NLHS Learning Targets Master File Algebra I(Last Updated: 05/15/12)

NLHS Learning Targets Master File Algebra I(Last Updated: 05/15/12)

NLHS—Learning Targets Master File—Algebra I(Last Updated: 05/15/12)

N.RN.1 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 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
Knowledge Learning Target(s) / DART Statements
  1. Define radical notation as a convention used to represent rational exponents.
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  1. I can define radical notation as a convention used to represent rational exponents.

Reasoning Learning Target(s) / DART Statements
  1. Explain the properties of operations of rational exponents as an extension of the properties of integer exponents.
  1. Explain how radical notation, rational exponents, and properties of integer exponents relate to one another.
Note from Appendix A: In implementing the standards in curriculum, these standards should occur before discussing exponential functions with continuous domains. /
  1. I will explain the properties of operations of rational exponents as an extension of the properties of integer exponents.
  1. I will explain how radical notation, rational exponents, and properties of integer exponents relate to one another.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Knowledge Learning Target(s) / DART Statements
  1. Using the properties of exponents, rewrite a radical expression as an expression with a rational exponent.
  1. Using the properties of exponents, rewrite an expression with a rational exponent as a radical expression.
Notes from Appendix A: In implementing the standards incurriculum, these standards shouldoccur before discussing exponentialfunctions with continuous domains. /
  1. Using the properties of exponents, I can rewrite a radical expression as an expression with a rational exponent.
  1. Using the properties of exponents, I can rewrite an expression with a rational exponent as a radical expression.

Reasoning Learning Target(s) / DART Statements
Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
N.RN.3 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 rational number and an irrational number is irrational.
Knowledge Learning Target(s) / DART Statements
  1. Find the sums and products of rational and irrational numbers.
  1. Recognize that the sum of a rational number and an irrational number is irrational.
  1. Recognize that the product of a nonzero rational number and an irrational number is irrational.
Note from Appendix A: Connect N.RN.3 to physical situations, e.g., finding the perimeter of a square of area 2. /
  1. I can find the sums and products of rational and irrational numbers.
  1. I can recognize that the sum of a rational number and an irrational number is irrational.
  1. I can recognize that the product of a nonzero rational number and an irrational number is irrational.

Reasoning Learning Target(s) / DART Statements
  1. Explain why rational numbers are closed under addition or multiplication.
Note from Appendix A: Connect N.RN.3 to physical situations, e.g., finding the perimeter of a square of area 2. /
  1. I can explain why rational numbers are closed under addition or multiplication.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
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.
Knowledge Learning Target(s) / DART Statements
  1. Calculate unit conversions.
  1. Recognize units given or needed to solve problem.
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  1. I can calculate unit conversions.
  1. I can recognize units needed to solve a problem.

Reasoning Learning Target(s) / DART Statements
  1. Use given units and the context of a problem as a way to determine if the solution to a multi-step problem is reasonable (e.g. length problems dictate different units than problems dealing with a measure such as slope)
  1. Choose appropriate units to represent a problem when using formulas or graphing.
  1. Interpret units or scales used in formulas or represented in graphs.
  1. Use units as a way to understand problems and to guide the solution of multi-step problems.
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  1. I can recognize units needed to solve a problem.
  1. A. I can determine if the solution to a multistep problem is reasonable using correct units in the context of the problem. This means that I can decide if my answer actually matches the problem.
B. I can choose correct units to represent a problem involving a formula.
  1. A. I can interpret units or scales in a formula.
B. I can interpret units or scales on a graph.
  1. I can use units to understand a real-world problem.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
Knowledge Learning Target(s) / DART Statements
  1. Define descriptive modeling.
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  1. I can define descriptive modeling.

Reasoning Learning Target(s) / DART Statements
  1. Determine appropriate quantities for the purpose of descriptive modeling.
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  1. I can determine appropriate units for descriptive modeling.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
N. Q. 3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Knowledge Learning Target(s) / DART Statements
  1. Identify appropriate units of measurement to report quantities.
  1. Determine the limitations of different measurement tools.
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  1. I can identify correct units of measurement to report data.
  1. I can determine the limits of measurement tools; such as rulers, protractors, compasses, and calculators.

Reasoning Learning Target(s) / DART Statements
  1. Choose and justify a level of accuracy and/or precision appropriate to limitations on measurement when reporting quantities.
  1. Identify important quantities in a problem or real-world context.
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  1. I can justify the level of accuracy and/or precision that is appropriate for the limitation of my measuring tool.
  1. I can identify important quantities in a real world problem.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
A.SSE.1 Interpret expressions that represent a quantity in terms of its context.*(Modeling standard)
a. Interpret parts of an expression, such as terms, factors, and coefficients.
Knowledge Learning Target(s) / DART Statements
  1. For expressions that represent a contextual quantity, define and recognize parts of an expression, such as terms, factors, and coefficients.
Notes from Appendix A: limit to linear expressions and to exponential expressions with integer exponents. /
  1. I can recognize and define parts of an expression, such as terms, factors, and coefficients.

Reasoning Learning Target(s) / DART Statements
  1. For expressions that represent a contextual quantity, interpret parts of an expression, such as terms, factors, and coefficients in terms of the context.
Notes from Appendix A: limit to linear expressions and to exponential expressions with integer exponents. /
  1. I can interpret parts of an expression. This means that I can identify terms, factors, and coefficients in the context of the problem.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
A.SSE.1 Interpret expressions that represent a quantity in terms of its context.* (Modeling standard)
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret as the product of P and a factor not depending on P.
Knowledge Learning Target(s) / DART Statements
The underpinning knowledge for this standard is addressed in
A.SSE.1a: For expressions that represent a contextual quantity, define and recognize parts of an expression, such as terms, factors, and coefficients.
Notes from Appendix A: Limit to linear expressions with integer exponents
Reasoning Learning Target(s) / DART Statements
  1. For expressions that represent a contextual quantity, interpret complicated expressions, in terms of the context, by viewing one or more of their parts as a single entity.
Notes from Appendix A: Limit to linear expressions with integer exponents /
  1. I can interpret complicated expressions by breaking them down into parts.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as adifference of squares that can be factored as (x2 – y2)(x2 + y2).
Knowledge Learning Target(s) / DART Statements

1.Identify ways to rewrite expressions, such as difference of squares, factoring out a common monomial, regrouping, etc.

  1. Identify various structures of expressions (e.g. an exponential monomial multiplied by a scalar of the same base, difference of squares in terms other than just x)
Notes from Appendix A: Focus on quadratics and exponential expressions /

1.I can identify ways to rewrite expressions, such as difference of squares, factoring out a common monomial, regrouping, etc.

  1. I can identify various structures of expressions.

Reasoning Learning Target(s) / DART Statements
  1. Use the structure of an expression to identify ways to rewrite it.
  1. Classify expressions by structure and develop strategies to assist in classification.
Notes from Appendix A: Focus on quadratics and exponential expressions /
  1. I can use the structure of an expression to identify ways to rewrite it.
  1. I can classify expressions by structure and develop strategies to assist in classification (e.g. use of conjugates in rewriting rational expressions, usefulness of Pythagorean triples, etc.).

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
A.SSE.3a Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*(Modeling standard)
a. Factor a quadratic expression to reveal the zeros of the function it defines.
Knowledge Learning Target(s) / DART Statements
  1. Factor a quadratic expression to produce an equivalent form of the original expression
  2. Explain the connection between the factored form of a quadratic expression and the zeros of the function it defines.
  3. Explain the properties of the quantity represented by the quadratic expression.
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  1. I can factor a quadratic expression to produce an equivalent form of the original expression.
  2. I can explain the connection between the factored form of a quadratic expression and the zeros of the function it defines.
  3. I can explain the properties of the quantity represented by the quadratic expression.

Reasoning Learning Target(s) / DART Statements
  1. Choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the original expression.
Notes from Appendix A: It is important to balance conceptual understanding and procedural fluency in work with equivalent expressions. For example, development of skill in factoring and completing the square goes hand-in-hand with understanding what different forms of a quadratic expression reveal. /
  1. I can choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the original expression.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
A.SSE.3b Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* (Modeling standard)
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Knowledge Learning Target(s) / DART Statements
  1. Complete the square on a quadratic expression to produce an equivalent form of an expression.
  2. Explain the connection between the completed square form of a quadratic expression and the maximum or minimum value of the function it defines.
  3. Explain the properties of the quantity represented by the expression.
/
  1. I can complete the square on a quadratic expression to produce an equivalent form of an expression.
  2. I can explain the connection between the completed square form of a quadratic expression and the maximum or minimum value of the function it defines.
  3. I can explain the properties of the quantity represented by the expression.

Reasoning Learning Target(s) / DART Statements
  1. Choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the original expression.
Notes from Appendix A: It is important to balance conceptual understanding and procedural fluency in work with equivalent expressions. For example, development of skill in factoring and completing the square goes hand-in-hand with understanding what different forms of a quadratic expression reveal. /
  1. I can choose and produce an equivalent form of a quadratic expression to reveal and explain properties of the quantity represented by the original expression.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
A.SSE.3c Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* (Modeling standard)
c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewrittenas (1.151/12)12t≈ 1.01212t to reveal the approximate equivalentmonthly interest rate if the annual rate is 15%.
Knowledge Learning Target(s) / DART Statements

1.Use the properties of exponents to transform simple expressions for exponential functions.

  1. Use the properties of exponents to transform expressions for exponential functions.
/

1.I can use the properties of exponents to transform simple expressions for exponential functions.

  1. I can use the properties of exponents to transform expressions for exponential functions.

Reasoning Learning Target(s) / DART Statements
  1. Choose and produce an equivalent form of an exponential expression to reveal and explain properties of the quantity represented by the original expression.
  1. Explain the properties of the quantity or quantities represented by the transformed exponentialexpression.
/
  1. I can choose and produce an equivalent form of an exponential expression to reveal and explain properties of the quantity represented by the original expression.
  1. I can explain the properties of the quantity or quantities represented by the transformed exponentialexpression.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
A.APR.1 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.
Knowledge Learning Target(s) / DART Statements
  1. Identify that the sum, difference, or product of two polynomials will always be a polynomial, which means that polynomials are closed under the operations of addition, subtraction, and multiplication.
  2. Define “closure”.
  3. Apply arithmetic operations of addition, subtraction, and multiplication to polynomials.
Note from Appendix A: Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of x. /
  1. I can identify that the sum, difference, or product of two polynomials will always be a polynomial.
  2. I can define “closure.”
  3. I can apply arithmetic operations of addition, subtraction, and multiplication to polynomials.

Reasoning Learning Target(s) / DART Statements
Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
A.CED.1Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadraticfunctions, and simple rational and exponential functions.
Knowledge Learning Target(s) / DART Statements
  1. Solve linear and exponential equations in one variable.
  2. Solve inequalities in one variable.
  3. Describe the relationships between the quantities in the problem (for example, how the quantities are changing or growing with respect to each other); express these relationships using mathematical operations to create an appropriate equation or inequality to solve.
Note from Appendix A: Limit to linear and exponential equations, and, in the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs. /
  1. I can solve linear and exponential equations in one variable.
  1. I can solve inequalities in one variable.
  2. A. I can describe the relationships between the quantities in a problem. This means that I can tell if one quantity changes as another changes.
B. I can express relationships using mathematics operations to create an appropriate equation or inequality.
Reasoning Learning Target(s) / DART Statements
  1. Create equations (linear and exponential) and inequalities in one variable and use them to solve problems.
  1. Create equations and inequalities in one variable to model real-world situations.
  2. Compare and contrast problems that can be solved by different types of equations (linear & exponential).
Note from Appendix A: In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs. /
  1. A. I can create equations or inequalities in one variable.
B. I can solve equations or inequalities that I create.
  1. I can create equations or inequalities in one variable to model real-world situations.
  2. I can compare and contrast problems that can be solved by different types of equations.

Performance Skill Learning Target(s) / DART Statements
Product Learning Target(s) / DART Statements
A.CED.2 Create equations in two or more variables to represent relationships between quantities, graph equations on a coordinate axes with labels and scales.
Knowledge Learning Target(s) / DART Statements
  1. Identify the quantities in a mathematical problem or real-world situation that should be represented by distinct variables and describe what quantities the variables represent.
  1. Graph one or more created equation on a coordinate axes with appropriate labels and scales.
Notes from Appendix A: The targets are limited to linear and exponential equations, and, in the case of exponential equations, limited to situations requiring evaluation of exponential functions at integer inputs /
  1. A. I can identify quantities in a mathematical problem or real world situation.
B. I can describe what quantities the variables represent.
  1. I can graph and label one or more created equations.

Reasoning Learning Target(s) / DART Statements
  1. Create at least two equations in two or more variables to represent relationships between quantities
  1. Justify which quantities in a mathematical problem or real-world situation are dependent and independent of one another and which operations represent those relationships.
  1. Determine appropriate units for the labels and scale of a graph depicting the relationship between equations created in two or more variables.
Notes from Appendix A: The targets are limited to linear and exponential equations, and, in the case of exponential equations, limited to situations requiring evaluation of exponential functions at integer inputs /
  1. I can create at least 2 equations with 2 or more variables to represent relationships between quantities.
  1. A. I can justify quantities in a mathematical or real world problem that are dependent or independent of each other.
B. I can decide which operations represent those relationships.
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