Download Algebra I -- HCPS3-CCSS Crosswalk (12-19-10)

Crosswalk between the Algebra I Hawaii Content and Performance Standards (HCPS) III and the Common Core State Standards (CCSS) for High School Mathematics
HSA Category
Linear Equations
and Functions
Linear Equations
and Functions
HCPS III
Code
AI.8.1
AI.8.2
HCPS III Algebra I Benchmark
Graph linear equations using
slope-intercept, point-slope, and
x- and y-intercept techniques
Determine the slope of a line
when given the graph of a line,
two points on the line, or the
equation of the line
Matched Common Core CLUSTER and Standard
F.IF.7: Analyze functions using different representations. Graph functions expressed symbolically
and show key features of the graph, by hand in simple cases and using technology for more
complicated cases.*
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Match*
1
Linear Equations
and Functions
Linear Equations
and Functions
AI.9.1
AI.10.4
AI.10.9
Determine if a linear pattern
exists in a set of data and
represent the data algebraically
and graphically
Determine the equation of a line
when given the graph of the line,
the slope and a point on the line,
or two points on the line
Analyze transformations of lines
and understand how the
transformations are represented
in equations
Comment
The taxonomic levels of the CC
standards are considerably different
from the cognitive demand of the HCPS
III benchmark.
A.CED.2: Create equations that describe numbers or relationship. Create equations in two or more
variables to represent relationships between quantities; graph equations on coordinate axes with
labels and scales.*
S.ID.7: Interpret linear models. Interpret the slope (rate of change) and the intercept (constant
term) of a linear model in the context of the data.*
1
A.CED.2: Create equations that describe numbers or relationship. Create equations in two or more
variables to represent relationships between quantities; graph equations on coordinate axes with
labels and scales.*
Linear Equations
and Functions
updated: 12-19-10
F.LE.1: Construct and compare linear, quadratic, and exponential models and solve problems.
Distinguish between situations that can be modeled with linear functions and with exponential
functions.*
a: Prove that linear functions grow by equal differences over equal intervals and that exponential
functions grow by equal factors over equal intervals.*
b: Recognize situations in which one quantity changes at a constant rate per unit interval relative
to another.*
A.CED.2: Create equations that describe numbers or relationships. Create equations in two or
more variables to represent relationships between quantities; graph equations on coordinate axes
with labels and scales.*
2
2
S.ID.7: Interpret linear models. Interpret the slope (rate of change) and the intercept (constant
term) of a linear model in the context of the data.*
F.IF.4: Interpret functions that arise in applications in terms of the context. For a function that
models a relationship between two quantities, interpret key features of graphs and tables in terms of
the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or
negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
1
* Degree of Match: 1 = WEAK (major aspect of the HCPS III benchmark not addressed in CCSS); 2 = GOOD (minor aspect of the HCPS III benchmark not addressed in CCSS); 3 = EXCELLENT
The CC standard emphasizes the
interpretation of the meaning of the
slope in terms of a given real-world
context.
This standard is a great opportunity to
address the Mathematical Practices by
incorporating the strategic use of
technology to promote students' sensemaking about mathematical ideas and
how these ideas can be used to make
sense of and model real-world
contexts.
The CC standard S.ID.7 extends the
HCPS III benchmark, expecting students
to apply their understanding and skills
in the context of interpreting data that
exhibit a linear trend.
Both the HCPS III benchmark and the
CC standard expect students to make
connections between linear
relationships presented in symbolic
form (equations), numeric form (table
of values) and graphic form.
page 1 of 6
Crosswalk between the Algebra I Hawaii Content and Performance Standards (HCPS) III and the Common Core State Standards (CCSS) for High School Mathematics
HSA Category
Modeling
Modeling
Modeling
Modeling
Modeling
HCPS III
Code
HCPS III Algebra I Benchmark
AI.1.1
Recognize situations that can be
represented by matrices
AI.3.3
Use addition, subtraction, and
scalar multiplication of matrices
to solve problems
AI.4.1
Use formulas, functions, or
conversion equations to solve
problems dealing with
determining a measurement
based on another derived or
given measurement
AI.9.2
AI.10.2
Compare and contrast the
concepts of direct and inverse
variation of a relation
Translate between verbal
mathematical situations and
algebraic expressions and
equations
Matched Common Core CLUSTER and Standard
N.VM.6 (+): Perform operations on matrices and use matrices in applications. Use matrices to
represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
Match*
updated: 12-19-10
Comment
2
N.VM.7 (+): Perform operations on matrices and use matrices in applications. Multiply matrices by
scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
N.VM.8 (+): Perform operations on matrices and use matrices in applications. Add, subtract, and
multiply matrices of appropriate dimensions.
A.CED.4: Create equations that describe numbers or relationships. 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.*
2
1
F.IF.4: Interpret functions that arise in applications in terms of the context. For a function that
models a relationship between two quantities, interpret key features of graphs and tables in terms of
the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or
negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
2
F.IF.5: Interpret functions that arise in applications in terms of the context. Relate the domain of a
function to its graph and, where applicable, to the quantitative relationship it describes. For example,
if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then
the positive integers would be an appropriate domain for the function.*
A.CED.1: Create equations that describe numbers or relationships. 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.*
The CC standard focuses only on solving
literal equations (e.g., solving for h in
the formula V = πr2h).
Students should be given various
opportunities to model real-world
situations that demonstrate direct and
inverse variation relationships. Both
the HCPS III benchmark and CC
standards are great opportunities to
strategically utilize technology to help
students make sense of rather abstract
ideas and to understand the
distinctions between direct variation
and inverse variation.
Algebra I teachers should refer to the
8th grade CC standard on proportional
relationships (8.EE.5) to design
instruction that builds on students’
prior knowledge.
2
* Degree of Match: 1 = WEAK (major aspect of the HCPS III benchmark not addressed in CCSS); 2 = GOOD (minor aspect of the HCPS III benchmark not addressed in CCSS); 3 = EXCELLENT
page 2 of 6
Crosswalk between the Algebra I Hawaii Content and Performance Standards (HCPS) III and the Common Core State Standards (CCSS) for High School Mathematics
HSA Category
Modeling
HCPS III
Code
AI.9.4
HCPS III Algebra I Benchmark
Compare and contrast the
properties of linear functions
and exponential functions
Matched Common Core CLUSTER and Standard
F.LE.1: Construct and compare linear, quadratic, and exponential models and solve problems.
Distinguish between situations that can be modeled with linear functions and with exponential
functions.*
a. Prove that linear functions grow by equal differences over equal intervals and that exponential
functions grow by equal factors over equal intervals.*
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative
to another.*
c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit
interval relative to another.*
Match*
2
F.LE.3: Construct and compare linear, quadratic, and exponential models and solve problems.
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more generally) as a polynomial function.*
updated: 12-19-10
Comment
Students should be given various
opportunities to model real-world
situations that exhibit linear or
exponential relationships. Both the
HCPS III benchmark and CC standards
are great opportunities to strategically
utilize technology to help students
make sense of rather abstract ideas and
to understand the distinctions between
linear and exponential growth.
Algebra I teachers should refer to the
7th and 8th grade CC standards relating
unit rates with slope to design
instruction that builds on students’
prior knowledge.
F.LE.5: Construct and compare linear, quadratic, and exponential models and solve problems.
Interpret the parameters in a linear or exponential function in terms of a context.*
S.ID.1: Summarize, represent, and interpret data on a single count or measurement variable.
Represent data with plots on the real number line (dot plots, histograms, and box plots).*
Modeling
Modeling
AI.12.1
AI.12.2
Compare data sets using
statistical techniques (e.g.,
measures of central tendency,
standard deviation, range, stemand-leaf plots, and box-andwhisker graphs)
Display bivariate data in a scatter
plot, describe its shape, and
determine the line of best fit
that models a trend (if a trend
exists)
S.ID.2: Summarize, represent, and interpret data on a single count or measurement variable. Use
statistics appropriate to the shape of the data distribution to compare center (median, mean) and
spread (interquartile range, standard deviation) of two or more different data sets.*
2
S.ID.3: Summarize, represent, and interpret data on a single count or measurement variable.
Interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).*
6.ID.6: Summarize, represent and interpret data on two categorical and quantitative variables.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are
related.
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the
data. Use given functions or choose a function suggested by the context. Emphasize linear,
quadratic, and exponential models.
c. Fit a linear function for a scatter plot that suggests a linear association.
2
Students should be given various
opportunities to collect, organize, and
analyze data sets to determine if the
phenomenon exhibits a linear trend.
Both the HCPS III benchmark and CC
standards are great opportunities to
strategically utilize technology.
S.ID.7: Interpret linear models. Interpret the slope (rate of change) and the intercept (constant
term) of a linear model in the context of the data.*
* Degree of Match: 1 = WEAK (major aspect of the HCPS III benchmark not addressed in CCSS); 2 = GOOD (minor aspect of the HCPS III benchmark not addressed in CCSS); 3 = EXCELLENT
page 3 of 6
Crosswalk between the Algebra I Hawaii Content and Performance Standards (HCPS) III and the Common Core State Standards (CCSS) for High School Mathematics
HSA Category
Operations on
Numbers and
Expressions
HCPS III
Code
AI.3.1
HCPS III Algebra I Benchmark
Apply arithmetic properties to
operate on and simplify
expressions that include radicals
and other real numbers
Matched Common Core CLUSTER and Standard
N.RN.1: Extend the properties of exponents to rational exponents. 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 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.
Match*
updated: 12-19-10
Comment
1
N.RN.2: Extend the properties of exponents to rational exponents. Rewrite expressions involving
radicals and rational exponents using the properties of exponents.
Instruction should be planned to
develop students’ understanding of
laws of exponents.
Operations on
Numbers and
Expressions
Operations on
Numbers and
Expressions
Operations on
Numbers and
Expressions
Operations on
Numbers and
Expressions
AI.3.2
Apply the laws of exponents to
perform operations on
expressions with integral
exponents
A.SSE.3: Write expressions in equivalent forms to solve problems. Choose and produce an
equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.*
3c. Use the properties of exponents to transform expressions for exponential functions.
1
AI.10.3
Justify the steps used in
simplifying expressions and
solving equations and
inequalities
A.REI.1: Understand solving equations as a process of reasoning and explain the reasoning.
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.
3
AI.10.6
AI.10.8
Factor first- and second-degree
binomials and trinomials in one
or two variables
Select and use a variety of
strategies (e.g., concrete objects,
pictorial representations,
algebraic manipulation) to
perform operations on
polynomials
A.SSE.3: Write expressions in equivalent forms to solve problems. Choose and produce an
equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.*
3a. Factor a quadratic expression to reveal the zeros of the function it defines.*
In general, teachers at all grade levels
need to engender the ability to READ
expressions and make sense of what
they mean, rather than solely focusing
on developing the ability to manipulate
them.
2
A.REI.4: Solve equations and inequalities in one variable. Solve quadratic equations in one
variable.
A.APR.1: Perform arithmetic operations on polynomials. 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.SSE.3: Write expressions in equivalent forms to solve problems. Choose and produce an
equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.*
3a. Factor a quadratic expression to reveal the zeros of the function it defines.*
2
* Degree of Match: 1 = WEAK (major aspect of the HCPS III benchmark not addressed in CCSS); 2 = GOOD (minor aspect of the HCPS III benchmark not addressed in CCSS); 3 = EXCELLENT
page 4 of 6
Crosswalk between the Algebra I Hawaii Content and Performance Standards (HCPS) III and the Common Core State Standards (CCSS) for High School Mathematics
HSA Category
HCPS III
Code
HCPS III Algebra I Benchmark
Matched Common Core CLUSTER and Standard
Match*
A.REI.4: Solve equations and inequalities in one variable. Solve quadratic equations in one
variable.
Solving
Equations,
Inequalities, and
Systems
Determine the zeros of a linear
or quadratic function
algebraically and graphically
F.IF.7: Analyze functions using different representations. Graph functions expressed symbolically
and show key features of the graph, by hand in simple cases and using technology for more
complicated cases.*
Comment
Both the HCPS III benchmark and CC
standards are great opportunities to
strategically utilize technology to help
students make sense of the connection
between determining the zeros of a
function algebraically and graphically.
A.SSE.3: Write expressions in equivalent forms to solve problems. Choose and produce an
equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.*
3a. Factor a quadratic expression to reveal the zeros of the function it defines.*
AI.9.3
updated: 12-19-10
2
A.APR.3: Understand the relationship between zeros and factors of polynomials. 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.
A.REI.3: Solve equations and inequalities in one variable. Solve linear equations and inequalities in
one variable, including equations with coefficients represented by letters.
Both the HCPS III benchmark and CC
standards emphasize that students
must understand what a solution
means for a particular equation or
inequality.
A.REI.10: Represent and solve equations and inequalities graphically. 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).
Solving
Equations,
Inequalities, and
Systems
AI.10.1
Solve linear equations and
inequalities in one variable using
a variety of strategies (e.g.,
algebraically, by graphing, by
using a graphing calculator)
A.REI.11: Represent and solve equations and inequalities graphically. Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the
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.*
2
In general, teachers at all grade levels
need to engender the ability to READ
expressions and make sense of what
they mean, rather than solely focusing
on developing the ability to manipulate
them.
A.REI.12: Represent and solve equations and inequalities graphically. Graph the solutions to a
linear inequality in two variables as a half-plane (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 half-planes.
* Degree of Match: 1 = WEAK (major aspect of the HCPS III benchmark not addressed in CCSS); 2 = GOOD (minor aspect of the HCPS III benchmark not addressed in CCSS); 3 = EXCELLENT
page 5 of 6
Crosswalk between the Algebra I Hawaii Content and Performance Standards (HCPS) III and the Common Core State Standards (CCSS) for High School Mathematics
HSA Category
HCPS III
Code
HCPS III Algebra I Benchmark
Matched Common Core CLUSTER and Standard
Match*
A.REI.5: Solve systems of equations. 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.
Solving
Equations,
Inequalities, and
Systems
AI.10.5
Solve systems of two linear
equations in two variables
algebraically and graphically
Comment
Both the HCPS III benchmark and CC
standards emphasize that students
must understand what a solution to a
system of equations means for a
particular system.
A.REI.6: Solve systems of equations. Solve systems of linear equations exactly and approximately
(e.g., with graphs), focusing on pairs of linear equations in two variables.
A.CED.3: Create equations that describe numbers or relationship. Represent constraints by
equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as
viable or non-viable options in a modeling context. For example, represent inequalities describing
nutritional and cost constraints on combinations of different foods.*
updated: 12-19-10
2
A.REI.4: Solve equations and inequalities in one variable. Solve quadratic equations in one
variable.
Solving
Equations,
Inequalities, and
Systems
AI.10.7
Solve quadratic equations in one
variable algebraically,
graphically, or by using graphing
technology
A.REI.11: Represent and solve equations and inequalities graphically. Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the
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.*
F.IF.7: Analyze functions using different representations. Graph functions expressed symbolically
and show key features of the graph, by hand in simple cases and using technology for more
complicated cases.*
2
A.SSE.3: Write expressions in equivalent forms to solve problems. Choose and produce an
equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.*
3a. Factor a quadratic expression to reveal the zeros of the function it defines.*
* Degree of Match: 1 = WEAK (major aspect of the HCPS III benchmark not addressed in CCSS); 2 = GOOD (minor aspect of the HCPS III benchmark not addressed in CCSS); 3 = EXCELLENT
page 6 of 6