Express Yourself!

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

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.

Phase

During/Explore/Explain
Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.4

Interpret linear, quadratic, and exponential expressions in terms of a context by viewing one or more of their parts as a single entity.

UP:MA19.A1.4

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.
Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.5

Use the structure of an expression to identify ways to rewrite it.

UP:MA19.A1.5

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.

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.

Activity Details

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.

Variation Tips

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.

Background / 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.

https://docs.google.com/document/d/1VLtcKMR7cbDPYgnO0o57H0m7QxXaKj2xhDIRd4FsxUA…

Approved Date

Owner (Author)

pamelawest
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