Download sample tasks - Deep Curriculum Alignment Project for Mathematics

Common Core Learning Standards for Mathematics
High School Algebra 1
Relationships Between Quantities and Reasoning with Equations
Common Core Learning
Standards
Concepts
Embedded Skills
Reason quantitatively and use units to solve
problems.
Working with quantities and the
relationships between them provides
grounding for work with expressions,
equations, and functions.
N.Q.1
N.Q.1 Use units as a way to understand problems
and to guide the solution of multi-step problems;
choose and interpret units consistently in
formulas; choose and interpret the scale and the
origin in graphs and data displays.
N.Q.2 Define appropriate quantities for the
purpose of descriptive modeling.
N.Q.3 Choose a level of accuracy appropriate to
limitations on measurement when reporting
quantities.
N.Q.2
Vocabulary
N.Q.3
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Interpret the structure of expressions.
Limit to linear expressions and to exponential
expressions with integer exponents.
A.SSE.1 Interpret expressions that represent a
quantity in terms of its
context.★
a. Interpret parts of an expression, such as terms,
factors, and coefficients.
b. Interpret complicated expressions by viewing
one or more of their parts as a single entity. For
example, interpret P(1+r)n as the product of P and
a factor not depending on P.
Concepts
Identify terms
and
coefficients in
an algebraic
expression
Identify parts
of multi term
expressions
and formulas
by breaking
them up into
their parts
Embedded Skills
A.SSE.1 Identify parts of an expression, including its
terms, factors and coefficients.
Identify the factors within a term
Identify the difference between monomials, binomials,
trinomials, and polynomials
Vocabulary
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Terms
Expression
Monomial
Binomial
Trinomial
Polynomial
Factor
Coefficient
Translate a complex expression by dissecting it into its
individual parts
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning Standards
Concepts
Embedded Skills
Create equations that describe numbers or
relationships.
Limit A.CED.1 and A.CED.2 to linear and
exponential equations, and, in the case of
exponential equations, limit to situations requiring
evaluation of exponential functions at integer
inputs.
Limit A.CED.3 to linear equations and inequalities.
Limit A.CED.4 to formulas which are linear in the
variable of interest.
Creating
equations,
inequalities,
quadratic, and
exponential
equations
A.CED.1 create a linear equation or inequality from
a word problem
Solve equations,
inequalities,
quadratics, and
exponential
equations
create equations arising from functions containing
square and cube roots with integer inputs and use
them to solve problems
Vocabulary
create a quadratic equation from a word problem
create an exponential equation from a word
problem
solve a linear equation or inequality from a word
problem
solve a quadratic equation from a word problem
solve an exponential equation from a word
problem
Graphing
equations and
inequalities in
two variables
Finding the
solution to the
system of
equations and
inequalities
A.CED.2 Write linear equations using two variables
Rewrite an equation in terms of one variable (y =
form)
Identify parts of the coordinate plane (axes and
quadrants)
Graph systems of equations with correct labels and
scales from a word problem
Write quadratic equations using two variables
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
Rewrite a quadratic equation in terms of one
variable (y = form)
Graph quadratic equations from a table of values
with an appropriate scale and labels from a word
problem
Write exponential equation using two variables
Rewrite exponential equations in terms of one
variable (y= form)
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.2 Create equations in two or more variables to
represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
A.CED.3 Represent constraints by equations or
inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example,
represent inequalities describing nutritional and cost
constraints on combinations of different foods.
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.
Constraints on
equations and
inequalities
Solving literal
equations
Graph an exponential equation from a table of
values with an appropriate scale from a work
problem
A.CED.3 explain whether solutions to a given
problem are valid
Explain what the solution to a problem represents
Solve inequalities and identify the correct domain
for the solution within the constraints of the word
problem
A.CED.4 rewrite equations in terms of a different
variable
Rewrite equations in terms of a different variable
with squared variables
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
SAMPLE TASKS continued:
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand solving equations as a process of
reasoning and explain the reasoning.
Students should focus on and master A.REI.1
for linear equations and be able to extend
and apply their reasoning to other types of
equations in future courses. Students will
solve exponential equations with logarithms
in Algebra II.
Concepts
Embedded Skills
A.REI.1
Vocabulary

A.REI.1 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.
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Solve equations and inequalities in one
variable. Extend earlier work with solving
linear equations to solving linear inequalities
in one variable and to solving literal
equations that are linear in the variable being
solved for. Include simple exponential
equations that rely only on application of the
laws of exponents, such as 5x=125 or
2x=1/16.
Concepts
Embedded Skills
A.REI.3
Vocabulary

A.REI.3 Solve linear equations and inequalities in
one variable, including equations with coefficients
represented by letters.
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.