The One-Step Equation & Its Many Faces

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Objective

SWBAT represent a one-step equation as a function table, a graph, a pattern, and as a word problem.

Big Idea

In How Many Ways Can I See Thee... Let Me Count The Ways: Understanding that a one-step equation can be represented in multiple ways.

Curriculum Reinforcer

5 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.

Engagement

5 minutes

For our opening exercise, I will have the students create an algebra poster. They will first be put into groups of no more than 3 students so that they may collaborate on the project. The students will be given approximately 5 minutes to create a poster that contains everything that they remember about what they have learned a it pertains to algebra. Their posters should include examples and vocabulary. Each group will place their poster on a specific spot on the classroom wall.I will then give my students approximately 2 minutes to complete a gallery walk of all the posters created.

Instruction & Teacher Modeling

10 minutes

Today, we will use the opening exercise to segue into instruction which, is a review of what we have learned so far during this unit. This means that the students and I will discuss what they have presented on their posters and if anything is missing, I will fill-in the blanks.

Also, I will navigate our discussion to focus on standard EE.9 which deals with understanding the relationship between two variables (dependent and independent variables) and being able to depict that relationship using tables and graphs while also describing that relationship using an equation.

In order to focus on this particular standard, I will present my students with a word problem from which I will describe what is happening in the problem, provide the rule for the pattern presented, and then, derive a one-step algebraic equation.  After doing so, I will represent the happenings of the word problem using a table and then I will graph the relationship on a coordinate plane.

Completing the activity above, as described, will review the concept of ratio and proportions which was presented and taught during unit 2. My reason for reviewing this concept is so that I can demonstrate to my students how the concept of ratio and proportions relate to equations that have dependent and independent variables. 

During this time, I will ensure that the students will know how to do the following:

  • Relate the concepts of patterns, ratios, and proportions to the concept of one-step equations.
  • Demonstrate the relationship between patterns, ratio, and proportions and one-step equations.
  • Depict the relationship between independent and dependent variables in multiple ways:
    • Table
    • Graph
    • Pattern
    • Words
    • Equation
  • Articulate in words how everything that they have learned so far this year is related.

 

This lesson should bring in all of the elements taught from unit 1 and unit 2 into this current unit, in a way that is meaningful to the students ensuring their retention of the information.

Try It Out

10 minutes

to guide students through what they have to know by the end of this lesson, I will provide them with a situation involving a proportional relationship. Students will have to represent this situation in multiple ways. First, I will ask my students to show this situation visually and then I will ask them to show this situation mathematically. After asking them to do this, I will then have students take note as the situation is revealed in many different ways (i.e. picture, table, rule, equation, and graph).

Independent Exploration

20 minutes

To explore the concepts that were taught in today's lesson, my students will create an organizer that will contain four word problems form which they will need to describe the patter presented in the problem, provide the rule, give the algebraic equation, create a table that represents the relationship, and graph the relationship. In each of the representations of the problem, the solution to the word problem should be presented.

The assignment will be completed on 11 x 14 sheets of paper and should be organized as follows:

Word Problem

Pattern

 

 

Rule

Graph

Table

 

 

Equation

Word Problem

Pattern

 

 

Rule

Graph

Table

 

 

Equation

 

Closing Summary

20 minutes

I will have selected students to come up to the front of the classroom and present the problem that I selected them to present, under the document camera. These students are to explain what they did and why. During this time, the students' work will be analyzed and critiqued by their peers. Furthermore, they will have to answer any questions that I or their peers may have concerning their work. It is at this point that we will discuss whether or not anything should have been done differently. And, we will pull out those learning elements that we deem significant enough that we should "take" them with us and remember them for later and place them on a bulleted list. The students should be copying what is on the bulleted list which can be pulled out at a later date for discussion purposes.