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Math and The Mind’s Eye
Common Core State Standards Correlation Charts
Unit 12 Modeling Real and Complex Numbers
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Unit 12 Modeling Real and Complex Numbers
8.NS.1 Know that numbers that are not rational are called
irrational. Understand informally that every number has
a decimal expansion; for rational numbers show that the
decimal expansion repeats eventually, and convert a decimal
expansion which repeats eventually into a rational number.
Activity 6
Complex Numbers
Activity 5
Squares and Square Roots
Activity 4
Fraction Products and
Quotients
Activity 3
Fractions Sums and
Differences
Activity 2
Decimals and Fractions
Standard
Activity 1
Heximals and Fractions
This unit of instruction provides students with an opportunity to solidify their understanding of rational number and integer exponents. In addition it provides students with a
concrete model of non-real number operation.
Comments
Activity 1 uses base six numbers to look at exponents
and place value. The activity lays the foundation for an
understanding of repeating and terminating decimals.
8.EE.1 Know and apply the properties of integer exponents
to generate equivalent numerical expressions. For example,
32 × 3–5 = 3–3 = 1/33 = 1/27.
8.EE.2 Use square root and cube root symbols to represent
solutions to equations of the form x2 = p and x3 = p, where p
is a positive rational number. Evaluate square roots of small
perfect squares and cube roots of small perfect cubes. Know
that √2 is irrational.
It is not uncommon for secondary students to still struggle
with rational number concepts and operations. This unit
gives them a different vehicle to try to understand and
become more efficient with some of these critical concepts
without it being "more of the same".
A-SSE.3a Choose and produce an equivalent form of an
expression to reveal and explain properties of the quantity
represented by the expression.
A-SSE.3c Use the properties of exponents to transform
expressions for exponential functions. For example the
expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to
reveal the approximate equivalent monthly interest rate if the
annual rate is 15%.
A-APR.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.
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.
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.
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Activity 6
Complex Numbers
Activity 5
Squares and Square Roots
Activity 4
Fraction Products and
Quotients
Activity 3
Fractions Sums and
Differences
Activity 2
Decimals and Fractions
Standard
Activity 1
Heximals and Fractions
Unit 12 Modeling Real and Complex Numbers continued
Comments
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 notation for radicals
in terms of rational exponents. For example, we define 51/3 to
be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold,
so (51/3)3 must equal 5.
N.RN.2 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. For example, we define 51/3 to
be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold,
so (51/3)3 must equal 5.
N-CN.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.
Models for complex numbers follow naturally from students' prior
work with algebraic models and models for arithmetic operations.
N-CN.2 Use the relation i2 = –1 and the commutative,
associative, and distributive properties to add, subtract, and
multiply complex numbers.
N-CN.7 Solve quadratic equations with real coefficients that
have complex solutions.
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