Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing


N.RN.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
notion for radicals in terms of rational exponents. For example, we define(5^{1/3})^{ 3}=5^{(1/3) 3}to
hold, so (5^{1/3})^{ 3}must equal 5.

How does
primary knowledge of fractions assist with the completion of problems with
rational exponents?
What is
the relationship between radicals and integers with fraction exponents?

Compare
similar appearing rational numbers raised to an exponent to determine the
relationship between the properties of integers and real numbers raised to a power

Rational
Irrational
Integers
Radicals
Rational
exponents

3 days


N.RN.2
Rewrite expressions involving radicals and rational exponents using the
properties of exponents.

What is
the relationship between radicals and numbers raised to a rational power?
What is
the relationship to a fractional exponent and the root of a given term?

Develop
a worksheet and answer key containing no less than 6 problems involving
radicals and rational exponents, distribute the worksheet to classmates to
complete, then correct their work

Expressions
Properties
of exponents

3 days


N.RN.3
Explain why the sum or product of two rational numbers is rational; that the
sum of a rational number and an irrational number is irrational; and that the
product of a nonzero rational number and an irrational number is irrational.

What is the
relationship between multiplication and division in terms of rational
numbers?

Create a
poster highlighting: “the sum or product of two rational numbers is rational;
that the sum of a rational number and an irrational number is irrational; and
that the product of a nonzero rational number and an irrational number is
irrational;” include examples for each statement

Sum
Product
Difference
Quotient
Irrational
number
Rational
number

1 day


Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing


N.Q.1 Use
units as a way to understand problems and to guide the solution of multistep
problems; choose and interpret units consistently in formulas; choose and
interpret the scale and the origin in graphs and data displays.

How do
units guide the process of completing multistep problems?

Select
the appropriate method to complete a word problem based on the units
provided.
Construct
a multistep word problem involving units of measure.

Units of
Measurement
Units^{2}
UOM for
Distance, Volume, and Area

3 days


How are
appropriate units determined when solving realworld problems?

Differentiate
the use of units in problems relating to distance, volume, and other forms of
measurement.

Distance
Volume
Area
Perimeter


How does
scale relate to the understanding of data on graphs and data displays?

Design
and conduct a small classroom study.
Develop
a graph or chart with appropriate scale and units of measure.

Scale
Data
Graphs


N.Q.2
Define appropriate quantities for the purpose of descriptive modeling.

How do
categories in the real number system relate to solving practical problems?

Determine
which type of number will provide the most accurate response to a given
problem.
Solve
problems relating to models, measures, and statistics.

Real
Number System
Set
Integer
Exponent
Scientific
Notation
Whole
Number
Rational
Number
Irrational
Number

3 days


N.Q.3
Choose a level of accuracy appropriate to limitations on measurement when
reporting quantities.

How do
limitations assist in determining the accuracy of a response?

Evaluate
a given response based on the limitations of the problem (e.g. distance must
be positive).

Limitation
Accuracy

3 days


Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing


N.CN.1
Know there is a complex number i
such that i^{2}=1, and
every complex number has the form a+bi
with a and b real.

What is
the role of imaginary numbers in mathematics?
What
fields of study are imaginary numbers most utilized?

Using a
mirror and a ruler, support the concept of imaginary numbers

Real
number
Complex
number
Irrational
number
i
i^{2}
a+bi

2 days


N.CN.2
Use the relation i^{2}=1
and the commutative, associative, and distributive properties to add,
subtract, and multiply complex numbers.

How are
the commutative, associative, and distributive properties open over the
complex number system?

Construct
a no less than seven term complex expression which requires the use of the
commutative, associative, and distributive properties to solve; solve your
creation

Commutative
Property
Associative
Property
Distributive
Property

2 days


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N.CN.7
Solve quadratic equations with real coefficients that have complex solutions.

In what
scenarios would the solution to a quadratic equation be complex?

Design a
visual representing the three possible combinations of solutions for a
quadratic equation

Coefficients
Complex
solutions
Discriminate

1 day


N.CN.8
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^{2}+4 as (x+2i)(x2i).

How could
imaginary numbers relate to additional dimensions?

Create
an equation with complex solutions for each polynomial identity

Complex
numbers
Polynomial
identities

1 day


N.CN.9
(+) Know the Fundamental Theorem of Algebra, show that it is true for
quadratic polynomials.

How could
an understanding of the Fundamental Theorem of Algebra help you on your next
test?

Support
the Fundamental Theorem of Algebra with 2 real and 2 complex examples

Fundamental
Theorem of Algebra
Roots

1 day


Standard

Essential Question

Bloom’s Taxonomy Activities

Vocabulary

Pacing


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Number and Quantity
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