Algebra 2 Common Core by Pearson © 2015
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: Reasoning with Equations and Inequalities: A-REI.5, A-REI.6, A-REI.7, A-REI.11
Functions: Interpreting Functions: F-IF.5, F-IF.7
Functions: Building Functions: F-BF.1, F-BF.1b, F-BF.3, F-BF.4a
Functions: Linear, Quadratic, and Exponential Media: F-LE.5
Statistics and Probability: Interpreting Categorical and Quantitative Data: S-ID.6, S-ID.6a
Unit — Quadratic, Polynomial, and Radical Functions and Relations
Essential Questions
What is the most effective method for solving a particular quadratic equation?
What are the advantages/disadvantages for the different forms of a quadratic function?
How can the rules of exponents be extended to rational exponents?
How can we extend our knowledge of numbers to those involving the square root of negative quantities?
How can we break a polynomial function into factors and use its degree to determine its end behavior in order to understand the function graphically?
Guiding Questions
How can we solve equations by utilizing the Zero Product Property, completing the square and the quadratic formula?
How can we graph a quadratic function given standard, vertex or locus form?
How can we model a real world scenario with a circle equation or quadratic function?
How can we perform mathematical operations with radical expressions?
How can we evaluate complex expressions?
How can we graph a polynomial function if we know its zeros (of varying multiplicity) and its end behavior?
Resources
Algebra 2 Common Core by Pearson © 2015
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: N-RN.1, N-RN.2
Number and Quantity: Quantities: N-Q.2
Number and Quantity: The Complex Number System: N-CN.1, N-CN.2, N-CN.7
Algebra: Seeing Structure in Expressions: A-SSE.2, A-SSE.3, A-SSE.3c
Algebra: Arithmetic with Polynomials and Rational Expressions: A-APR.2, A-APR.3, A-APR.4, A-APR.6
Algebra: Creating Equations: A-CED.1
Algebra: Reasoning with Equations and Inequalities: A-REI.1, A-REI.2, A-REI.4, A-REI.4b, A-REI.11
Functions: Interpreting Functions: F-IF.4, F-IF.5, F-IF.6, F-IF.7c, F-IF.8, F-IF.9
Functions: Building Functions: F-BF.3
Geometry: Expressing Geometric Properties with Equations: G-GPE.2
Unit — Advanced Functions and Relations
Essential Questions
How can we use our knowledge of mathematics with fractions to simplify and perform operations on rational expressions?
How can we model real world scenarios like half-life decay and compound interest in a bank account using exponential functions?
Can we come up with different ways of describing a sequence mathematically?
Guiding Questions
How can we use factoring to help us simplify and perform operations with rational expressions?
How can we evaluate a logarithmic expression?
How can we come up with an explicit/recursive formula for a sequence?
Resources
Algebra 2 Common Core by Pearson © 2015
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: Quantities: N-Q.2
Algebra: Seeing Structure in Expressions: A-SSE.2, A-SSE.3c, A.SSE.4
Algebra: Creating Equations: A-CED.1
Algebra: Reasoning with Equations and Inequalities: A-REI.2, A-REI.4b, A-REI.11
Functions: Interpreting Functions: F-IF.3, F-IF.7e, F-IF.8b
Functions: Building Functions: F-BF.1a, F-BF.1b, F-BF.2, F-BF.3, F-BF.4, F-BF.4a
Functions: Linear, Quadratic, and Exponential Models: F-LE.2, F-LE.4, F-LE.5
Unit — Probability and Statistics
Essential Questions
What is the difference between two events being “mutually exclusive” and two events being “independent”?
Can certain data be exactly modeled by a normal curve?
How can we simulate the repetition of taking samples or the repetition of randomizing treatments?
Guiding Questions
How can we use the mathematical operations of addition and multiplication to calculate probabilities based on a given probability context?
When data is approximately normally distributed, how can we estimate the probability of a given range of events?
How can we determine if the results of an experiment are statistically significant?
Resources
Algebra 2 Common Core by Pearson © 2015
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: S-ID.4
Statistics and Probability: Making Inferences and Justifying Conclusions: S-IC.1, S-IC.2, S-IC.3, S-IC.4, S-IC.5, S-IC.6
Statistics and Probability: Conditional Property and the Rules of Probability: S-CP.1, S-CP.2, S-CP.3, S-CP.4, S-CP.5, S-CP.6, S-CP.7
Unit — Trigonometry
Essential Questions
How can we extend our knowledge of right triangle trigonometry (i.e. “SOHCAHTOA”) to help us evaluate trigonometric values?
How can the behavior of periodic phenomena (like tides, height of a moving Ferris wheel car) be modeled with a sinusoidal curve?
Guiding Questions
How can we use the unit circle to evaluate trigonometric functions of common angles?
How can we evaluate trigonometric function values of angles given in radian measure?
Resources
Algebra 2 Common Core by Pearson © 2015
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.
Functions: Interpreting Functions: F-IF.4, F-IF.6, F-IF.7e
Functions: Building Functions: F-BF.1a, F-BF.3
Functions: Trigonometric Functions: F-TF.1, F-TF.2, F-TF.5, F-TF.8