Algebra 1, Geometry, and Algebra 2 Common Core

144 Pages·2012·0.52 MB·English

A Correlation of

Pearson
Algebra 1, Geometry, and Algebra 2
Common Core
©2012

to the

Common Core State Standards
Comparison with
Arkansas
Student Learning Expectations
for Mathematics

Grades 9-12
Pearson Algebra 1, Geometry, and Algebra 2 Common Core, ©2012
to the Common Core State Standards Comparison with
Arkansas Student Learning Expectations for Mathematics

Table of Contents

Number and Quantity...............................................................................1

Algebra ..................................................................................................19

Functions...............................................................................................53

Geometry...............................................................................................92

Statistics and Probability .....................................................................118

Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved
Pearson Algebra 1, Geometry, and Algebra 2, Common Core ©2012
to the Common Core State Standards Comparison with
Arkansas Student Learning Expectations for Mathematics

Arkansas Student Pearson Algebra 1, Geometry,
Common Core State Standards
Learning Expectations Algebra 2, Common Core
for Mathematics
for Mathematics ©2012
Number and Quantity
CC.9-12.N.RN.1 Extend the AR.9-12.PRF.AII.4.7 Algebra 1:
properties of exponents to (PRF.4.AII.7) Establish the SE/TE: 448-452
rational exponents. Explain relationship between radical TE: 452A Lesson Resources
how the definition of the expressions and expressions
meaning of rational exponents containing rational exponents Geometry:
follows from extending the SE/TE: 399
properties of integer
exponents to those values, Algebra 2:
allowing for a notation for SE/TE: 631-366, 381-388
radicals in terms of rational TE: 366A Lesson Resources
exponents. For example, we
define 5^(1/3) to be the cube AR.9-12.PRF.AII.4.8 Algebra 1:
root of 5 because we want (PRF.4.AII.8) Simplify variable SE/TE: 425-431
[5^(1/3)]^3 = 5^[(1/3) x 3] expressions containing TE: 431 Lesson Resources
to hold, so [5^(1/3)]^3 must rational exponents using the
equal 5. laws of exponents Geometry:
SE/TE: 399

Algebra 2:
SE/TE: 363, 368-370, 376

AR.9-12.QEF.AII.3.1 Algebra 1:
(QEF.3.AII.1) Perform SE/TE: 448-452, 619-625, 626-
computations with radicals: 631, 633-638
-- simplify radicals with TE: 625A Lesson Resources,
different indices, 638A Lesson Resources
-- add, subtract, multiply and
divide radicals, Geometry:
-- rationalize denominators, SE/TE: 399
-- solve equations that contain
radicals or radical expressions Algebra 2:
SE/TE: 361-368, 367-373, 374-
380, 381-388, 390-396

AR.9-12.LA.AI.1.8 (LA.1.AI.8) Algebra 1:
Simplify radical expressions SE/TE: 619-624
such as 3 / (√7).
Geometry:
SE/TE: 399

Algebra 2:
SE/TE: 369-370, 377

Key: SE = Student Edition; TE = Teacher’s Edition; (cid:31) = Modeling Standard 1
Pearson Algebra 1, Geometry, and Algebra 2 Common Core, ©2012
to the Common Core State Standards Comparison with
Arkansas Student Learning Expectations for Mathematics

Arkansas Student Pearson Algebra 1, Geometry,
Common Core State Standards
Learning Expectations Algebra 2, Common Core
for Mathematics
for Mathematics ©2012
(Continued) AR.9-12.PRF.AIII.2.5 Algebra 1:
CC.9-12.N.RN.1 Extend the (PRF.2.AIII.5) Establish the SE/TE: 633-638, 639-644
properties of exponents to relationship between radical TE: 638A Lesson Resources,
rational exponents. Explain expressions and expressions 644A Lesson Resources
how the definition of the containing rational exponents,
meaning of rational exponents and simplify variable Geometry:
follows from extending the expressions containing SE/TE: 399
properties of integer rational exponents using the
exponents to those values, laws of exponents Algebra 2:
allowing for a notation for SE/TE: 361-366, 368-370, 376,
radicals in terms of rational 381-388
exponents. For example, we TE: 366A Lesson Resources
define 5^(1/3) to be the cube
root of 5 because we want
[5^(1/3)]^3 = 5^[(1/3) x 3]
to hold, so [5^(1/3)]^3 must
equal 5.

CC.9-12.N.RN.2 Extend the AR.9-12.PRF.AII.4.7 Algebra 1:
properties of exponents to (PRF.4.AII.7) Establish the SE/TE: 448-452;
rational exponents. Rewrite relationship between radical TE: 452A Lesson Resources
expressions involving radicals expressions and expressions
and rational exponents using containing rational exponents Geometry:
the properties of exponents. SE/TE: 399

Algebra 2:
SE/TE: 631-366, 381-388
TE: 366A Lesson Resources

AR.9-12.PRF.AII.4.8 Algebra 1:
(PRF.4.AII.8) Simplify variable SE/TE: 433-438, 439-443
expressions containing
rational exponents using the Geometry:
laws of exponents SE/TE: 399

Algebra 2:
SE/TE: 363, 368-370, 376

Key: SE = Student Edition; TE = Teacher’s Edition; (cid:31) = Modeling Standard 2
Pearson Algebra 1, Geometry, and Algebra 2 Common Core, ©2012
to the Common Core State Standards Comparison with
Arkansas Student Learning Expectations for Mathematics

Arkansas Student Pearson Algebra 1, Geometry,
Common Core State Standards
Learning Expectations Algebra 2, Common Core
for Mathematics
for Mathematics ©2012
(Continued) AR.9-12.QEF.AII.3.1 Algebra 1:
CC.9-12.N.RN.2 Extend the (QEF.3.AII.1) Perform SE/TE: 448-452, 619-625, 626-
properties of exponents to computations with radicals: 631, 633-638
rational exponents. Rewrite -- simplify radicals with TE: 625A Lesson Resources,
expressions involving radicals different indices, 638A Lesson Resources
and rational exponents using -- add, subtract, multiply and
the properties of exponents. divide radicals, Geometry:
-- rationalize denominators, SE/TE: 399
-- solve equations that contain
radicals or radical expressions Algebra 2:
SE/TE: 361-368, 367-373, 374-
380, 381-388, 390-396

AR.9-12.LA.AI.1.9 (LA.1.AI.9) Algebra 1:
Add, subtract, and multiply SE/TE: 619-625, 626-631
simple radical expressions like TE: 625A Lesson Resources,
3√20 + 7√5 and (4√5)(2√3). 631A Lesson Resources

Geometry:
SE/TE: 399

Algebra 2:
SE/TE: 367-368, 374-376

AR.9-12.PRF.AIII.2.5 Algebra 1:
(PRF.2.AIII.5) Establish the SE/TE: 633-638, 639-644
relationship between radical TE: 638A Lesson Resources,
expressions and expressions 644A Lesson Resources
containing rational exponents,
and simplify variable Geometry:
expressions containing SE/TE: 399
rational exponents using the
laws of exponents Algebra 2:
SE/TE: 361-366, 368-370, 376,
381-388
TE: 366A Lesson Resources

CC.9-12.N.RN.3 Use Properties No Matches in Arkansas Studied in 4th year course.
of rational and irrational Frameworks
numbers. 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 number and an
irrational number is irrational.

Key: SE = Student Edition; TE = Teacher’s Edition; (cid:31) = Modeling Standard 3
Pearson Algebra 1, Geometry, and Algebra 2 Common Core, ©2012
to the Common Core State Standards Comparison with
Arkansas Student Learning Expectations for Mathematics

Arkansas Student Pearson Algebra 1, Geometry,
Common Core State Standards
Learning Expectations Algebra 2, Common Core
for Mathematics
for Mathematics ©2012
CC.9-12.N.Q.1 Reason AR.9-12.DIP.AI.5.5 Algebra 1:
quantitatively and use units to (DIP.5.AI.5) Use two or more SE/TE: 746-751, 732-737, 336-
solve problems. Use units as a graphs (i.e., box-and- whisker, 343
way to understand problems histograms, scatter plots) to TE: 751A Lesson Resources/
and to guide the solution of compare data sets Histograms, 737A Lesson
multi-step problems; choose Resources, 343A Lesson
and interpret units Resources
consistently in formulas;
choose and interpret the scale Algebra 2:
and the origin in graphs and SE/TE: 92-98, 713-714
data displays.* TE: 98A Lesson Resources

AR.9-12.DIP.AI.5.6 Algebra 1:
(DIP.5.AI.6) Construct and SE/TE: 732-737
interpret a cumulative TE: 737A Lesson Resources
frequency histogram in real
life situations Algebra 2:
SE/TE: 695

AR.9-12.DIP.AI.5.1 Algebra 1:
(DIP.5.AI.1) Construct and use SE/TE: 336-343
scatter plots and line of best TE: 343A Lesson Resources
fit to make inferences in real
life situations Algebra 2:
SE/TE: 92-98, 713-714
TE: 98A Lesson Resources

AR.9-12.SEI.AI.2.5 Algebra 1:
(SEI.2.AI.5) Solve real world SE/TE: 116-121, 137-143
problems that involve a TE: 121A Lesson Resources,
combination of rates, 143A Lesson Resources
proportions and percents
Geometry:
SE/TE: 432-435, 443,446
TE: 438A

AR.9-12.SEI.AI.2.6 Algebra 1:
(SEI.2.AI.6) Solve problems SE/TE: 698-704
involving direct variation and TE: 704A Lesson Resources
indirect (inverse) variation to
model rates of change Algebra 2:
SE/TE: 68-72, 498-504
TE: 73A Lesson Resources,
505A Lesson Resources

Key: SE = Student Edition; TE = Teacher’s Edition; (cid:31) = Modeling Standard 4
Pearson Algebra 1, Geometry, and Algebra 2 Common Core, ©2012
to the Common Core State Standards Comparison with
Arkansas Student Learning Expectations for Mathematics

Arkansas Student Pearson Algebra 1, Geometry,
Common Core State Standards
Learning Expectations Algebra 2, Common Core
for Mathematics
for Mathematics ©2012
(Continued) AR.9-12.LF.AI.3.5 (LF.3.AI.5) Algebra 1:
CC.9-12.N.Q.1 Reason Interpret the rate of SE/TE: 294-300
quantitatively and use units to change/slope and intercepts TE: 300A Lesson Resources
solve problems. Use units as a within the context of everyday
way to understand problems life Geometry:
and to guide the solution of SE/TE: 189-195
multi-step problems; choose
and interpret units Algebra 2:
consistently in formulas; SE/TE: 70, 501-502, 504
choose and interpret the scale
and the origin in graphs and AR.9-12.M.G.3.2 (M.3.G.2) Algebra 1:
data displays.* Apply, using appropriate units, SE/TE: 110
appropriate formulas (area,
perimeter, surface area, Geometry:
volume) to solve application SE/TE: 699-707
problems involving polygons, TE: 707A Lesson Resources,
prisms, pyramids, cones, 708-715, 715A Lesson Resources,
cylinders, spheres as well as 717-724, 724A Lesson Resources,
composite figures, expressing 726-732, 732A Lesson Resources,
solutions in both exact and 733-740, 740A Lesson Resources,
approximate forms 742-749, 749A Lesson Resources

AR.9-12.PS.AC.1.5 (PS.1.AC.5) Algebra 1:
Interpret and evaluate, with SE/TE: 726-731, 732-737, 738-
and without appropriate 744, 746-751, 753-759
technology, graphical and TE: 731A Lesson Resources,
tabular data displays for: 737A Lesson Resources,
-- consistency with the data, 744A Lesson Resources,
-- appropriateness of type of 751A Lesson Resources,
graph or data display, 759A Lesson Resources
-- scale,
-- overall message Geometry:
SE/TE: 83, 111-112, 658, 660,
748

Algebra 2:
SE/TE: 711-718
TE: 718A Lesson Resources

AR.9-12.ME.TDM.3.1 Algebra 1:
(ME.3.TDM.1) Solve problems SE/TE: 116-121
using dimensional analysis TE: 121A Lesson Resources
(factor-label method) (e.g.,
construction, medical, metric, Geometry:
standard to metric, rate SE/TE: T886
conversions)
Algebra 2:
SE/TE: 845

Key: SE = Student Edition; TE = Teacher’s Edition; (cid:31) = Modeling Standard 5
Pearson Algebra 1, Geometry, and Algebra 2 Common Core, ©2012
to the Common Core State Standards Comparison with
Arkansas Student Learning Expectations for Mathematics

Arkansas Student Pearson Algebra 1, Geometry,
Common Core State Standards
Learning Expectations Algebra 2, Common Core
for Mathematics
for Mathematics ©2012
CC.9-12.N.Q.2 Reason AR.9-12.M.G.3.2 (M.3.G.2) Algebra 1:
quantitatively and use units to Apply, using appropriate units, SE/TE: 110
solve problems. Define appropriate formulas (area,
appropriate quantities for the perimeter, surface area, Geometry:
purpose of descriptive volume) to solve application SE/TE: 699-707, 708-715, 717-
modeling.* problems involving polygons, 724, 11-5 726-732, 733-740,
prisms, pyramids, cones, 742-749
cylinders, spheres as well as TE: 707A Lesson Resources,
composite figures, expressing 715A Lesson Resources,
solutions in both exact and 724A Lesson Resources,
approximate forms 732A Lesson Resources,
740A Lesson Resources,
749A Lesson Resources

AR.9-12.SEI.AI.2.5 Algebra 1:
(SEI.2.AI.5) Solve real world SE/TE: Rates 116-121, 137-143
problems that involve a TE: 121A Lesson Resources
combination of rates,
proportions and percents Geometry:
SE/TE: 432-435, 443,446

AR.9-12.SEI.AI.2.6 Algebra 1:
(SEI.2.AI.6) Solve problems SE/TE: 698-704
involving direct variation and TE: 704A Lesson Resources
indirect (inverse) variation to
model rates of change Algebra 2:
SE/TE: 68-72, 498-504,
TE: 73A Lesson Resources,
505A Lesson Resources

AR.9-12.SEI.AC.3.6 Algebra 1:
(SEI.3.AC.6) SLE 6. Apply SE/TE: 8, 169, 249-242, 348,462
linear, piece-wise and step
functions to real world Algebra 2:
situations that involve a SE/TE: 64, 84, 90-91, 576
combination of rates,
proportions and percents such
as sales tax, simple interest,
social security, constant
depreciation and appreciation,
arithmetic sequences,
constant rate of change,
income taxes, postage, utility
bills, commission, and traffic
tickets

Key: SE = Student Edition; TE = Teacher’s Edition; (cid:31) = Modeling Standard 6
Pearson Algebra 1, Geometry, and Algebra 2 Common Core, ©2012
to the Common Core State Standards Comparison with
Arkansas Student Learning Expectations for Mathematics

Arkansas Student Pearson Algebra 1, Geometry,
Common Core State Standards
Learning Expectations Algebra 2, Common Core
for Mathematics
for Mathematics ©2012
AR.9-12.ME.TDM.3.1 Algebra 1:
(Continued) (ME.3.TDM.1) Solve problems SE/TE: 116-121
CC.9-12.N.Q.2 Reason using dimensional analysis TE: 121A Lesson Resources
quantitatively and use units to (factor-label method) (e.g.,
solve problems. Define construction, medical, metric, Geometry:
appropriate quantities for the standard to metric, rate SE/TE: 62
purpose of descriptive conversions) TE: T886
modeling.*
Algebra 2:
SE/TE: 845

CC.9-12.N.Q.3 Reason AR.9-12.M.G.3.2 (M.3.G.2) Algebra 1:
quantitatively and use units to Apply, using appropriate units, SE/TE: 110
solve problems. Choose a level appropriate formulas (area,
of accuracy appropriate to perimeter, surface area, Geometry:
limitations on measurement volume) to solve application SE/TE: 699-707, 708-715, 717-
when reporting quantities.* problems involving polygons, 724, 726-732, 733-740, 742-749
prisms, pyramids, cones, TE: 707A Lesson Resources,
cylinders, spheres as well as 715A Lesson Resources,
composite figures, expressing 724A Lesson Resources,
solutions in both exact and 732A Lesson Resources,
approximate forms 740A Lesson Resources,
749A Lesson Resources
CC.9-12.N.CN.1 Perform AR.9-12.QEF.AII.3.2 Algebra 2:
arithmetic operations with (QEF.3.AII.2) Extend the SE/TE: 248-252
complex numbers. Know there number system to include the TE: 255A Lesson Resources
is a complex number i such complex numbers:
that i^2 = −1, and every -- define the set of complex
complex number has the form numbers,
a + bi with a and b real. -- add, subtract, multiply, and
divide complex numbers,
-- rationalize denominators

CC.9-12.N.CN.2 Perform AR.9-12.QEF.AII.3.2 Algebra 2:
arithmetic operations with (QEF.3.AII.2) Extend the SE/TE: 248-252
complex numbers. Use the number system to include the TE: 255A Lesson Resources
relation i^2 = –1 and the complex numbers:
commutative, associative, and -- define the set of complex
distributive properties to add, numbers,
subtract, and multiply complex -- add, subtract, multiply, and
numbers. divide complex numbers,
-- rationalize denominators

Key: SE = Student Edition; TE = Teacher’s Edition; (cid:31) = Modeling Standard 7
Pearson Algebra 1, Geometry, and Algebra 2 Common Core, ©2012
to the Common Core State Standards Comparison with
Arkansas Student Learning Expectations for Mathematics

Arkansas Student Pearson Algebra 1, Geometry,
Common Core State Standards
Learning Expectations Algebra 2, Common Core
for Mathematics
for Mathematics ©2012
CC.9-12.N.CN.3 (+) Perform AR.9-12.QEF.AII.3.2 Algebra 2:
arithmetic operations with (QEF.3.AII.2) Extend the SE/TE: 248-252
complex numbers. Find the number system to include the TE: 255A Lesson Resources
conjugate of a complex complex numbers:
number; use conjugates to -- define the set of complex
find moduli and quotients of numbers,
complex numbers. -- add, subtract, multiply, and
divide complex numbers,
-- rationalize denominators

CC.9-12.N.CN.4 (+) Represent AR.9-12.PC.PCT.8.1 Studied in a 4th year course.
complex numbers and their (PC.8.PCT.1) Convert polar
operations on the complex coordinates to rectangular
plane. Represent complex coordinates and rectangular
numbers on the complex plane coordinates to polar
in rectangular and polar form coordinates
(including real and imaginary
numbers), and explain why the AR.9-12.PC.PCT.8.2 Studied in a 4th year course.
rectangular and polar forms of (PC.8.PCT.2) Represent
a given complex number equations given in rectangular
represent the same number. coordinates in terms of polar
coordinates

AR.9-12.PC.PCT.8.3 Studied in a 4th year course.
(PC.8.PCT.3) Graph polar
equations and use appropriate
technology when needed

AR.9-12.PC.PCT.8.4 Studied in a 4th year course.
(PC.8.PCT.4) Apply polar
coordinates to real world
situations and use appropriate
technology when needed

CC.9-12.N.CN.5 (+) Represent No Matches in Arkansas Algebra 2:
addition, subtraction, Frameworks SE/TE: 248-252
multiplication, and conjugation TE: 255A Lesson Resources
of complex numbers
geometrically on the complex
plane; use properties of this
representation for
computation. For example, (-1
+ √3 i)3 = 8 because (-1 + √3
i) has modulus 2 and
argument 120º.

Key: SE = Student Edition; TE = Teacher’s Edition; (cid:31) = Modeling Standard 8