ALEX Classroom Resource

  

Algebra I Module 1, Topic B: The Structure of Expressions

  Classroom Resource Information  

Title:

 Algebra I Module 1, Topic B: The Structure of Expressions

URL:

 https://www.engageny.org/resource/algebra-i-module-1-topic-b-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In middle school, students applied the properties of operations to add, subtract, factor, and expand expressions (6.EE.3, 6.EE.4, 7.EE.1, 8.EE.1). Now, in Module 1, Topic B, students use the structure of expressions to define what it means for two algebraic expressions to be equivalent. In doing so, they discern that the commutative, associative, and distributive properties help link each of the expressions in the collection together, even if the expressions look very different themselves (A-SSE.2). They learn the definition of a polynomial expression and build fluency in identifying and generating polynomial expressions as well as adding, subtracting, and multiplying polynomial expressions (A-APR.1). The Mid-Module Assessment follows Topic B.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
4. Interpret linear, quadratic, and exponential expressions in terms of a context by viewing one or more of their parts as a single entity.

Example: Interpret the accrued amount of investment P(1 + r)t , where P is the principal and r is the interest rate, as the product of P and a factor depending on time t.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Make sense of algebraic expressions by identifying structures within the expression which allow them to rewrite it in useful ways to assist in the solution of given problems.
  • Interpret the meaning of the parts of an expression. For example, see that 3 + (x-2)2 is a sum of a constant and a square, that the square contains the expression x-2, and that the value of the expression is always greater than 3.
  • Justify their selection of a form for an expression by explaining which features of the expression are revealed by the particular form and how these features aid in resolving a problem situation.
Teacher Vocabulary:
  • Linear expression
  • Quadratic expression
  • Exponential expression
  • Equivalent expressions
Knowledge:
Students know:
  • How to recognize the parts of linear, quadratic and exponential expressions and what each part represents.
  • When one form of an algebraic expression is more useful than an equivalent form of that same expression to solve a given problem.
  • That one or more parts of an expression can be viewed as a single entity.
Skills:
Students are able to:
  • Use algebraic properties to produce equivalent forms of the same expression by recognizing underlying mathematical structures.
  • Interpret expressions in terms of a context.
  • View one or more parts of an expression as a single entity and determine the impact parts of the expression have in terms of the context.
Understanding:
Students understand that:
  • Making connections among the parts of an expression reveals the roles of important mathematical features of a problem.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.4.1: Define linear, quadratic and exponential functions.
ALGI.4.2: Classify an expression as linear, quadratic or exponential from a table.
ALGI.4.3: Classify an expression as linear, quadratic or exponential from an equation.
ALGI.4.4: Classify an expression as linear, quadratic or exponential from a graph.
ALGI.4.5: Define terms, factors, and coefficients.
ALGI.4.6: Identify factors in linear, exponential and quadratic expressions.
ALGI.4.7: Identify coefficients in linear, exponential and quadratic expressions.
ALGI.4.8: Identify terms in linear, exponential and quadratic expressions.
ALGI.4.9: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient).
ALGI.4.10: Recognize one or more parts of an exponential expression as a single entity.
ALGI.4.11: Recognize one or more parts of a quadratic expression as a single entity.
ALGI.4.12: Recognize one or more parts of a linear expression as a single entity.

Prior Knowledge Skills:
  • Recognize ordered pairs.
  • Identify ordered pairs.
  • Recognize linear equations.
  • Recall how to solve problems using the distributive property.
  • Define linear functions, nonlinear functions, slope, and y-intercept.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.4 Identify an algebraic expression involving addition or subtraction to represent a real-world problem.

Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
5. Use the structure of an expression to identify ways to rewrite it.

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).
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Make sense of algebraic expressions by identifying structures within the expression which allow them to rewrite it in useful and more efficient ways.
Teacher Vocabulary:
  • Terms
  • Linear expressions
  • Equivalent expressions
  • Difference of two squares
  • Factor
  • Difference of squares
Knowledge:
Students know:
  • Algebraic properties.
  • When one form of an algebraic expression is more useful than an equivalent form of that same expression.
Skills:
Students are able to:
  • Use algebraic properties to produce equivalent forms of the same expression by recognizing underlying mathematical structures.
Understanding:
Students understand that:
  • Generating equivalent algebraic expressions facilitates the investigation of more complex algebraic expressions.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.5.1: Define equivalent expressions.
ALGI.5.2: Rewrite an exponential expression in an alternative way.
ALGI.5.3: Rewrite a quadratic expression in an alternative way.
ALGI.5.4: Rewrite a linear expression in an alternative form.
ALGI.5.5: Understand that rewriting an expression in different forms in a problem context can shed light on the problem.
ALGI.5.6: Recall properties of exponents.

Prior Knowledge Skills:
    li>Give examples of the properties of operations including distributive, commutative, and associative.
  • Recall how to find the greatest common factor.
  • Combine like terms of a given expression.
  • Recognize the property demonstrated in a given expression.
  • Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
  • Simplify an expression by dividing by the greatest common factor (Ex. 18x + 6y= 6(3x + y).
  • Define linear expression, rational, coefficient, and rational coefficient.
    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).
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.5 Solve simple algebraic equations using real-world scenarios with one variable using multiplication or division.

Tags: algebra, coefficients, expressions, factors, terms
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Author: Hannah Bradley
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