Download Curriculum Overview Map Detroit Public Safety Academy 2015

Curriculum Overview Map
Detroit Public Safety Academy 2015-2016
Course/Subject: ALGEBRA II
Grade:
11
Quarter: 1st
Essential Questions-Units-Chapters-Concepts
UNIT 1 LINEAR FUNCTIONS AND EQUATIONS: How do variables help you model real-world
situations? How can you use the properties for real numbers to simplify algebraic expressions?
How do you solve an equation or inequality?
 How are patterns represented using variables?
 How can you represent mathematical phrases and real-world quantities using algebraic
expressions?
 What are sets and subsets of numbers and how are real numbers related in specific ways?
 How do properties of real numbers allow you to solve equations and inequalities?
UNIT 2 UNIVARIATE DATA AND DISTRUBUTIONS: How can visual displays and statistical
calculations be used to organize, analyze, and evaluate data sets?
 How is data collected (types of samples)?
 What are some possible sources of bias that occur in collecting data? What are some methods of
reducing bias?
 What is the different between observational studies, randomized experiments, and sample
surveys? What conclusions can be drawn from each?
 Given a frequency distribution graph, what is the relationship between the median and the mean
in a distribution that is skewed to the left? Skewed to the right? Explain why this relationship
exists.
 How can you use mean and standard deviation of a normal distribution to compare two pieces of
data?
UNIT 3 USING TOOLS TO MODEL AND SOLVE MATRICES & VECTORS: How can matrices
and vectors be used to solve problems in mathematics and other related fields?
 How can you tell whether two matrices can be multiplied together?
 What process is used to solve a system of linear equations using matrices?
Resources (include websites)
Atlas Rubicon Oakland Schools (2015). https://oaklandk12public.rubiconatlas.org/Atlas/Browse/Vie
w/Calendars
Pearson Education(2015). www.pearsonsuccess.net
(2012). Algebra 2
Curriculum Crafterhttps://curriculumcrafter.org/login.aspx
Sims. (2015). Algebra Housewww.algebrahouse.com
Kuta Software (2015). https://www.kutasoftware.com/freeia2.ht
ml
Khan Academy, 2015.
https://www.khanacademy.org/
Teacher Tube, 2015
www.teachertube.com
Learning Focused, 2013.
Higher Order Thinking
Learning Focused Lessons
http://www.learningfocused.com/index.p
hp/page/lfs-engaged
Standards-CCSS/GLCEs/HSCEs-KC4
Unit 1: A.REI.1, A.REI.2, A.REI.7, A.REI.11 F.IF.4, F.IF.6, F.BF.1, F.BF.2, F.LE.5
Unit 2: N.Q.A.2, N.Q.A.3, S.ID.A.1, S.ID.A.2, S.ID.A.3, S.ID.A.4, S.IC.A.1, S.IC.A.2, S.IC.B.3
Unit 3: N.VM.A.1, N.VM.A.2, N.VM.A.3, N.VM.B.4, N.VM.C.7, N.VM.C.8, N.VM.C.9, A.REI.C.8, A.REI.C.9, N.Q.A.2, N.Q.A.3
Vocabulary/Key Concepts
Unit 1: Variable, Numerical Expression, Algebraic Expression,
Properties of Real Numbers, Evaluate, term, coefficient,
constant term, like terms, Properties of Algebraic Expressions,
Properties of Equality, equation, inverse operations, identity,
literal equation, Properties of Inequalities, Compound
Inequalities, Extraneous Solutions, Absolute Value
Assessments/Projects
Standard Based Assessment: Interpreting Data through charts, tables and graphs.
(Pre/Post x 2)
Unit 1, 2, & 3 Assessments (pre/post)
STEM Cross Curricular Projects
Unit 2: Dot plots, relative frequency histograms, bar graphs, box
plots, skewed distribution, symmetric distribution, outlier,
M-STEP & SAT Prep
measures of center (mean, median, mode), Measure of variation
(percentiles, quartiles, range, IQR, variance, standard deviation),
normal distribution, margin of error, simulation, sample, census,
bias, sampling methods, observational study, experimental study
Unit 3: Associative Property, Commutative Property, Cramer’s
Rule, Determinant, dimension, element, identity matrix, inverse
matrix, linear programming, matrix operations, multiplication
by a scalar, solving systems of equations, transformation
matrices, vector , components, magnitude, direction, initial
point, terminal point, add and subtract vectors, resultant,
parallelogram rule, scalar, scalar multiplication
Curriculum Overview Map
Detroit Public Safety Academy 2015-2016
Course/Subject: ALGEBRA II
Grade:
11
Essential Questions-Units-Chapters-Concepts
UNIT 3 USING TOOLS TO MODEL AND SOLVE MATRICES & VECTORS: How
can matrices and vectors be used to solve problems in mathematics and other related
fields?
 How can you tell whether two matrices can be multiplied together?
 How can two vectors be added together?
 How do you represent a vector by using a matrix?
UNIT 4 EXPONENTIAL & LOG FUNCTIONS: What is the connection between
exponential and logarithmic functions? What patterns of change are modeled by
logarithmic functions as seen in real-world situations, and the tables, graphs, and
function rules that represent these situations?
 How can the properties of logarithms be used to write algebraic expression
inequivalent forms?
 What types of real world relationships are best described using a logarithmic scale?
Why?
 What relationships- graphical, algebraic, numeric- exist between a function and its
inverse?
 Why can’t a logarithm have an argument of zero or a negative number?
 What are the similarities and differences between exponential and logarithmic
functions?
UNIT 5 RATIONAL EXPRESSIONS AND FUNCTIONS: How does understanding
polynomial functions (and other function families) aid in making sense of rational
functions?
 How can equations and tables of values for rational functions help reveal key features
in their graphs?
 How can the key features of graphs of rational functions be used to create an
algebraic model?
 How do different forms of rational functions highlight structures where polynomial
functions and transformations can aid in making sense of rational functions?
 How does understanding operations with rational numbers inform operations with
rational expressions?
Quarter: 2nd
Resources (include websites)
Atlas Rubicon Oakland Schools- https://oaklandk12public.rubiconatlas.org/Atlas/Browse/View/Calendars
Pearson- www.pearsonsuccess.net
Curriculum Crafterhttps://curriculumcrafter.org/login.aspx
Pearson. (2012). Algebra 2
Sims. (2015). Algebra Housewww.algebrahouse.com
Kuta Software (2015). https://www.kutasoftware.com/freeia2.html
Khan Academy, 2015.
https://www.khanacademy.org/
Teacher Tube, 2015
www.teachertube.com
Learning Focused, 2013.
Higher Order Thinking
Learning Focused Lessons
http://www.learningfocused.com/index.php/page/lfsengaged
Standards-CCSS/GLCEs/HSCEs-KC4
Unit 3: N.VM.A.1, N.VM.A.2, N.VM.A.3, N.VM.B.4, N.VM.C.7, N.VM.C.8, N.VM.C.9
Unit 4: F.IF.C.7e, IF.C.8b, IF.C.9, F.BF.A.1c, F.BF.B.4b, F.BF.B.5, F.LE.A.2, F.LE.A.4
Unit 5: A.APR.B.2, A.APR.D.6, A.APR.D.7, F.IF.C.7d, F.BF.B.3
Vocabulary/Key Concepts
Unit 3: Associative Property, Commutative Property, Cramer’s
Rule, Determinant, dimension, element, identity matrix, inverse
matrix, linear programming, matrix operations, multiplication by
a scalar, solving systems of equations, transformation matrices,
vector , components, magnitude, direction, initial point, terminal
point, add and subtract vectors, resultant, parallelogram rule,
scalar, scalar multiplication
Assessments/Projects
Standard Based Assessment: Interpreting Data through charts, tables and graphs.
(Pre/Post x 2)
Unit 3, 4, & 5 Assessments (pre/post)
STEM Cross Curricular Projects
Unit 4: Asymptote, base of a logarithm, base ten logarithms
M-STEP & SAT Prep
(common logarithms), composition of functions, domain, e, end
behavior, exponential functions, exponential models (compound
Final Exam Semester 1
interest, populations, radioactivity), f(x)= - e^x, f(x)= ab^x,
inverse function, logarithmic function, logarithmic scales (Richter
scale for earthquakes, decibel for acoustic power, entropy, pH for
acidity, stellar magnitude scale for brightness of stars), log b x=y,
natural logarithms, properties of exponents, range, transformation
of functions
Unit 5: Asymptote (horizontal, vertical, slant), continuity
(continuous, discontinuous, holes/undefined points), domain and
range, end behavior, rational function, solutions to rational
equations (extraneous solutions and solutions), intercepts (xintercept, y-intercept)
Curriculum Overview Map
Detroit Public Safety Academy 2015-2016
Course/Subject: ALGEBRA II
Grade:
11
Quarter: 3rd
Essential Questions-Units-Chapters-Concepts
UNIT 6 SEQUENCES AND SERIES: What connections exist between arithmetic and geometric
sequences and linear and exponential functions?
 Given a sequence of numbers, how can you determine if it is arithmetic, geometric, or neither?
 Find the recursive and explicit formulas for a given arithmetic or geometric sequence.
 Translate between sigma notation and expanded form.
 What are the strategies for finding an arithmetic or geometric series?
 Given an arithmetic or geometric sequence, what information is needed to find the nth term?
UNIT 7 QUADRATIC RELATIONS AND CONIC SECTIONS: How can algebraic and
geometric ideas be used to explore and connect representations of quadratic relations from the
conic sections?
 What shapes result from passing a plane though a cone?
 How are the equation and the properties of a circle and ellipse similar and different?
 Given the equation of a conic section, how can you identify whether the graph will be a circle,
ellipse, parabola, or hyperbola?
 How can you use a line for the directrix and a point for the focus to sketch a resulting
parabola?
 What methods are available to convert an equation in the general conic from into a form more
suitable for graphing?
Resources (include websites)
Atlas Rubicon Oakland Schoolshttps://oaklandk12public.rubiconatlas.org/Atlas/Browse/View
/Calendars
Pearson- www.pearsonsuccess.net
Curriculum Crafterhttps://curriculumcrafter.org/login.aspx
Pearson. (2012). Algebra 2
Sims. (2015). Algebra Housewww.algebrahouse.com
Kuta Software (2015). https://www.kutasoftware.com/freeia2.htm
l
Khan Academy, 2015.
https://www.khanacademy.org/
Teacher Tube, 2015
www.teachertube.com
Learning Focused, 2013.
Higher Order Thinking
Learning Focused Lessons
http://www.learningfocused.com/index.ph
p/page/lfs-engaged
Standards-CCSS/GLCEs/HSCEs-KC4
Unit 6: A.SSE.B.4, IF.A.3, F.BF.A.2, F.LE.A.1b, F.LE.A.1c, F.LE.A.2
Unit 7: N.CN.A.1, N.CN.A.2, N.CN.A.3, N.CN.C.7, N.CN.C.8, N.CN.C.9, A.SSE.B.3, A.SSE.B.3a, A.SSE.B.3b, A.CED.A.1, A.CED.A.2,
A.REI.B.4a, A.REI.B.4b, A.REI.C.7, A.REI.D.10, F.IF.A.1, F.IF.B.4, F.IF.B.5, F.IF.B.6, F.IF.C.7, F.IF.C.7a, F.IF.C.7d, F.IF.C.8, F.IF.C.8a,
F.IF.C.9, F.BE.A.1, F.BF.A.1a, F.BF.A.1b, F.BF.B.3, G.GPE.A.1, G.GPE.A.2, G.GPE.A.3, G.GMD.B.4
Vocabulary/Key Concepts
Unit 6: Arithmetic sequence, arithmetic series, convergence,
divergence, explicit formulas, finite series, geometric series,
infinite series, nth term, recursive formulas, subscripted notation,
sum of a series, summation/sigma notation
Unit 7: Relationship of (circles, ellipses, and hyperbolas to cones),
circle, ellipse, parabola, hyperbola, locus of points, completing the
square, discriminant, symmetry (lines and axes of graphs of conic
sections), major axis and minor axis, transverse axis and conjugate
axis, asymptotes, focus, foci, vertex, vertices
Assessments/Projects
Standard Based Assessment: Interpreting Data through charts, tables and
graphs. (Pre/Post x 2)
Unit 6 & 7 Assessments (pre/post)
STEM Cross Curricular Projects
M-STEP & SAT
Curriculum Overview Map
Detroit Public Safety Academy 2015-2016
Course/Subject: ALGEBRA II
Grade:
11
Quarter: 4th
Essential Questions-Units-Chapters-Concepts
UNIT 8 TRIGONOMETRIC FUNCTIONS: How can the unit circle be used to develop a circular
definition of trigonometric functions?
 What is the relationship between degree and radian measures of angles? Why or when would you
use degree or radian?
 How can the effect of transformations on the sine and cosine curves be seen in the graphs and tables
of these functions?
 How can the unit circle be used to generate the sine and cosine graphs?
 Why are the trigonometric functions periodic?
 How do you know if a function is periodic?
UNIT 9 PROBABILITY: How can the ideas of independence and conditional probability, along with
expected value, be used to evaluate the outcomes of decision in a variety of contexts?
 How can you generate the numerical values of Pascal’s Triangle?
 How do you recognize when to use conditional probability rules?
 What is the difference between permutations and combinations? Give an example of a situation
where each would be used.
 If the probability of an event occurring is p, what is the probability of that event not occurring?
Explain why your answer makes sense.
 What is the meaning of expected value?
Resources (include websites)
Atlas Rubicon Oakland Schoolshttps://oaklandk12public.rubiconatlas.org/Atlas/Browse/
View/Calendars
Pearson- www.pearsonsuccess.net
Curriculum Crafterhttps://curriculumcrafter.org/login.asp
x
Pearson. (2012). Algebra 2
Sims. (2015). Algebra Housewww.algebrahouse.com
Kuta Software (2015). https://www.kutasoftware.com/freeia2.
html
Khan Academy, 2015.
https://www.khanacademy.org/
Teacher Tube, 2015
www.teachertube.com
Learning Focused, 2013.
Higher Order Thinking
Learning Focused Lessons
http://www.learningfocused.com/index
.php/page/lfs-engaged
Standards-CCSS/GLCEs/HSCEs-KC4
Unit 8: N.Q.A.2, N.Q.A.3, F.IF.A.2, F.BF.A.1, F.BF.A.1b, F.BF.B.4, F.BF.B.4a, F.BF.B.4c, F.BF.B.4d, A.TF.A.1, A.TF.A.2, F.TF.A.3, F.TF.A.4,
F.TF.B.5, F.TF.B.6, F.TF.B.7, F.TF.C.8, F.TF.C.9
Unit 9: F.IF.A.1, F.IF.B.4, F.IF.B.5, F.IF.C.7, F.BF.A.1, F.BF.A.1a, F.BF.B.3, S.CP.A.1, S.CP.A.2, S.CP.A.3, S.CP.A.4, S.CP.A.5, S.CP.B.6,
S.CP.B.7, S.CP.B.8, S.CP.B.9, S.MD.A.1, S.MD.A.2, S.MD.A.3, S.MD.A.4, S.MD.B.5, S.MD.B.5b, S.MD.B.6, S.MD.B.7
Vocabulary/Key Concepts
Unit 8: Amplitude, asymptote, cosecant, cosine, cotangent,
degree and radian relationship and conversion, domain, maxima,
minima, period, phase shift, range, relate graphs of trigonometric
functions to their inverses, secant, sine, tangent, transformations
of trig functions form the parent functions, unit circle
Assessments/Projects
Standard Based Assessment: Interpreting Data through charts, tables and graphs.
(Pre/Post x 2)
Unit 8 & 9 Assessments (pre/post)
Unit 9: Pascal’s Triangle and its connections to combinations,
STEM Cross Curricular Projects
Permutation P(n,k)=n!/(n-k)!, Combination C(n,k)=n!/[(n-k)!k!],
Fundamental principle of Counting, Tree diagram, Sample space, Final Exam Semester 2
Probability Distribution, Independent vents, Addition Rules for
Mutually Exclusive Events, Compound events, Complementary
events, Conditional Probability P(A│B)=P(A and B)/P(B),
Applications of probability to real-world situations, Simulation,
Law of Large Numbers, Expected Value, Two-way Frequency
Table