ALEX Learning Activity

  

Express Yourself!

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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  This learning activity provided by:  
Author: Pamela West
System:Montgomery County
School:Montgomery County Board Of Education
  General Activity Information  
Activity ID: 2375
Title:
Express Yourself!
Digital Tool/Resource:
Interpreting Expressions Worksheet
Web Address – URL:
Overview:

This learning activity will be used during a lesson on Algebraic Expressions. Students will work in pairs to translate between words, tables, symbols, and area representation of algebraic expressions.

This learning activity results from the ALEX Resource Development Summit.
  Associated Standards and Objectives  
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.

Learning Objectives:

Students will be able to interpret expressions and rewrite verbal expressions for algebraic expressions.

Students will be able to interpret expressions and rewrite algebraic expressions for verbal expressions.

Students will be able to recognize equivalent expressions.
  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

This activity will be used during a lesson on Algebraic Expressions. Students will explore and work in pairs to translate between words, symbols, table of values, and area representations of expressions. Students will find a different representation of expressions and will be able to explain their reasoning.

During/Explore/Explain

(I DO)

The teacher will demonstrate how to write verbal and algebraic expressions by providing examples and explaining verbally and visually in detail. Students will observe, take notes, and ask questions.

1. Write a verbal expression for each phrase:

a)  n + 8      (the sum of n and 8)    

b) b - 6         (six less than b)

c) 4a + 7       (7 more than the product 4 times a)

The teacher will have the students turn and talk about other phrases or words that can be used to represent the verbal expressions. 

Ex: the word sum --- can be replaced with add, plus, more than, increased by .......

2. Write an algebraic expression for each verbal expression.

a) a number n more than 8                    (8 + n or n + 8)

b)  15 less than the product of 8 and g    (8g - 15)

c) one-fourth of the area a                       (1/4 a)

 (We Do)

We will collaborate and discuss various types of expressions and review any misconceptions and allow students to explain their reasoning.

The teacher will issue whiteboards, pens, and erasers to the class. 

The teacher will ask students to demonstrate an algebraic expression or verbal expression on their whiteboards. This will be used as a formative assessment to see if students understand the lesson.

Show an algebraic expression that means:

1) Add 3 to n and then multiply your answer by 3.  4(3 + n)

2) Multiply n by 5 and then square your answer.  (5n)2

Write a verbal expression for each algebraic expression:

1)  3n2               (Multiply n by n and then multiply your  

                           answer by 3)

2) 5n + 2             (Multiply n by 5 and then add 2)

Important: The teacher will need to verbal and discuss any problems and have students to explain their thinking.

(You'll Do)

The teacher will hand out the worksheet "Interpreting Expressions".

The teacher will allow the students to work in pairs as they explore and collaborate as they translate expressions in various forms.

The teacher will monitor and facilitate as needed and ask probing questions as students work.

Upon completion, students will do a reflection journal on the common mistakes they made and what strategies they used to help eliminate or prevent from making the same mistake again.

The teacher will allow students to share out in whole groups and a comparison chart will be plotted and discussed to comparison preventive techniques to help the students in the future.
Assessment Strategies:

The teacher will monitor students working in pairs and provide timely feedback to help eliminate any misconceptions.

Upon completion, the teacher will take up the completed worksheet and ensure at least 80% mastery of the skill.

The teacher will review the reflective journal response as a form of formative assessment.
Advanced Preparation:

The teacher will need copies of the worksheet "Interpreting Expressions" in advance. 

The teacher will provide each student with a copy of the worksheet, a whiteboard, a dry erase pen, and an eraser.

The teacher will need a large chart paper and markers.

The teacher will need to pair students in advance or allow students to pick their partners.
Variation Tips (optional):

You may have students to continue to work with a different partner. Allow students to explore and create various types of expressions through various forms of representations such as tables, symbols, verbal, algebraically.  

Have Student A create their own algebraic expression and ask Student B to create an equivalent expression using a different representation for the expression. Students continue to take turns until the time is called.
Notes or Recommendations (optional):
 
  Keywords and Search Tags  
Keywords and Search Tags: Algebraic Expressions, Equivalent Expressions, Verbal Expressions