1. Topic-
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In this unit of study, students will apply the properties of exponents.
They will represent very small or very large numbers in scientific
notation, perform operations and learn how to interpret when "E"�
appears on the calculator. Students will provide examples of linear
equations with one, infinitely many, or no solution. Students will
understand that real numbers are rational or irrational; will place
them on the number line and compare them.
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2. Content-
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laws of exponents, power, perfect squares, perfect cubes, root,
square root, cube root, scientific notation, standard form of a number.
intersecting, parallel lines, coefficient, distributive property,
like terms
real numbers, irrational numbers, rational numbers, integers, whole
numbers, natural numbers, radical, radicand, square roots, perfect
squares, cube roots, terminating decimals, repeating decimals, truncate
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3. Goals: Aims/Outcomes-
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Domains: Expressions and Equations (8.EE), Number System (8.NS)
Clusters: Work with radicals and integer exponents.
Analyze and solve linear equations and pairs of simultaneous linear
equations.
Know that there are numbers that are not rational, and approximate
them by rational numbers.
Standards:
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.
8.EE.3 USE numbers expressed in the form of a single digit times an
integer power of 10 to ESTIMATE very large or very small quantities,
and to EXPRESS how many times as much one is than the other. For example,
estimate the population of the United States as 3 × 108 and the population
of the world as 7 × 109, and determine that the world population
is more than 20 times larger.
8.EE.4 PERFORM operations with numbers expressed in scientific notation,
including problems where both decimal and scientific notation are
used. USE scientific notation and CHOOSE units of appropriate size
for measurements of very large or very small quantities (e.g., use
millimeters per year for seafloor spreading). Interpret scientific
notation that has been generated by technology.
8.EE.7 SOLVE linear equations in one variable.
a. Give examples of linear equations in one variable with one solution,
infinitely many solutions, or no solutions. Show which of these possibilities
is the case by successively transforming the given equation into simpler
forms, until an equivalent equation of the form x = a, a = a, or a
= b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including
equation whose solutions require expanding expressions using the distributive
property and collecting like terms.
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.
8.NS.2 USE rational approximations of irrational numbers to COMPARE
the size of irrational numbers, LOCATE them approximately on a number
line diagram, and ESTIMATE the value of expressions (e.g., π2). For
example, by truncating the decimal expansion of √2, show that √2
is between 1 and 2, then between 1.4 and 1.5, and explain how to continue
on to get better approximations
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4. Objectives-
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Standards:
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.
8.EE.3 USE numbers expressed in the form of a single digit times an
integer power of 10 to ESTIMATE very large or very small quantities,
and to EXPRESS how many times as much one is than the other. For example,
estimate the population of the United States as 3 × 108 and the population
of the world as 7 × 109, and determine that the world population
is more than 20 times larger.
8.EE.4 PERFORM operations with numbers expressed in scientific notation,
including problems where both decimal and scientific notation are
used. USE scientific notation and CHOOSE units of appropriate size
for measurements of very large or very small quantities (e.g., use
millimeters per year for seafloor spreading). Interpret scientific
notation that has been generated by technology.
8.EE.7 SOLVE linear equations in one variable.
a. Give examples of linear equations in one variable with one solution,
infinitely many solutions, or no solutions. Show which of these possibilities
is the case by successively transforming the given equation into simpler
forms, until an equivalent equation of the form x = a, a = a, or a
= b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including
equation whose solutions require expanding expressions using the distributive
property and collecting like terms.
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.
8.NS.2 USE rational approximations of irrational numbers to COMPARE
the size of irrational numbers, LOCATE them approximately on a number
line diagram, and ESTIMATE the value of expressions (e.g., π2). For
example, by truncating the decimal expansion of √2, show that √2
is between 1 and 2, then between 1.4 and 1.5, and explain how to continue
on to get better approximations
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5. Procedures/Methods-
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A. Introduction-
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B. Practice-
SE TASK:
Aliens from the Outer Space Galactic Task Force have been watching
the recent gains in mathematical understanding developing in human
brains from Planet Earth. They have become alarmed that Planet Earth
might soon develop the capabilities to discover that life exists on
other planets with this increased mathematical knowledge. To slow
the progress, they have organized an attack on the World Wide Web
and all other forms of math textbooks. All words have been eradicated
from the mathematics examples! Humans will now be forced to study
the patterns of numbers and previously worked examples to rediscover
the properties of mathematics! They are confident that humans will
not persevere in the challenge of making sense of problems, reasoning
abstractly and quantitatively, constructing viable arguments, looking
for and making use of structure, and using repeated reasoning to recreate
the language of mathematics. They have already declared MISSION ACCOMPLISHED!
The next standard in your mathematics class requires knowledge of
the properties of integer exponents. Can your team recreate and name
the properties by using the Standards for Mathematical Practice to
examine the examples that remain? |
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