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AnnotatedDCA-+CCLS+Alg+1-+RELATIONSHIPS+BETWEEN+QUANTITIES+AND+REASONING+WITH+EQUATIONS

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AnnotatedDCA-+CCLS+Alg+1-+RELATIONSHIPS+BETWEEN+QUANTITIES+AND+REASONING+WITH+EQUATIONS Powered By Docstoc
					                           Common Core Learning Standards for Mathematics
                                         High School Algebra 1
                     Relationships Between Quantities and Reasoning with Equations
     Common Core Learning
                                                        Concepts                             Embedded Skills                                  Vocabulary
         Standards
Reason quantitatively and use units to solve              Units of          N.Q.1 create and translate units consistently with data          Accuracy
problems.                                               measurement         and graphs                                                       Measurement
Working with quantities and the                           in data                                                                            Quantities
relationships between them provides                                         Create a reasonable and appropriate scale for graphs             Limitations
                                                                            and data displays (charts)                                       Units
grounding for work with expressions,                       Units of
                                                                                                                                             Formulas
equations, and functions.                                 measure in
                                                                                                                                             Scale
                                                           solving                                                                           Origin
                                                          problems                                                                           Data displays
                                                                                                                                             Graphs
                                                                                                                                             Solution
                                                                                                                                             Modeling
                                                                                                                                             Conversions
                                                                                                                                             Table
                                                                                                                                             Chart

                                                         Appropriate
N.Q.1 Use units as a way to understand problems                             N.Q.2 create appropriate units for multi-step problems
                                                          scales and
and to guide the solution of multi-step problems;
choose and interpret units consistently in
                                                           units for        Create appropriate units to write an equation for a real
formulas; choose and interpret the scale and the         descriptive        world situation
origin in graphs and data displays.                       modeling




   Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
N.Q.2 Define appropriate quantities for the                                  N.Q.3 identify variable quantities, choose a level of
purpose of descriptive modeling.                          Limiting data      accuracy based on the problem situation
N.Q.3 Choose a level of accuracy appropriate to                for
limitations on measurement when reporting                 measurement
quantities.


                                                                 SAMPLE TASKS
   I.)          a.) You are purchasing jeans and T-shirts. Jeans cost $35 and T-shirts cost $15. You only have $115 to spend and plan on purchasing a total
                of 5 items. Graph the system                      and            on the grid below.




          b.)   What variable represents the number of jeans purchased?
          c.)   What variable represents the number of T-shirts purchased?
          d.)   How many pairs of jeans and how many T-shirts can you buy?
          e.)   Explain why a point in the fourth quadrant does not satisfy the system.

   II.)

   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
                                                         Concepts                             Embedded Skills                                 Vocabulary
              Standards
Interpret the structure of expressions.                 Identify terms       A.SSE.1 Identify parts of an expression, including its              Terms
Limit to linear expressions and to exponential          and                  terms, factors and coefficients.                                    Expression
expressions with integer exponents.                     coefficients in                                                                          Monomial
                                                        an algebraic         Identify the factors within a term                                  Binomial
                                                                                                                                                 Trinomial
                                                        expression
A.SSE.1 Interpret expressions that represent a                               Identify the difference between monomials, binomials,               Polynomial
quantity in terms of its                                                     trinomials, and polynomials                                         Factor
                                                        Identify parts                                                                           Coefficient
context.★
a. Interpret parts of an expression, such as terms,     of multi-term        Translate a complex expression by dissecting it into its
factors, and coefficients.                              expressions          individual parts
b. Interpret complicated expressions by viewing         and formulas
one or more of their parts as a single entity. For      by breaking
example, interpret             as the product of P      them up into
and a factor not depending on P.                        their parts

                                                                SAMPLE TASKS
    I.)      Match the following with their classification

            _____ 1.)                              A.) Monomial
            _____2.)                               B.) Binomial
            _____ 3.)                              C.) Trinomial
            _____ 4.)                              D.) Polynomial


   Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
   II.)    a.) Simplify the following:
           b.) When in standard form what is the leading coefficient?

   III.)   In the expression
           a.) List the term(s)
           b.) List the coefficient(s)
           c.) List the constant(s)




Common Core Learning Standards                                  Concepts                          Embedded Skills                               Vocabulary
Create equations that describe numbers or                         Creating      A.CED.1 create and solve a linear equation or                       linear
relationships.                                                   equations,     inequality from a word problem                                      exponential
Limit A.CED.1 and A.CED.2 to linear and                       inequalities, and
exponential equations, and, in the case of                      exponential                                                                         equation
                                                                                Create and solve an exponential equation from a                     inequality
exponential equations, limit to situations requiring             equations
                                                                                    word problem
evaluation of exponential functions at integer
                                                                                                                                                    systems of
inputs.                                                       Solve equations,                                                                      equations
Limit A.CED.3 to linear equations and inequalities.             inequalities,
Limit A.CED.4 to formulas which are linear in the             and exponential                                                                       systems of
variable of interest.                                            equations                                                                          inequalities

                                                                                                                                                    solution set of
   Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
                                                                                                                                                    equations and
                                                                                                                                                    inequalities




                                                                 Graphing           A.CED.2 Write linear equations using two variables          Variable
                                                               equations and        (y= form)
                                                               inequalities in                                                                  Coordinate plane
                                                               two variables        Identify parts of the coordinate plane (axes and
                                                                                    quadrants)                                                  Axes

                                                                                    Graph linear with correct labels and scales from a          Quadrants
                                                                                    word problem
                                                                                                                                                Labels
                                                                                    Write exponential equation using two variables
                                                                                    (y= form)                                                   Scales

                                                                                    Graph an exponential equation from a table of               Standard form
                                                                                    values with an appropriate scale from a word
                                                                                    problem                                                     Appropriate

                                                                                                                                                Table of values

                                                                                                                                                Growth and decay
                                                                 Finding the
                                                               solution to the
A.CED.1 Create equations and inequalities in one                                    A.CED.3 Graph systems of equations and or                   Domain
variable and use them to solve problems. Include                  system of         inequalities with correct labels and scales from a
equations arising from linear and quadratic functions,         equations and        word problem                                                Constraints
and simple rational and exponential functions.                  inequalities
A.CED.2 Create equations in two or more variables to                                explain whether solutions to a given problem are            Solution set
represent relationships between quantities; graph             Constraints on        valid
equations on coordinate axes with labels and scales.          equations and
A.CED.3 Represent constraints by equations or                 inequalities          Explain what the solution to a problem represents
inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or non-                             Solve inequalities and identify the correct domain
   Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
viable options in a modeling context. For example,                                  for the solution within the constraints of the word
represent inequalities describing nutritional and cost                              problem
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.                                                             A.CED.4 rewrite equations in terms of a different           Literal equations
                                                               Solving literal
                                                                                    variable
                                                                equations
                                                                                    Rewrite equations in terms of a different variable
                                                                                    with squared variables




                                                                 SAMPLE TASKS
   I.)     a.) Sue’s total cell phone bill was $56.60. If her plan includes $50 for 1000 minutes a month plus $0.30 for every minute over 1000, how many
           extra minutes did Sue use this month? Write and solve a linear equation to prove your answer. Only an algebraic solution will be accepted.

           b.) Explain why 18 minutes is not a solution to the equation.


   II.)    The volume of a rectangular solid is K cm3, the height is represented by M cm, and the length is represented by N cm. Solve for the width in
           terms of K, M, and N.




   Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
III
a.) A new museum had 7500 visitors this year. The museum expects the number of visitors to grow by 5% each year. The function
                              models the predicted number of visitors each year after x years. Graph the function for the domain                        .




           b.) Predict the number of visitors in year 7.

           c.) How many years would it take for the museum to reach 20,000 visitors? Explain how you arrived at your answer.


   Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
III.)   Write a system of linear inequalities with the given characteristics.
        a.) All solutions are in Quadrant III.
        b.) Graph to prove your work




Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
IV.)    Graph the system of linear inequalities:
        a.) Describe the shape of the solution region
        b.) Find the vertices of the solution region
        c.) Find the area of the solution region




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
                                                         Concepts                             Embedded Skills                                 Vocabulary
         Standards
Understand solving equations as a process of                                 A.REI.1                                                             Properties
reasoning and explain the reasoning.                     Explain steps       Assuming an equation has a solution, create a convincing            Method
Students should focus on and master A.REI.1              to solving an       argument that justifies each step in the solution process.          Reasonable
for linear equations and be able to extend                 equation          Justifications may include the associative, commutative,            Solution
                                                                             and division properties, combining like terms,                      Justify
and apply their reasoning to other types of
                                                                             multiplication by 1
equations in future courses. Students will
solve exponential equations with logarithms
in Algebra II.




   Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
A.REI.1 Explain each step in solving a simple                                Explain the steps in solving an equation from another
equation as following from the equality of                                   students work
numbers asserted at the previous step, starting
from the assumption that the original equation has                           Describe the reasonableness of a solution
a solution. Construct a viable argument to justify a
solution method.                                                             Describe the method used to solve an equation




                                                                 SAMPLE TASKS
    I.)     Use properties of equality and other properties to justify the solution below

                 Equation                        Property Reasons

                                                ____________________
                                                ____________________
                    -12 -12
                  4x =  32                      ____________________
                  4     4
                  x = 8                         ____________________


    II.)    Two students solved the same inequality for x. Explain which student solved the inequality correctly and describe where the error occurred.

            Student A                                Student B




   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
                                                         Concepts                             Embedded Skills                                 Vocabulary
              Standards
Solve equations and inequalities in one                   Solve linear       A.REI.3                                                             Construct
variable. Extend earlier work with solving                 equations         Construct a solution to a linear equation in one variable           Coefficients
linear equations to solving linear inequalities                                                                                                  Variables
in one variable and to solving literal                    Solve simple       Solve simple exponential equations that use the laws of             Exponential
                                                                             exponents                                                           Literal
equations that are linear in the variable being           exponential
                                                                                                                                                 Solution set
solved for. Include simple exponential                     equations
                                                                             Construct a solution to an equation with variable
equations that rely only on application of the                               coefficients
laws of exponents, such as             or                 Solve literal
         .                                                 equations
A.REI.3 Solve linear equations and inequalities in
one variable, including equations with coefficients       Solve linear
represented by letters.                                   inequalities




                                                                SAMPLE TASKS
    I.)      Solve for x:

    II.)     Solve for x:

    III.)    Solve for p in the equation

    IV.)     Solve for x:                          and explain why your solution is unique.

    V.)      Solve for x:                               and explain why your solution is unique.


   Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.
VI.)    Is the point (5, -2) a solution to              , justify your answer.




Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.

				
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