A - Seeing Structure in Expressions

This text resource illustrates the Standards Map for the Algebra Overview Seeing Structure in Expressions domain in the Common Core State Standards.

Standards

Common Core Mathematics: Algebra

Algebra - see introductory remarks
Common Core Mathematics: Algebra > SSE

Seeing Structure in Expressions (SSE)
Common Core Mathematics: Algebra > SSE > C.1

Interpret the structure of expressions.

Common Core Mathematics: Algebra > SSE > C.1 > S.1

Interpret expressions that represent a quantity in terms of its context.

Interpret parts of an expression, such as terms, factors, and coefficients.
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret

Content	Skills	Learning Targets	Big Ideas	Essential Questions
Expressions Interpretation Context Terms Factors Coefficients Parts as a single entity	2 - Interpret (expressions in terms of context) 2 - Interpret (parts of expression [a]) 2 - Interpret (expressions by viewing parts as a single entity [b])	2 - I can interpret expressions in terms of context. 2 - I can interpret parts of an expression, such as terms, factors, and coefficients [a]. 2 - I can interpret complicated expressions by viewing one or more parts as a single entity [b].	A. Expressions represent quantities in problem solving. B. Viewing parts of an expression as a single entity can simplify the problem.	A.1 How can I use expressions when I am solving problems? B.1 Why should I try to view parts of an expression as a single entity?

Common Core Mathematics: Algebra > SSE > C.1 > S.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 a difference of squares that can be factored as (x² – y²)(x²+ y²).

Content	Skills	Learning Targets	Big Ideas	Essential Questions
Expressions Revision	3 - Use (expression's structure to rewrite it)	3 - I can use an expression's structure to rewrite it.	A. The ability to rewrite an expression is useful in problem solving,	A.1 Why would I want to rewrite an expression?

Common Core Mathematics: Algebra > SSE > C.2

Write expressions in equivalent forms to solve problems.

Common Core Mathematics: Algebra > SSE > C.2 > S.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Factor a quadratic expression to reveal the zeros of the function it defines.
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^tcan be rewritten as (1.15^1/12)^12t ≈ 1.012^12tto reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Content	Skills	Learning Targets	Big Ideas	Essential Questions
Expressions Equivalent form Properties Quadratic expressions Factor Zeros Complete the square Maxima Minima Exponential functions Properties of exponents Transformation of expressions	3 - Choose (equivalent form of an expression) 3 - Produce (equivalent form of an expression) 1 - Reveal (properties of a quantity represented by expression) 2 - Explain (properties of quantity represented by expression.) 3 - Factor (quadratic expression [a]) 3 - Reveal (zeros of the function [a]) 3 - Complete (the square in quadratic expression [b]) 3 - Reveal (maximum or minimum value of function [b]) 2 - Use (properties of exponents [c]) 3 - Transform (expressions for exponential functions [c])	3 - I can choose equivalent forms of an expression. 3 - I can produce equivalent form of an expression. 1 - I can reveal properties of a quantity represented by expression. 2 - I can explain properties of a quantity represented by expression. 3 - I can factor a quadratic expression [a]. 3 - I can reveal the zeros of the function [a]. 3 - I can complete the square in a quadratic expression [b]. 3 - I can reveal the maximum or minimum value of a function [b]. 2 - I can use properties of exponents [c]. 3 - I can transform expressions for exponential functions [c].	A. One can gain better understanding of the properties of an quadratic expression by substitution of equivalent expressions. B. The zeros of a quadratic expression can be revealed algebraically or graphically. C. Completing the square is one method of identifying maximum or minimum value of a quadratic function. D. Properties of exponents are useful in transforming expressions for exponential functions.	A.1 How do equivalent expressions help me understand the properties of the quantity represented? A. 2 What is a quadratic expression? A. 3 How can equivalent expressions be produced? A. 4 How can an equivalent expression reveal the properties of a quadratic expression? B. 1 How do I factor a quadratic expression? B. 2 What are the zeros of a quadratic function? B. 3 How can factoring a quadratic expression reveal its zeros? B. 4 What is the relationship between finding zeros graphically and finding zeros algebraically? C. 1 What does it mean to complete the square in a quadratic expression? C. 2 How can completing the square reveal the maximum or minumun value of a quadratic function? D. 1 How can properties of exponents be used to transform an exponential function in a real-word application?

Common Core Mathematics: Algebra > SSE > C.2 > S.4

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

For example, calculate mortgage payments.

Content	Skills	Learning Targets	Big Ideas	Essential Questions
Formula Sum of geometric series Problem solving	6 - Derive (formula for sum of finite geometric series) 3 - Use (formula to solve problems)	6 - I can derive the formula for the sum of finite geometric series. 3 - I can use the formula to solve problems.	A. Mathematical formulas can be used to solve real world problems.	A.1 How can I use formulas? A.2 Where do mathematical formulas come from?

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