Asbury Park High School

Asbury Park High School
Unit Plan
Department: Mathematics Unit designation: #1 Probability & Statistics
Course: Algebra II Anticipated timeframe: Day 1-9
Standards addressed:
·  S.1C Making inferences and justifying conclusions
o  S.1C.1; S.1C.2 Understand and evaluate random processes underlying statistical experiments
o  S.1C.3; S.1C.4; S.1C.5; S.1C.6 Make inferences and justify conclusions from sample surveys, experiments, and observation studies.
·  S.1D Interpreting categorical and qualitative data
o  S.1D.4 Summarize, represent, and interpret data on a single count or measurement
·  S.MD Use probability to make decisions
o  S.MD.6; S.MD.7 Use probability to evaluate outcomes of decisions
·  S.CP Conditional probability and the rules of probability
o  S.CP.2;S.CP.3;S.CP.4;S.CP.5 Understand independence and conditional probability and use them to interpret data
o  S.CP.6;S.CP.7;S.CP.8;S.CP.9 Use the rules of probability to compute the probabilities of compound events in a uniform probability model
Transfer Goals:
·  Distinguish between and calculate permutations and combinations to make real life decisions when given options.
·  Understand that repeated trials of experimental probability will approach theoretical probability.
·  Decide which measure of central tendency best describes a set of data.
Enduring Understandings:
·  You can use multiplication to quickly count the number of ways certain things can happen.
·  The probability of an impossible event is zero, and of a certain event is 1, which is 100%. (Otherwise the probability is between 0 and 1.)
·  When the occurrence of one event affects how a second event can occur, the events are dependent. Otherwise, the events are independent.
·  Measures of central tendency are used to describe and compare sets of data.
·  Standard deviation is a measure of how far numbers in data set deviate from the mean.
·  Normal distribution has data that vary randomly from the mean. The graph of a normal distribution is a normal curve (bell curve). / Essential Questions:
·  What is the difference between a permutation and a combination?
·  What is the difference between experimental and theoretical probability?
·  How are measures of central tendency different from standard deviation?
Learners will know:
·  Permutations and combinations (fundamental counting principle)
·  Probability
·  Probability of multiple events
·  Conditional probability
·  Analyzing data
·  Standard deviation
·  Samples and surveys
·  Binomial distributions
·  Normal distributions
·  Key terms: pg. 743 chapter vocabulary; (pg 672, ELL) / Learners will be able to:
·  Count permutations and combinations.
·  Find the probability of an event using theoretical, experimental, and simulations methods.
·  Find the probability of events “a” AND “b”.
·  Find the probability of events “a” OR “b”.
·  Find conditional probabilities.
·  Use tables and tree diagrams to determine conditional probabilities.
·  Calculate the measures of central tendency.
·  Draw and interpret box and whisker plots.
·  Find standard deviation and variance for a set of values.
·  Apply standard deviation and variance.
·  Identify sampling methods.
·  Recognize bias in samples and surveys.
·  Find binomial probabilities and use binomial distributions.
·  Use normal distribution.
Performance Tasks:
·  Mid-unit quiz
·  Unit test
·  Group station products
·  Authentic assessment
·  Dynamic Activities (found a few times in each chapter) / Other Evidence:
·  Daily class work
·  Class participation
·  Group collaborations
·  Do Now quizzes
Authentic Assessment: “pull it all together”, pg. 742, choose #1 or #2 or #3
Learning Plan
Anticipated daily sequence of activities:
·  Permutations and combinations 11-1
·  Probability 11-2
·  Probability of multiple events 11-3
·  Conditional probability 11-4
·  Analyzing data 11-5
·  Standard deviation 11-6
·  Samples and surveys 11-7
·  Binomial distributions 11-8
·  Normal distributions 11-9
Anticipated resources:
·  Pearson/Prentice Hall Algebra II text
·  Student Skills Handbook
·  Student Visual Glossary
·  Spanish version of materials
·  Pearson MathXL system and resources
·  Pearson test bank generating software
·  ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics Unit designation: #2 Expressions/Equations/Inequalities
Course: Algebra II Anticipated timeframe: Day 9-14
Standards addressed:
·  A.SSE Seeing structure in expressions
o  A.SSE .1.b See structure in expressions
·  A.CED.1 Create equations that describe numbers or relationships
Transfer Goals:
·  Understand that absolute value is a measure of the distance from zero.
·  Know that between and two real numbers, there exists an infinite amount of other real numbers. (State a value between any two given real values.)
·  Understand that inequalities yield a range of solutions.
·  Real world quantities can be expressed in a variety of forms (diagrams, words, tables, graphs, expressions).
Enduring Understandings:
·  You can represent some patterns and real-world quantities using diagrams, words, numbers, or algebraic expressions.
·  You can graph every real number as a point on the number line.
·  You can use the properties of equality and inverse operations to solve equations.
·  You can use properties of equality to solve inequalities.
·  Absolute value is never negative (distance is always positive). / Essential Questions:
·  How do variables help you model real world situations?
·  How can you use the properties of real numbers to simplify algebraic expressions?
·  How do you solve an equation or inequality?
Learners will know:
·  Patterns and expressions
·  Properties of real numbers
·  Algebraic expressions
·  Solving equations
·  Solving inequalities
·  Absolute value equations and inequalities
·  Key terms: pg. 50 chapter vocabulary (text); pg. 2, ELL / Learners will be able to:
·  Identify and describe patterns.
·  Graph and order real numbers; identify properties of real numbers.
·  Evaluate and simplify algebraic expressions.
·  Solve equations.
·  Solve problems by writing equations.
·  Solve and graph inequalities.
·  Write and solve compound inequalities.
·  Write and solve equations and inequalities involving absolute value.
Performance Tasks:
·  Mid-unit quiz
·  Unit test
·  Group station products
·  Authentic assessment
·  Dynamic Activities (found a few times in each chapter) / Other Evidence:
·  Daily class work
·  Class participation
·  Group collaborations
·  Do Now quizzes
Authentic Assessment: “pull it all together”, pg. 49, choose #1 or #2
Learning Plan
Anticipated daily sequence of activities:
·  Patterns and expressions 1-1
·  Properties of real numbers 1-2
·  Algebraic expressions 1-3
·  Solving equations 1-4
·  Solving inequalities 1-5
·  Absolute value equations and inequalities 1-6
Anticipated resources:
·  Pearson/Prentice Hall Algebra II text
·  Student Skills Handbook
·  Student Visual Glossary
·  Spanish version of materials
·  Pearson MathXL system and resources
·  Pearson test bank generating software
·  ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics Unit designation: #3 Functions/Equations/Graphs
Course: Algebra II Anticipated timeframe: Day 15-24
Standards addressed:
·  F.IF Interpreting functions
o  F.IF.4; F.IF.6 Interpret functions that arise in applications in terms of the context
o  F.IF.7; F.IF.8; F.IF.9 Analyze functions using different representations
·  F.BF Building functions
o  F.BF.3 Build a function that models a relationship between two quantities
Transfer Goals:
·  Model real-world situations using data sets and creating linear equations.
·  Recognize that transformations from the parent functions (translations, dilations, reflections) can be seen in the graph as well as the equation.
Enduring Understandings:
·  A relation is a set of pairs of input and output values.
·  A function is a special type of relation in which for every input, there is exactly one output. (The “x” can’t repeat.)
·  A direct variation is a linear equation where the y-intercept is 0 (goes through the origin).
·  Slope is the rate of change; m = ∆y/∆x; m = rise/run.
·  Parallel lines have the same slope; m1 = m2
·  Scatter plots can be used to determine if a correlation exists (strong/weak; negative/positive; none).
·  Sets of functions called are “families.” Each function is a transformation from the “parent.”
·  The graph of the absolute value of a linear function in two variables is V-shaped and symmetric about the axis of symmetry.
·  The solutions of a linear inequality are represented by a half plane. The boundary may or may not be included in the solution set. / Essential Questions:
·  Does it matter which form of a linear equation you use?
·  How do you use transformations to help graph absolute value functions?
·  How can you model data with a linear function?
Learners will know:
·  Relations and functions
·  Direct variation
·  Linear functions and slope-intercept form
·  More about linear equations
·  Using linear models
·  Families of functions
·  Absolute value functions and graphs
·  Two-variable inequalities
·  Key terms: pg. 122 chapter vocabulary; pg. 58, ELL / Learners will be able to:
·  Graph relations and identify functions.
·  Write and interpret direct variation equations.
·  Graph linear equations.
·  Write equations of lines.
·  Write an eq1uation of a line given slope and a point on the line.
·  Analyze transformations of functions.
·  Graph absolute value functions.
·  Graph two-variable inequalities.
Performance Tasks:
·  Mid-unit quiz
·  Unit test
·  Group station products
·  Authentic assessment
·  Dynamic Activities (found a few times in each chapter) / Other Evidence:
·  Daily class work
·  Class participation
·  Group collaborations
·  Do Now quizzes
Authentic Assessment: “pull it all together”, pg. 121, choose #2
Learning Plan
Anticipated daily sequence of activities:
·  Relations and functions 2-1
·  Direct variation 2-2
·  Linear functions and slope-intercept form 2-3
·  More about linear equations 2-4
·  Using linear models 2-5
·  Families of functions 2-6
·  Absolute value functions and graphs 2-7
·  Two-variable inequalities 2-8
Anticipated resources:
·  Pearson/Prentice Hall Algebra II text
·  Student Skills Handbook
·  Student Visual Glossary
·  Spanish version of materials
·  Pearson MathXL system and resources
·  Pearson test bank generating software
·  ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics Unit designation: #4 Linear Systems
Course: Algebra II Anticipated timeframe: Day 25-32
Standards addressed:
·  A.CED Creating Equations
o  A.CED.2; A.CED.3 Create equations that describe numbers or relationships
·  A.REI Reasoning with equations and inequalities
o  A.REI.5; A.REI.6; A.REI.8 Solve systems of equations
o  A.REI.11; A.REI.12 Represent and solve equations and inequalities graphically
Transfer Goals:
·  Systems can be solved using a variety of methods. Determine which method is best to use with a given set of equations.
Enduring Understandings:
·  To solve a system of equations, find a point (x, y) that makes both equations true simultaneously.
·  You can solve systems using guess-and-check, graphically, using tables, algebraically, or using matrices.
·  Inequalities can be solved in more than one way. The solution set consists of the intersection of two half-planes.
·  Some real-world problems can be solved using linear programming because there are multiple constraints.
·  You can use a matrix to represent and solve a system of equations without writing the variables. / Essential Questions:
·  How does representing functions graphically help you solve a system of equations?
·  How does writing equivalent equations help you solve a system of equations?
·  How are the properties of equality used in the matrix solution of a system of equations?
Learners will know:
·  Solving systems using tables and graphs
·  Solving systems algebraically
·  Systems of inequalities
·  Linear programming
·  Solving systems using matrices
·  Key terms: pg. 183 chapter vocabulary; pg. 132 ELL / Learners will be able to:
·  Solve a linear system using a graph or table.
·  Solve linear systems algebraically.
·  Solve systems of linear inequalities.
·  Learners will be able to solve problems using linear programming.
·  Represent a system if linear equations with a matrix.
·  Solve a system of linear equations using matrices.
Performance Tasks:
·  Mid-unit quiz
·  Unit test
·  Group station products
·  Authentic assessment
·  Dynamic Activities (found a few times in each chapter) / Other Evidence:
·  Daily class work
·  Class participation
·  Group collaborations
·  Do Now quizzes
Authentic Assessment: “pull it all together”, pg. 182, choose #2
Anticipated daily sequence of activities:
·  Solving systems using tables and graphs 3-1
·  Solving systems algebraically 3-2
·  Systems of inequalities 3-3
·  Linear programming 3-4
·  Solving systems using matrices 3-6
Anticipated resources:
·  Pearson/Prentice Hall Algebra II text
·  Student Skills Handbook
·  Student Visual Glossary
·  Spanish version of materials
·  Pearson MathXL system and resources
·  Pearson test bank generating software
·  ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics Unit designation: #5 Quadratic Functions & Equations
Course: Algebra II Anticipated timeframe: Day 33-39
Standards addressed:
·  N.CN The complex number system
o  N.CN.1; N.CN.2 Perform arithmetic operations with complex numbers
o  N.CN.7; N.CN.8 Use complex numbers in polynomial identities and equations
·  F.IF Interpreting functions
o  F.IF.4; F.IF.5; F.IF.6 Interpret functions that arise in applications in terms of the context
·  F.BF
o  F.BF.1; F.BF.3 Build new functions from existing functions
Transfer Goals:
·  Use quadratic functions to model real life situations (ex: gravity, area, projectiles).
·  Utilize the various forms of a quadratic (standard, vertex, completed square, function form) to solve equations.
Enduring Understandings:
·  The graph of any quadratic function is a transformation of the graph of the parent function y = x2.
·  The vertex of a quadratic function in standard form is . You need two additional points to graph.