6th Grade Math : Unit #3 - Expressions : Lesson #9

Equivalent Expression With Area Models

Objective: SWBAT demonstrate equality among different mathematical expressions using area models
Standards: 6.EE.A.3 6.EE.A.4
Subject(s): Math
60 minutes
1 Curriculum Reinforcer - 10 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.

2 Engagement - 10 minutes

To engage my students in this lesson, I start off by presenting them with an area model that contains a total of 21 units made up of 12 green units and 9 yellow units. The 12 green units are oriented in three rows and 4 columns and the yellow units are in three rows and three columns. Using this area model, I have my students provide me with as many ways as they can think of to express the number 21. The trick is that their expressions must take the area model into consideration.

Examples of the types of responses that I should receive during this exercise are as follows:

  • 12 plus 9
  • 4 times three plus 3 times 3
  • 3 plus 4 then multiply by 3



An Adjustment to the Area Model
Adjustments to Practice

When executing this portion of this lesson, the students weren't providing me with very many responses when I first presented them with the two colored area model. But then, I separated the two colors and that seemed to spark new responses from my students. I was able to separate the colors due to the fact that, even though I have attached a PowerPoint for the area model for this activity to the section, in my actual classroom, I used manipulatives and presented them under a document camera. When my students did not respond with as much vigor as I would have liked, I went to the document camera and separated the colors. Being that this sparked more responses, I recommend that this little adjustment to this lesson remain permanent. You should still present the first area model but, in the event that students do not respond well, I have attached another PowerPoint to this reflection that includes the first area model as well as another slide with that same area model with the colors separated.

3 Instruction & Teacher Modeling - 10 minutes

To develop my students understanding of equivalent expressions, I will first connect their understanding of numerical expressions to area models, while demonstrating the equivalency of expressions abstractly. My students are aware that the area of a rectangle is represented by the length times the width. Using that knowledge, students will learn to demonstrate this algebraically as well, in multiple ways.

This development of understanding will occur as I am taking my students through the engagement activity, which will be a major part of my instruction. For this particular lesson, the instructional proportional and the engagement portion work together to cultivate understanding of the concept of equivalent expressions. It is during this time that my students will be providing as many different numerical representations of the area model presented during the engagement and while doing that, will come to the conclusion that all the different representations are equivalent to each other, as they all represent the same thing.

After completing the engagement, I will then connect what we did during the engagement to the standard that we are covering in this lesson.

4 Try It Out - 5 minutes

During today's "Try It Out", I will display two area models. One will feature whole numbers, while the other will feature some variables. Using these models and what we already know about area of rectangles, we will explore the concept of equivalent expressions by determining which expressions represent each of the models presented. Any expressions that represent the same area model are equivalent to each other.


5 Independent Exploration - 20 minutes

During today's Independent Exploration, I will display three area models. One will feature whole numbers, while the other two will feature some variables. Using these models and what we already know about area of rectangles the students will explore expressions and equivalency using the same methods uncovered during the engagement of this lesson.

Specifically, this assignment requires the students to determine two expressions that represent the first area model, and they are to do the same with the second area model presented. Then, they will have to write an expression to represent the perimeter as well as an expression to represent the area of the third and last area model.

This is an assignment that is to be completed alone. My students will not be working in partnerships or in groups. However, I do allow my students to use each other as a resource if they are stuck and I am unavailable.

6 Closing Summary - 15 minutes

To close out this lesson, I will select one of my students to present their solutions to the task that they had to complete. This student will present their answers and answer any questions that their peers or I have.