Download Stage 1 - Madison Public Schools

Algebra II Level 3 Curriculum
Unit A - Rebuilding Algebra Skills
Overview
This brief unit is a review of Pre-Algebra and Algebra 1 topics that are integral for succeeding in Algebra 2. Although some procedure is
necessary, students may really struggle with solving equations, and care should be given to teach each topic in a way that illuminates the
reasons behind the methodology. For example, students should understand why, when terms are on the same side of an equations, they are
combined, but when on opposite sides of the equation, we need to add the opposite to eliminate a term from one side, or why absolute value
equations may have two solutions, one, or no solutions at all.
21st Century Capacities: Analyzing
Stage 1 - Desired Results
ESTABLISHED GOALS/ STANDARDS
Transfer:
Students will be able to independently use their learning in new situations to...
MP 1 Make sense sense of problems and persevere in
solving them
MP2 Reason abstractly and quantitatively
MP7 Look for and make use of structure
CCSS.MATH.CONTENT.HSN.Q.A.1
Use units as a way to understand problems and to guide
the solution of multi-step problems; choose and interpret
units consistently in formulas; choose and interpret the
scale and the origin in graphs and data displays.
CCSS.MATH.CONTENT.HSN.Q.A.2
Define appropriate quantities for the purpose of
descriptive modeling.
Interpret the structure of expressions.
CCSS.MATH.CONTENT.HSA.SSE.A.1
Interpret expressions that represent a quantity in terms of
its context.*
1. Manipulate equations/expressions or objects to create order and establish relationships.
2. Represent and interpret patterns in numbers, data and objects.
3. Make sense of a problem, initiate a plan, execute it, and evaluate the reasonableness of the
solution. (Analyzing)
Meaning:
UNDERSTANDINGS: Students will
understand that:
ESSENTIAL QUESTIONS: Students will
explore & address these recurring questions:
1. Mathematicians understand that placing a
problem in a category gives one a familiar
approach to solving it.
2. Mathematicians examine the impact of
operations and how they relate to one
another.
3. Mathematicians flexibly use different
tools, strategies, and operations to build
conceptual knowledge or solve problems.
A. What have I seen in the past that might help
me now?
B. How do operations relate to one another?
C. What does the solution tell me?
D. How else might I solve this problem?
E. What is another to represent this number?
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
CCSS.MATH.CONTENT.HSA.SSE.A.1.A
Interpret parts of an expression, such as terms, factors,
and coefficients.
CCSS.MATH.CONTENT.HSA.SSE.A.1.B
Interpret complicated expressions by viewing one or
more of their parts as a single entity.
CCSS.MATH.CONTENT.HSA.SSE.A.2
Use the structure of an expression to identify ways to
rewrite it.
CCSS.MATH.CONTENT.HSA.CED.A.1
Create equations and inequalities in one variable and use
them to solve problems.
Acquisition:
Students will know…
Students will be skilled at…
1. Unless told otherwise, answers should be
given as an exact answer, so a repeating
decimal should be indicated or left as a
decimal.
2. Why there are two solutions to an
absolute equation
3. The meaning of the word solution, and
how to tell if an equation has one,
multiple, infinite, or no solutions.
4. Vocabulary: rational, irrational, terms,
variables, base, exponents, equation,
expression, cube, squared, product,
inequality, absolute value
1. Simplifying expressions using the order of
operations
2. Identifying properties of commutative,
inverse and distributive
3. Rewrite an expression using exponents
4. Evaluating an expression using substitution
5. Write algebraic expressions from words
6. Solving equations - including literal
7. Checking solutions to equations
8. Modeling with equations and inequalities
9. Solving inequalities
10. Solving absolute value equations
CCSS.MATH.CONTENT.HSA.CED.A.4
Rearrange formulas to highlight a quantity of interest,
using the same reasoning as in solving equations.
CCSS.MATH.CONTENT.HSA.REI.A.1
Explain each step in solving a simple equation as
following from the equality of numbers asserted at the
previous step, starting from the assumption that the
original equation has a solution. Construct a viable
argument to justify a solution method
CCSS.MATH.CONTENT.HSA.REI.B.3
Solve linear equations and inequalities in one variable,
including equations with coefficients represented by
letters.
CCSS.MATH.CONTENT.HSF.BF.A.1
Write a function that describes a relationship between
two quantities.*
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
Unit B - Equations on the Coordinate Plane
Overview
The purpose of this unit is to use math to analyze situations in which the rate of change is constant and to model those situations using linear
equations. Students should make a connection between tabular, algebraic, and graphic representations of relations. In later units students will
use the concepts and skills from this unit to work with quadratic and exponential functions.
21st Century Capacities: Analyzing, Presentation
Stage 1 - Desired Results
ESTABLISHED GOALS/ STANDARDS
Transfer:
Students will be able to independently use their learning in new situations to...
MP4 Model with Mathematics
MP7 Look for and make use of structure
MP8 Look for and express regularity in repeated reasoning
CCSS.MATH.CONTENT.HSN.Q.A.2 Define appropriate quantities
for the purpose of descriptive modeling.
CCSS.MATH.CONTENT.HSA.SSE.A.1.B Interpret complicated
expressions by viewing one or more of their parts as a single entity.
CCSS.MATH.CONTENT.HSA.CED.A.2 Create equations in two or
more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
CCSS.MATH.CONTENT.HSA.CED.A.3 Represent constraints by
equations or inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or nonviable options in a
modeling context.
CCSS.MATH.CONTENT.HSA.REI.C.6 Solve systems of linear
equations exactly and approximately (e.g., with graphs), focusing on
pairs of linear equations in two variables.
CCSS.MATH.CONTENT.HSA.REI.D.10 Understand that the graph of
an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).
CCSS.MATH.CONTENT.HSA.REI.D.11 Explain why the x-
1. Model relationships among quantities. (Analyzing)
2. Represent and interpret patterns in numbers, data and objects. (Analyzing and
Presentation)
3. Draw conclusions about graphs, shapes, equations, or objects. (Analyzing and
Presentation)
Meaning:
UNDERSTANDINGS: Students will
understand that:
1. Mathematicians apply the
mathematics they know to solve
problems occurring in everyday life.
2. Mathematicians examine
relationships to discern a pattern,
generalizations, or structure.
3. Mathematicians can describe
patterns, relations, and/or functions
to access strategies to solve
problems.
ESSENTIAL QUESTIONS: Students
will explore & address these recurring
questions:
A. How can change be described?
B. How can a variable/ expression /
equation/graph tell a story?
C. How do you express and describe a
pattern and use it to make
predictions and solve a problem?
D. How can the solutions to an
equation or inequality be
represented?
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
coordinates of the points where the graphs of the equations y = f(x) and
y = g(x) intersect are the solutions of the equation f(x) = g(x); find the
solutions approximately, e.g., using technology to graph the functions,
make tables of values, or find successive approximations. Include cases
wheref(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.*
CCSS.MATH.CONTENT.HSA.REI.D.12 Graph the solutions to a
linear inequality in two variables as a half-plane (excluding the
boundary in the case of a strict inequality), and graph the solution set to
a system of linear inequalities in two variables as the intersection of the
corresponding half-planes.
CCSS.MATH.CONTENT.HSF.IF.C.7 Graph functions expressed
symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases.*
CCSS.MATH.CONTENT.HSF.IF.C.7.A Graph linear and quadratic
functions and show intercepts, maxima, and minima.
CCSS.MATH.CONTENT.HSF.BF.A.1 Write a function that describes
a relationship between two quantities.*
CCSS.MATH.CONTENT.HSF.BF.A.1.A Determine an explicit
expression, a recursive process, or steps for calculation from a context.
CCSS.MATH.CONTENT.HSF.LE.A.1.B Recognize situations in
which one quantity changes at a constant rate per unit interval relative
to another.
CCSS.MATH.CONTENT.HSF.LE.A.2 Construct linear and
exponential functions, including arithmetic and geometric sequences,
given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
CCSS.MATH.CONTENT.HSF.LE.B.5 Interpret the parameters in a
linear or exponential function in terms of a context.
CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for
parallel and perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or perpendicular to a
given line that passes through a given point).
CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of
change) and the intercept (constant term) of a linear model in the
context of the data.
Acquisition:
Students will know…
Students will be skilled at…
1. That situations that have a constant
rate of change can be modeled with a
linear equation
2. Slope of a line can tell you what the
function of a graph looks like in
graphical form
3. Point-slope and slope - y intercept
form of a line
4. The meaning of the slope and
intercepts of a function in context
5. Any point on a graph is a solution to
the equation or
inequality….conversely, any point
not on the graph is not a solution
6. When using linear programing vertex points are often key points in
solving the problem
7. Vocabulary: vertical, horizontal,
slope, rise, run, parallel,
perpendicular, intercept, solution,
system, intersection, vertex
1. Graphing a linear equation using a
table, slope and y-intercept, and/or
intercepts
2. Finding the slope of a function
from an equation, graph or table
3. Comparing functions in table,
equation, or graphical form
4. Using linear models to predict
5. Graphing linear inequalities
6. Graphing absolute value functions
7. Finding the solution to a system of
equations by graphing, elimination
algorithm and by substitution
8. Modeling situations using a system
of equations
9. Solving systems of inequalities by
graphing
10. Using linear programing to model
and find solutions to problems
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
Unit C - Quadratic Equations and Parabolas
Overview
The purpose of this unit is to move beyond linear functions and to learn strategies to solve quadratic equations. Students should understand
that the power of 2 creates a specific shaped graph (parabola). Students should also learn the importance of the complex number system, and
should be taught about the history of complex numbers not being all that different from the history of negative numbers.
21st Century Capacities: Analyzing
Stage 1 - Desired Results
ESTABLISHED GOALS/ STANDARDS
Transfer:
Students will be able to independently use their learning in new situations to...
MP 1 Make sense of problems and persevere in solving them
MP2 Reason abstractly and quantitatively
MP6 Attend to precision
MP7 Look for and make use of structure
CCSS.MATH.CONTENT.HSN.Q.A.2
Define appropriate quantities for the purpose of descriptive modeling.
Perform arithmetic operations with complex numbers.
CCSS.MATH.CONTENT.HSN.CN.A.1
Know there is a complex number i such that i2 = -1, and every complex
number has the form a + bi with a and b real.
CCSS.MATH.CONTENT.HSN.CN.A.2
Use the relation i2 = -1 and the commutative, associative, and
distributive properties to add, subtract, and multiply complex numbers.
CCSS.MATH.CONTENT.HSN.CN.C.7
Solve quadratic equations with real coefficients that have complex
solutions.
CCSS.MATH.CONTENT.HSA.SSE.A.1.B
Interpret complicated expressions by viewing one or more of their parts
as a single entity.
CCSS.MATH.CONTENT.HSA.SSE.A.2
Use the structure of an expression to identify ways to rewrite it.
CCSS.MATH.CONTENT.HSA.SSE.B.3
1. Manipulate equations/expressions or objects to create order and establish
relationships. (Analyzing)
2. Draw conclusions about graphs, shapes, equations, or objects. (Analyzing)
Meaning:
UNDERSTANDINGS: Students will
understand that:
1. Mathematicians examine
relationships to discern a pattern,
generalizations, or structure.
2. Mathematicians continually
evaluate their process and the
reasonableness of the intermediate
results.
3. Mathematicians identify relevant
tools, strategies, relationships,
and/or information in order to draw
conclusions.
ESSENTIAL QUESTIONS: Students
will explore & address these recurring
questions:
A. How can I use symbols to
communicate?
B. What is another way that this
problem could be solved?
C. What math
tools/models/strategies can I use to
solve the problem?
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.*
CCSS.MATH.CONTENT.HSA.SSE.B.3.A
Factor a quadratic expression to reveal the zeros of the function it
defines.
CCSS.MATH.CONTENT.HSA.SSE.B.3.B
Complete the square in a quadratic expression to reveal the maximum
or minimum value of the function it defines.
CCSS.MATH.CONTENT.HSA.CED.A.2
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and
scales.
CCSS.MATH.CONTENT.HSA.REI.B.4
Solve quadratic equations in one variable.
CCSS.MATH.CONTENT.HSA.REI.B.4.A
Use the method of completing the square to transform any quadratic
equation in x into an equation of the form (x- p)2 = q that has the same
solutions. Derive the quadratic formula from this form.
CCSS.MATH.CONTENT.HSA.REI.B.4.B
Solve quadratic equations by inspection (e.g., for x2 = 49), taking square
roots, completing the square, the quadratic formula and factoring, as
appropriate to the initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write them as a ± bi for
real numbers a and b.
CCSS.MATH.CONTENT.HSA.REI.D.10
Understand that the graph of an equation in two variables is the set of
all its solutions plotted in the coordinate plane, often forming a curve
(which could be a line).
CCSS.MATH.CONTENT.HSF.IF.C.7
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.*
CCSS.MATH.CONTENT.HSF.IF.C.7.A
Graph linear and quadratic functions and show intercepts, maxima, and
minima.
CCSS.MATH.CONTENT.HSF.BF.A.1
Write a function that describes a relationship between two quantities.*
Acquisition:
Students will know…
Students will be skilled at…
1. The meaning of the imaginary
number i
2. That an equation must be in
standard form before attempting to
use the quadratic formula to solve
it
3. A parabola is symmetric
4. A quadratic equation may have 0,1
or 2 solutions (real or imaginary)
5. -b/2a gives the x value of the
vertex of a parabola
6. The leading coefficient of a
quadratic tells you if the graph
opens up or down
7. Quadratic equations model
parabolic situations
8. Vocabulary: roots, zeros,
solutions, imaginary, vertex
1. Simplifying square roots
2. Combining complex numbers
3. Solving quadratic equations using
isolating x2 ,factoring, graphing and
the quadratic formula
4. Multiplying binomials
5. Factoring trinomials where a=1
6. Sketching graphs of quadratic
equations
7. Working with quadratic functions in
context
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
Unit D - Functions
Overview
The focus of Unit D is for students to learn what is a mathematical function and its importance in problem solving. Students will also
explore and learn to use the concept of function notation. Even though function notation is awkward to learn and seems more cumbersome,
it is a great tool that allows mathematicians to communicate more clearly. Students will learn to work flexibly between all representations of
a relation or function (table, list, equation, graph, and mapping diagram).
21st Century Capacities: Synthesizing
Stage 1 - Desired Results
ESTABLISHED GOALS/ STANDARDS
MP1 Make sense sense of problems and persevere in solving them
MP2 Reason abstractly and quantitatively
MP6 Attend to precision
MP7 Look for and make use of structure
CCSS.MATH.CONTENT.HSA.SSE.A.1.B Interpret complicated expressions by
viewing one or more of their parts as a single entity.
CCSS.MATH.CONTENT.HSA.SSE.A.2 Use the structure of an expression to
identify ways to rewrite it.
CCSS.MATH.CONTENT.HSA.SSE.B.3 Choose and produce an equivalent
form of an expression to reveal and explain properties of the quantity represented
by the expression.*
CCSS.MATH.CONTENT.HSA.APR.A.1 Understand that polynomials form a
system analogous to the integers, namely, they are closed under the operations of
addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
CCSS.MATH.CONTENT.HSA.REI.D.10 Understand that the graph of an
equation in two variables is the set of all its solutions plotted in the coordinate
plane, often forming a curve (which could be a line).
Transfer:
Students will be able to independently use their learning in new situations
to...
1. Manipulate equations/expressions or objects to create order and
establish relationships.
2. Draw conclusions about graphs, shapes, equations, or objects.
(Synthesizing)
Meaning:
UNDERSTANDINGS: Students
will understand that:
ESSENTIAL QUESTIONS:
Students will explore & address
these recurring questions:
1. Mathematicians use symbols
and notations to make it easier
to express themselves.
2. Mathematicians flexibly use
different tools, strategies, and
operations to build conceptual
knowledge or solve problems.
A. How can I use symbols to
communicate?
B. What does the function/graph
tell me?
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
CCSS.MATH.CONTENT.HSF.IF.B.5 Relate the domain of a function to its
graph and, where applicable, to the quantitative relationship it describes.
CCSS.MATH.CONTENT.HSF.IF.C.7 Graph functions expressed symbolically
and show key features of the graph, by hand in simple cases and using technology
for more complicated cases.*
CCSS.MATH.CONTENT.HSF.IF.C.9 Compare properties of two functions each
represented in a different way (algebraically, graphically, numerically in tables,
or by verbal descriptions).
CCSS.MATH.CONTENT.HSF.BF.A.1 Write a function that describes a
relationship between two quantities.*
CCSS.MATH.CONTENT.HSF.BF.A.1.B Combine standard function types
using arithmetic operations.
CCSS.MATH.CONTENT.HSF.BF.A.1.C (+) Compose functions.
CCSS.MATH.CONTENT.HSF.BF.B.3 Identify the effect on the graph of
replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both
positive and negative); find the value of k given the graphs. Experiment with
cases and illustrate an explanation of the effects on the graph using technology.
Include recognizing even and odd functions from their graphs and algebraic
expressions for them.
Acquisition:
Students will know…
Students will be skilled at…
1. A function and its inverse are
reflections over the x = y line
2. A composition can verify an
inverse function
3. Components of a function can
be used to visualize the
function
4. Vocabulary: composition,
inverse, transformation,
domain, range, relation,
function, composition
1. Identifying the domain and
range of a function
2. Identifying if a relation is a
functions
3. Finding the value of f(x) for a
specific x value
4. Adding, subtracting,
multiplying and dividing
functions
5. Finding the composition of two
functions
6. Finding the inverse of a
function
7. Graphing transformations of
f(x) = x2 and f(x) = |xl with
vertical and/or horizontal shifts
and/or vertical flips
CCSS.MATH.CONTENT.HSF.BF.B.4 Find inverse functions.
CCSS.MATH.CONTENT.HSF.BF.B.4.A Solve an equation of the form f(x) = c
for a simple function f that has an inverse and write an expression for the inverse.
CCSS.MATH.CONTENT.HSF.BF.B.4.B (+) Verify by composition that one
function is the inverse of another.
CCSS.MATH.CONTENT.HSF.BF.B.4.C (+) Read values of an inverse function
from a graph or a table, given that the function has an inverse.
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
Unit E - Trigonometry
Overview
Students will learn the basics of right triangle trigonometry, and will be able to apply trig ratios to solve word problems. Students will learn
how to measure angles using radians, how to sketch angles in standard position, etc. The goal of this unit is to expose students to enough
trigonometry for them to understand its value in the real world and to be successful in higher math.
21st Century Capacities: Analyzing, Synthesizing
Stage 1 - Desired Results
ESTABLISHED GOALS/ STANDARDS
Transfer:
Students will be able to independently use their learning in new situations to...
MP 1 Make sense sense of problems and
persevere in solving them
MP5 Use appropriate tools strategically
MP7 Look for and make use of structure
CCSS.MATH.CONTENT.HSN.Q.A.3
Choose a level of accuracy appropriate to
limitations on measurement when reporting
quantities.
CCSS.MATH.CONTENT.HSA.SSE.A.1.B
Interpret complicated expressions by viewing
one or more of their parts as a single entity.
CCSS.MATH.CONTENT.HSA.SSE.A.2
Use the structure of an expression to identify
ways to rewrite it.
CCSS.MATH.CONTENT.HSF.TF.A.1
Understand radian measure of an angle as the
length of the arc on the unit circle subtended
1. Draw conclusions about graphs, shapes, equations, or objects. (Analyzing and Synthesizing)
2. Make sense of a problem, initiate a plan, execute it, and evaluate the reasonableness of the solution.
(Analyzing and Synthesizing)
3. Use appropriate tools to make reaching solutions more efficient, accessible and accurate.
(Analyzing and Synthesizing)
Meaning:
UNDERSTANDINGS: Students will understand that:
1. Effective problem solvers work to make sense of
the problem before trying to solve it.
2. Mathematicians identify relevant tools, strategies,
relationships, and/or information in order to draw
conclusions.
3. Mathematicians use geometric models, and spatial
sense to interpret and make sense of the physical
environment.
4. Mathematicians analyze characteristics and
properties of geometric shapes to develop
mathematical arguments about geometric
relationships.
ESSENTIAL QUESTIONS: Students will
explore & address these recurring questions:
A.
B.
C.
What math strategies can I use to solve
the problem?
How does classifying bring clarity?
How can I use what I know in the world?
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
Acquisition:
by the angle.
CCSS.MATH.CONTENT.HSF.TF.B.7
(+) Use inverse functions to solve
trigonometric equations that arise in modeling
contexts; evaluate the solutions using
technology, and interpret them in terms of the
context.*
CCSS.MATH.CONTENT.HSG.SRT.C.6
Understand that by similarity, side ratios in
right triangles are properties of the angles in
the triangle, leading to definitions of
trigonometric ratios for acute angles.
Students will know…
Students will be skilled at…
1. Definitions of sin, cos, tan trig ratios
2. The relationship between the sides of a 30-60-90
and a 45-45-90 triangle
3. The relationship between sin and cos of
complementary angles
4. The definition / meaning of a radian
5. Vocabulary: opposite, adjacent, hypotenuse
1. Solving right triangles using trigonometry
2. Using a calculator to find a trig function
or an inverse of a trig function
3. Converting between degrees and radians
4. Drawing anges in the coordinate plane in
standard position
5. Determining if two angles are coterminal
or finding coterminal angles of an angle
6. Finding sector areas
7. Finding the arc length of sectors
CCSS.MATH.CONTENT.HSG.SRT.C.7
Explain and use the relationship between the
sine and cosine of complementary angles.
CCSS.MATH.CONTENT.HSG.SRT.C.8
Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in
applied problems.*
CCSS.MATH.CONTENT.HSG.C.B.5
Derive using similarity the fact that the length
of the arc intercepted by an angle is
proportional to the radius, and define the radian
measure of the angle as the constant of
proportionality; derive the formula for the area
of a sector.
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
Unit F - Exponential and Logarithmic Functions
Overview
The purpose of this unit to expose students to ways of manipulating expressions using exponents. Students are expected to have a conceptual
understanding of the rules around exponents and logarithms. They should explore the logic behind the development of negative exponents,
zero as an exponent, and rational exponents. These should not just be taught as rules.
21st Century Capacities: Analyzing
Stage 1 - Desired Results
ESTABLISHED GOALS/ STANDARDS
Transfer:
Students will be able to independently use their learning in new situations to...
MP2 Reason abstractly and quantitatively
MP7 Look for and make use of structure
CCSS.MATH.CONTENT.HSN.RN.A.1 Explain how the definition of
the meaning of rational exponents follows from extending the properties
of integer exponents to those values, allowing for a notation for radicals
in terms of rational exponents.
CCSS.MATH.CONTENT.HSN.RN.A.2 Rewrite expressions involving
radicals and rational exponents using the properties of exponents.
CCSS.MATH.CONTENT.HSN.Q.A.3 Choose a level of accuracy
appropriate to limitations on measurement when reporting quantities.
CCSS.MATH.CONTENT.HSA.SSE.A.2 Use the structure of an
expression to identify ways to rewrite it.
CCSS.MATH.CONTENT.HSA.SSE.B.3 Choose and produce an
equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.*
1. Manipulate equations/expressions or objects to create order and establish
relationships. (Analyzing)
2. Demonstrate fluency with math facts, computation and concepts.
Meaning:
UNDERSTANDINGS: Students will
understand that:
ESSENTIAL QUESTIONS: Students
will explore & address these recurring
questions:
1. Mathematicians create or use
A. How can I break a problem down
into manageable parts?
models to examine, describe,
B. What math tools/models/strategies
solve.
can I use to solve the problem?
2. Mathematicians can describe
patterns, relations, and/or functions C. How can I simplify the problem?
D. How can I use symbols to
to access strategies to solve
communicate?
problems.
3. Mathematicians represent and
analyze mathematical situations
and structures using algebraic
symbols to communicate thinking.
Madison Public Schools | July 2016
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Algebra II Level 3 Curriculum
CCSS.MATH.CONTENT.HSA.SSE.B.3.C Use the properties of
exponents to transform expressions for exponential functions.
Acquisition:
Students will know…
Students will be skilled at…
CCSS.MATH.CONTENT.HSA.SSE.B.4 Derive the formula for the sum 1. Know the properties of exponents
of a finite geometric series (when the common ratio is not 1), and use the
and why they work
formula to solve problems.
2. That with C> 0 if a>1 the function
represents growth and if 0 < a < 1
CCSS.MATH.CONTENT.HSA.REI.A.2 Solve simple rational and
the function represents decay
radical equations in one variable, and give examples showing how
3.
The
definition of a log
extraneous solutions may arise.
4. Common logarithmic function has
base 10, natural log has base e
CCSS.MATH.CONTENT.HSA.REI.D.10 Understand that the graph of
5.
The Product, Quotient and Power
an equation in two variables is the set of all its solutions plotted in the
Properties of logarithms
coordinate plane, often forming a curve (which could be a line).
6. Vocabulary: index, argument,
logarithm, base, decay,
CCSS.MATH.CONTENT.HSF.IF.A.1 Understand that a function from
one set (called the domain) to another set (called the range) assigns to
each element of the domain exactly one element of the range. If f is a
function and xis an element of its domain, then f(x) denotes the output of
fcorresponding to the input x. The graph of f is the graph of the equation
y = f(x).
CCSS.MATH.CONTENT.HSF.IF.A.2 Use function notation, evaluate
functions for inputs in their domains, and interpret statements that use
function notation in terms of a context.
1. Simplifying expressions using the
properties of exponents
2. Using y = Cax type equations to
graph exponential growth and decay
and solve application problems
3. Using a = P(1 + r/n)nt to solve
compound interest problems
4. Identifying if a relationships is
exponential or linear
5. Converting between radical notation
and rational exponent notation
6. Solving radical equations
7. Converting between exponential
and logarithmic form
8. Sketching graphs of logarithmic
functions
9. Using logarithms to solve equations
and in applications
CCSS.MATH.CONTENT.HSF.IF.C.7 Graph functions expressed
symbolically and show key features of the graph, by hand in simple
cases and using technology for more complicated cases.*
CCSS.MATH.CONTENT.HSF.IF.C.7.E Graph exponential and
logarithmic functions, showing intercepts and end behavior, and
trigonometric functions, showing period, midline, and amplitude.
CCSS.MATH.CONTENT.HSF.IF.C.8.B Use the properties of
exponents to interpret expressions for exponential functions. For
example, identify percent rate of change in functions such as y = (1.02)ᵗ,
y = (0.97)ᵗ, y = (1.01)12ᵗ, y = (1.2)ᵗ/10, and classify them as representing
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Algebra II Level 3 Curriculum
exponential growth or decay.
CCSS.MATH.CONTENT.HSF.BF.A.1 Write a function that describes a
relationship between two quantities.*
CCSS.MATH.CONTENT.HSF.BF.A.1.A Determine an explicit
expression, a recursive process, or steps for calculation from a context.
CCSS.MATH.CONTENT.HSF.BF.B.5 (+) Understand the inverse
relationship between exponents and logarithms and use this relationship
to solve problems involving logarithms and exponents.
CCSS.MATH.CONTENT.HSF.LE.A.1 Distinguish between situations
that can be modeled with linear functions and with exponential
functions.
CCSS.MATH.CONTENT.HSF.LE.A.1.A Prove that linear functions
grow by equal differences over equal intervals, and that exponential
functions grow by equal factors over equal intervals.
CCSS.MATH.CONTENT.HSF.LE.A.1.C Recognize situations in which
a quantity grows or decays by a constant percent rate per unit interval
relative to another.
CCSS.MATH.CONTENT.HSF.LE.A.2 Construct linear and exponential
functions, including arithmetic and geometric sequences, given a graph,
a description of a relationship, or two input-output pairs (include reading
these from a table).
CCSS.MATH.CONTENT.HSF.LE.A.4 For exponential models, express
as a logarithm the solution to abct = d where a, c, and d are numbers and
the base b is 2, 10, or e; evaluate the logarithm using technology.
CCSS.MATH.CONTENT.HSF.LE.B.5 Interpret the parameters in a
linear or exponential function in terms of a context.
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