Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing

A.SSE.1
Interpret expressions that represent a quantity in terms of its context.*

How do
context clues assist in developing an appropriate expression or equation to
solve?

Write an
expression or equation based on the information provided in a problem.

Expression
Equation
Sum
Difference
Quantity
Quotient

3 days

A.SSE.1a
Interpret parts of an expression, such as terms, factors, and coefficients.

How do
numbers and symbols relate to each other in a given problem?

Distinguish
between the various parts of an expression or an equation.

Term
Factor
Coefficient
Variable

3 days

A.SSE.1b
Interpret complicated expressions by viewing one or more of their parts as a
single entity.

Why is it
important to consider every aspect of a given problem or scenario before
attempting to solve the problem?
How do
terms in an expression or equation relate to each other?

Manipulate
quantities in an equation to demonstrate the relationship between terms
Evaluate
the necessity and use of information provided in a word problem.
When
given a word problem, determine which information is needed to solve the
problem and which information is extraneous.

Inverse
Operation
Extraneous
Information

3 days

A.SSE.2Use
the structure of an expression to identify ways to rewrite it. For example, see x^{4}y^{4}as
(x^{2})^{2}(y^{2})^{2}, thus recognizing it
as a difference of squares that can be factored as (x^{2}y^{2})
(x^{2}+y^{2}).

What
qualities of a given function signify the possibility the function could be
simplified using difference of squares?

Develop
a visual demonstrating the steps needed to factor a function of a degree
higher than 2

Structure
of an expression
Factoring

3 days

A.SSE.3
Choose and produce an equivalent form of an expression to reveal and explain
properties of the quantity represented by the expression.*

When is
an understanding of equivalent expressions beneficial?

Create a
visual with samples of two equivalent expressions and two expressions which
are not equivalent; Explain your findings

Equivalent
Expression

3 days

A.SSE.3a
Factor a quadratic expression to reveal the zeros of the function it defines.

What is
the relationship between the zeros of a function and its corresponding graph?

Examine
a set of graphs and a list of equations to determine which equations match
each graph by first determining the zeros

Factor
Zeros

3 days

A.SSE.3b
Complete the square in a quadratic expression to reveal the maximum or
minimum value of the function it defines.

What is
the correlation between maximum and minimum and a roller coaster?

Design
your own rollercoaster using an online rollercoaster tycoon game and four
quadratic equations of your creation

Complete
the square
Maximum
Minimum

3 days

A.SSE.3c
Use the properties of exponents to transform expressions for exponential
functions. For example, the expression 1.15^{t} can be rewritten as (1.15^{1/12})^{12t} ≈1.012^{12t} to reveal the approximate equivalent monthly interest rate if the
annual rate is 15%.

How does
monthly interest rate affect the overall cost of an item?

Choose
an item you would like to buy with a credit card; then use an online
calculator to determine what the overall cost of the item would be based on
the minimum payments you would pay and the interest rate

Exponents
Exponential
functions
Interest
Annual
rate

3 days

A.SSE.4 Derive the formula for the sum of a
finite geometric series (when the common ration is not 1), and use the
formula to solve problems. For example,
calculate mortgage payments.*

Would you
rather have $1 million or the sum of a penny doubled every day for a month?

Create a
collage or visual of the items you would purchase with your new found wealth

Geometric
series
Finite

3 days

Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing

A.APR.1Understand
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.

What is
the difference between an open and a closed system?

Design
a graphic, including examples, which demonstrates the difference between an
open and closed system
Create a
worksheet of no less than six problems involving completing arithmetic
operations on polynomials

Polynomial
Analogous
Open
System
Closed
System
Like
terms

3 days

A.APR.2 Know and apply the Remainder
Theorem: For a polynomial p(x) and
a number a, the remainder on
division by xa is p(a), so p(a) = 0 if and only if (xa)
is a factor of p(x)

How does
use of synthetic division assist in solving for the solution of a polynomial
with a given xvalue?

Experiment
with different coefficients to create a 5^{th} degree polynomial with
3 as a factor.

Remainder
Division
Polynomial
division
Synthetic
division
Remainder
Theorem

3 days

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.

What is
the relationship between the zeros of a polynomial and the xaxis?

Given a
4^{th} degree polynomial, determine the zeros and (from Common Core)
construct a rough graph of the function defined by the polynomial.

Zeros
Polynomials
Concavity
Increasing
Decreasing
Factor

3 days

A.APR.4
Prove polynomial identities and use them to describe numerical relationships.
For example, the polynomial identity (x^{2}+y^{2})^{
2} = (x^{2}y^{2})^{ 2}+ (2xy)^{2} can
be used to generate Pythagorean
triples.

When an
identity is proven valid, what may be said about it?

Choose a
polynomial identity and prove its truth in a visual to be displayed in the
classroom; use at least three examples (+//0)

Polynomial
identities

1 day

A.APR.5
(+) Know and apply the Binomial Theorem for the expansion of (x + y)^{n} in powers x and y for a positive integer n,
where x and y are any numbers, with coefficients determined for example by
Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical
induction or by a combinatorial argument.)

In what
fields is knowledge of Pascal’s Triangle useful? Why?

Research
Pascal’s Triangle; create a brief (approximately 5 minute) presentation on
one area of study in which Pascal’s Triangle is useful. Present your research
to the class and other educators in the building.

Binomial
Theorem
Expansion
Pascal’s
Triangle

1 day

A.APR.6
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree
of r(x) less than the degree of b(x), using inspection, long division,
or, for the more complicated examples, a computer algebra system.

With the
accessibility of the internet, how is higher level mathematics more reachable
to high school learners than 20 years ago?

Experiment
with three different computer algebra systems available at http://www.sai.msu.su/sal/A/1/ and recommend a system which most assists in
completing polynomial division

Rational
expression
Long
division

1 day

A.APR.7 (+)Understand that rational
expressions form a system analogous to the rational numbers, closed under
addition, subtraction, multiplication, and division by a nonzero rational
expression; add, subtract, multiply, and divide rational expressions.

What does
it mean for a system to be closed?

Create a
worksheet and answer key with no less than seven problems which require the addition, subtraction,
multiplication and/or division of rational expressions

Rational
expressions
Analogous

1 day

Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing

A.CED.1
Create equations and inequalities in one variable and use them to solve
problems. Include equations arising
from linear and quadratic functions, and simple rational and exponential
functions.

How does
the use of the inverse operation assist in solving algebraic word problems?

Explain
the relationship between inverse operations and both sides of the equation or
inequality.
Select
the appropriate sequence of operations to complete the problem.

Inequality
Order of
Operations

3 days

A.CED.2
Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.

What
strategies may be used to effectively create equations with two or more
variables?
How do
the elements of an equation assist in accurately graphing the equation on
coordinate axes?

Based on
a given word problem, create and solve an equation which results in an
accurate response to the question.
Construct
an accurate geometric response to a given word problem or set of equations.

Slope
Intercept
Coordinate
Plane
Graph
Graphing
Calculator

3 days

A.CED.3
Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and
interpret solutions as viable or nonviable options.

What
limitations exist when solving problems algebraically and/or graphically?
Why is
flipping the inequality necessary when multiplying or dividing by a negative
number?

Distinguish
between rational and irrational responses when solving equations.
Examine
the reasons why a solution is viable or nonviable.

Viable
Inequality
Constraint
Systems
of Equations

3 days

A.CED.4
Rearrange formulas to highlight a quantity of interest, using the same
reasoning as in solving equations. For
example, rearrange Ohm’s law V=IR to highlight resistance R.

How are
inverse operations used to highlight a quantity of interest?

Explain
how knowledge of inverse operations allow for the rearrangement of variables
and terms to solve for a requested quantity of interest

Quantity
of Interest
Reasoning

3 days

Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing

A.REI.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.

Why is it
important to complete a step to both sides of the equation?

Create a
diagram outlining the steps to solve an equation; provide multiple examples
of the process.
Explain
each step of the process outlined in the diagram.

Solving
equations
Inverse
operation

3 days

A.REI.2 Solve simple rational and radical
equations in one variable, and give examples showing how extraneous solutions
may arise

How do
the fundamental rules of order of operations assist in solving rational and
radical equations?

Create a
2minute video teaching how to solve either rational or radical equations;
post your video on the class webpage or YouTube

Rational
equations
Radical
equations
Variables

3 days

A.REI.3
Solve linear equations and inequalities in one variable, including equations
with coefficients represented by letters.

Why is
knowledge of the inverse operation necessary in solving equations?

Support
the relationship between inverse operations and solving equations by
providing both linear examples and those including inequalities.

Equation
Inequality
Coefficient
Variable

3 days

A.REI.4
Solve quadratic equations in one variable.

What is
the relationship between driving a car and quadratic equations?

Given an
equation and its derivative, experiment with different values of x to
determine the distance a car travels and it’s speed

Variable
Factor
Quadratic
equation

3 days

A.REI.4a
Use the method of completing the square to transform any quadratic equation
in x into an equation of the form (xp)^{2} = q that has the same solutions. Derive
the quadratic formula from this form.

How does
knowledge of completing the square assist in the derivation of the quadratic formula?

Create a
poster for display of 1) an example of completing the square on an equation
of your choosing and 2) the creation of the quadratic formula from the
equation ax^{2}+bx+c=0

Completing
the square
Quadratic
formula

3 days

A.REI.4b
Solve quadratic equations by inspection (e.g., for x^{2}=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 writing them as a±bi for real numbers a
and b.

What
aspects of an equation should be considered when determining which method to
utilize to solve the equation?

Evaluate
a given problem to determine the best method to solve the equation and then
support your selection in three to five sentences

Square
roots
Completing
the square
Quadratic
formula
Factoring

3 days

A.REI.5
Prove that, given a system of two equations in two variables, replacing one
equation by the sum of that equation and a multiple of the other produces a
system with the same solutions.

Why is it
acceptable to increase or decrease an equation by a chosen factor when
solving systems of equations with two variables?

Defend
that increasing or decreasing an equation by a chosen factor does not affect
the solutions to the equation.

System of
equations
Substitution

2 days

A.REI.6
Solve systems of linear equations exactly and approximately (e.g. with
graphs), focusing on pairs of linear equations in two variables.

How can
the graph of a system of equations assist in determining the solutions?

Examine a
system of equations and develop a strategy to determine the exact and
graphical approximation of the result.

Pairs of
equations

2 days

A.REI.7
Solve a simple system consisting of a linear equation and a quadratic
equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x
and the circle x^{2}+y^{2}=3.

How is
the solution to a system of equations determined by looking at their graphs?

Design
a simple systems of a linear equation
and a quadratic equation in two variables and solve 1) By hand, 2) Using a TI
Graphing Calculator (Take a picture), AND 3) using Microsoft Mathematics
(Print out); Display your work by

System
of equation
Linear
equation
Quadratic
equation
Circle
formula

2 days

Arei8


Arei9


A.REI.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).

How do the
solutions of a twovariable equation relate to its graph?
How do the
qualities of an equation dictate what the graph looks like it?

Construct
an accurate coordinate plan and graph when given a twovariable equation.
Formulate
the equation of a given graph.
Contrast
the differences between linear and quadratic graphs and equations.

Graph
Linear
Quadratic
Polynomial
Function
Origin
Solution

3 days

A.REI.11
Explain why the xcoordinate of the points where the graphs of the equations y=f(x) and y=g(x) intersect are 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 where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.*

How does
the intersection of a graph to the xaxis relate to the solution of the
equation?
How does
the intersection of two functions relate to solutions of the functions?
How can
technology be utilized to solve geometric problems?

Support
how the intersection of two functions is a common solution of the functions.
Experiment
with various modes on a graphing calculator to contrast changes in the graph
based on mode selected (e.g. how does a trigonometric graph look in radian
versus degree mode)

Absolute
Value
Exponential
Logarithmic
Approximate
Radian
Degree

3 days

A.REI.12
Graph the solutions to a linear inequality in two variables as a halfplane
(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 halfplanes.

When is
the structure of a line significant in considering inequalities?
What is
significant about the shading of inequalities on a coordinate plane?

Compare
the solutions of two inequalities based on the shading of a graph.
When
given two inequalities, construct a coordinate plane and accurate graph the
equations to determine the appropriate solution through shading.

Inequalities
Shade
Equal to
Linear
Inequality
Graph the
Solution

3 days

Algebra
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