Download 3rd 9 weeks

2016.17, Algebra I, Quarter 3
The following practice standards will be used throughout the quarter:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Ongoing Standards
Note to Teachers: The following ongoing standards will be practiced all year long and embedded into your instruction instead of being taught
in isolation.
AI.WCE.1 Evaluate expressions and solve equations fluently using substitution to verify solutions.
AI.WCE.2 Understand the relationships of numbers and number sets within the real number system.
AI.WCE.3 Convert unit rates of measurements in multistep arithmetic problems. (i.e. feet per second to miles per hour.)
AI.WCE.4 Identify the independent and dependent variables in situations represented by linear functions.
AI.WCE.5 Add, subtract and multiply radicals to simplify expressions.
AI.WCE.6 I can differentiate between linear and non-linear functions.
AI.WCE.7 I can move fluently between different representations of numbers, such as graphs, tables and equations.
**Unless otherwise noted, all resources are from HMH Algebra I, 2015 Edition.
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Standards
Student Friendly “I Can” Statements
Unit 6 Exponential Relationships (con’t)
A.SSE.3 Choose and produce an equivalent form of an expression
I can define an exponential functions, 𝑓(𝑥) = 𝑎𝑏 𝑥 .
to reveal and explain properties of the quantity represented by the
expression.
I can rewrite exponential functions using the properties of exponents.
c. Use the properties of exponents to transform expressions for
exponential functions. For example the expression 1.15t can be
I can use properties of exponents, including rational exponents (such
rewritten as
as power of a power, product of powers, power of a product, and
(1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent
rational exponents, etc…) to write an equivalent form of an
monthly interest rate if the annual rate is 15%.
exponential function to reveal and explain specific information about
its approximate rate of growth or decay.
(including negative and zero exponents). (*ACT)
I can write exponential functions to represent growth, decay and
compound interest.
F.BF.1 Write a function that describes a relationship between two
quantities.
a. Determine an explicit expression, a recursive process, or steps for
calculation from a context.
I can write an explicit expression, define a recursive process, or
describe the calculations needed to model a function between two
quantities.
F.IF.5 Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes. For example, if
the function h(n) gives the number of person-hours it takes to
assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function.
I can (given the graph) choose the practical domain of the function as
it relates to the numerical relationship it describes.
I can describe a situation that matches a graph based on its shape.
I can explain when a relation is determined to be a function, use f(x)
notation.
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I can state the appropriate domain of a function that represents a
problem situation, defend my choice, and explain why other numbers
might be excluded from the domain.
F.LE.1 Distinguish between situations that can be modeled with linear
functions and with exponential functions.
a. Prove that linear functions grow by equal differences over equal
intervals; and that exponential functions grow by equal factors over
equal intervals.
b. Recognize situations in which one quantity changes at a constant
rate per unit interval relative to another.
c. Recognize situations in which a quantity grows or decays by a
constant percent rate per unit interval relative to another.
I can describe whether a given situation in question has a linear
pattern of change or an exponential pattern of change.
I can show that linear functions change at the same rate over time and
that exponential functions change by equal factors over time.
I can describe situations where one quantity changes at a constant
rate per unit interval as compared to another.
I can describe situations where a quantity grows or decays at a
constant percent rate per unit interval as compared to another.
Unit 7 Polynomial Operations
A.SSE.1 Interpret expressions that represent a quantity in terms of its
I can decompose polynomial expressions and make sense of multiple
context.
factors and terms by explaining the meaning of the individual parts
a. Interpret parts of an expression, such as terms, factors, and
focusing on quadratic and exponential expressions.
coefficients.
b. Interpret complicated expressions by viewing one or more of their
parts as a single entity. For example, interpret P(1+r)n as the product
of P and a factor not depending on P.
A.APR.1 Understand that polynomials form a system analogous to the
integers, namely, they are closed under the operations of addition,
I can apply the definition of an integer to explain why adding,
subtracting, or multiplying two integers always produces an integer.
I can add, subtract, and multiply polynomials.
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subtraction, and multiplication; add, subtract, and multiply
polynomials.
I can understand how closure applies under these operations. (*ACT)
Unit 8 Quadratic Functions
F.IF.7 Graph functions expressed symbolically and show key features
I can graph quadratic functions and show intercepts, maxima, and
minima.
of the graph, by hand in simple cases and using technology for more
complicated cases.
a. Graph linear and quadratic functions and show intercepts,
maxima, and minima.
A.APR.3 Identify zeros of polynomials when suitable factorizations are
available, and use the zeros to construct a rough graph of the function
defined by the polynomial.
I can find the zeros of a polynomial when the polynomial is factored.
A.REI.4 Solve quadratic equations in one variable.
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.
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.
I can transform a quadratic equation written in standard form to an
equation in vertex form (x – p)2 = q by completing the square.
I can use the zeros of a function to sketch the graph of the function.
I can derive the quadratic formula by completing the square on the
standard form of a quadratic equation.
I can solve quadratic equations in one variable by simple inspection,
taking the square root, factoring, and completing the square. (*ACT)
I can understand why taking the square root of both sides of an
equation yields two solutions.
I can use the quadratic formula to solve any quadratic equation,
recognizing the formula produces all complex solutions.
I can write a complex solution as a + bi for real numbers a and b.
I can solve quadratic equations by taking square roots.
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I can solve quadratic equations by completing the square.
I can solve quadratic equations by factoring.
Unit 9 Quadratic Equations and Modeling
A.SSE.3 Choose and produce an equivalent form of an expression
I can recognize the connection among factors, solutions (roots), zeros
to reveal and explain properties of the quantity represented by the
of related functions, and x-intercepts in quadratic functions.
expression.
a. Factor a quadratic expression to reveal the zeros of the function it
I can identify and factor perfect-square trinomials.
defines.
b. Complete the square in a quadratic expression to reveal the
I can complete the square to rewrite a quadratic expression (𝑎𝑥 2 +
maximum or minimum value of the function it defines.
𝑏𝑥 + 𝑐)with the form 𝑎(𝑥 − ℎ)2 + 𝑘.
I can predict whether a quadratic will have a minimum or a maximum
based on the value of a.
A.SSE.2 Use the structure of an expression to identify ways to rewrite
it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a
difference of squares that can be factored as (x2 – y2)(x2 + y2).
I can rewrite algebraic expressions in different equivalent forms such
as combining like terms and factoring.
I can simplify expressions including combine like terms, using the
distributive property and other operations with polynomials.
I can factor using greatest common factors and grouping.
I can factor using a difference of two squares.
I can factor using the sum or difference of two cubes.
I can choose the appropriate methods for factoring a polynomial.
(*ACT)
F.IF 8. Write a function defined by an expression in different but
equivalent forms to reveal and explain different properties of the
function.
I can explain how complex solutions affect the graph of a quadratic
equation.
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a. Use the process of factoring and completing the square in a
quadratic function to show zeros, extreme values, and symmetry of
the graph, and interpret these in terms of a context.
I can use the process of factoring and completing the square in a
quadratic function to determine the vertex, axis of symmetry,
direction of opening, and zeros/roots from the graph of a quadratic
function.
I can sketch the graph of a quadratic function.
I can describe all of the properties of a quadratic function.
AI.WCE.12 Understand imaginary numbers and how to write them.
I can simplify a radical that represents an imaginary number.
I can explain and demonstrate why imaginary numbers occur in square
roots.
Honors Addendum:
Note for Teachers of Honors: Do not teach this Honors Addendum at
the end of the quarter.
Embed the Honors Addendum within the regular Scope & Sequence.
AI.WCE.15(+) Represent a system of linear equations as a single matrix
equation in a vector variable.
AI.WCE.16 (+) Find the inverse of a matrix if it exists and use it to solve
systems of linear equations (using technology for matrices of
dimension 3×3 or greater).
AI.WCE.17 Solve simple rational and radical equations in one variable,
and give examples showing how extraneous solutions may arise.
I can perform matrix operations.
I can find the inverse of a matrix.
I can solve a system of linear equations using matrices.
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I can solve radical equations, graph square root functions, and operate
with radicals that have indexes > 2.
I can solve an equation that contains a rational expression in one
variable with a monomial denominator.
AI.WCE.18 Simplify and restrict the domain of a rational expression in
one variable.
I can evaluate and interpret the discriminant, using it to describe the
roots of a quadratic function.
AI.WCE.19 Perform operations on rational expressions in one variable.
I can explain when an extraneous solution might occur in these types
of equations.
I can simplify a rational expression in one variable and restrict the
domain.
I can multiply and divide rational expressions in one variable.
I can add/subtract rational expressions in one variable with like
denominators.
I can add/subtract rational expressions in one variable with
unlike denominators.
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