Perimeter Introduction and Exploration

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The students will be able to see that volume adds layers or depth to the shape , using perimeter and area review introduce the concept.

Big Idea

When dimensions change the perimeter, and area, can remain the same!


I teach students in a multiage 4th and 5th grade classroom. To meet the needs and standards of both grade levels, I use activities that will be build a stronger conceptual foundation for my fifth graders while introducing concepts new to my fourth graders. 

I start lessons with Inclusion.  This is to connect to a student's prior knowledge as well as to recognize and make each student feel included.  I find that when students feel included in a lesson. they do not try to "steal" influence by acting out. 

The main concept in this lesson is to introduce perimeter and area vocabulary (MP6) and have the students actively engage in exploring perimeter and area through manipulation of centimeter cubes. This lesson includes a table tour - students walk around to each seat and write the perimeter and area of other students' creations.  

I find that when students are given the time to explore each other's work, they develop a better sense of the math while developing their social skills. In my lessons, I create opportunities for students to interact with each other, politely analyzing each others work. 

I end each lesson with reflection on content and behavior.  My goal as a teacher is to not only give students a challenge, and success, with the academic content but also social skills.  I am working towards having students be lifelong learners and productive citizens.

Inclusion - Engaging Students

5 minutes

When I was setting up, by putting centimeter cubes into table bins, I was thinking about how I can tie perimeter to something the kids have experience with - all in one inclusion question.  I decide to ask my students to share with their groups any time they had to measure around a flat surface. 

I ask for volunteers to share their experiences to make sure I had made the question is clear enough.  One student shared they had to help their uncle measure so they could buy decorative tile to go around the edges of a room.  Another student shares they helped their father build a fence around a horse corral.  The third student talks about measuring around the outside of a quilt to buy fabric to make a boarder.  After hearing these three students. I believe the question is clear. The examples given help all of the students to understand the discussion topic.

During a couple of minutes of discussion, I walk around straightening/organizing things in the room.  I want to to hear my students' discussions, so I can assess the level of understanding in perimeter and pick up more great examples to share with the class.  At this point. I do not interrupt conversations, unless there is a disagreement. Then I hover to see if the students can solve the issue on their own. 

I believe that if I step in immediately, I haven't given them the chance to solve problems, or use the interpersonal strategies I am teaching.  Sometimes, a student will catch my eye during a disagreement and I will nod to them if they working towards solving the problem .... or when they make eye contact they will start to use some of the strategies we have practiced in class.   

One of the things I love about using Tribes strategies in my classroom is they are built into my everyday teaching. The heart of Tribes strategies is teaching students to be able to resolve conflict, no matter how minor, and teaching students to become leaders.  You will see these characteristics in the video where students are working together. 

Exploration of Perimeter

30 minutes

This lesson is very basic, but an important building block to taking the abstract algorithm for perimeter and giving students the chance to manipulate it physically with their own hands. It also helps students understand the properties of volume - building layers to create depth.  

After the inclusion question discussion, I know which students have had actual experience with perimeter in their lives outside the classroom. I hope the others who haven't had these experiences have been able to get the idea or a picture of perimeter from hearing about their peers' experiences. 

My instruction now is to build a simple shape that is either a rectangle or a square.  There can be no empty spaces and ever block has to touch another block along its edge.  I have introduced the word edge as a side because one of our "bridge standards" for our state testing includes Vertex Edge Graphs.  I find it easier to introduce the vocabulary and build upon it for each concept I teach.  By the time I get to Vertex Edge graphs I do not have to teach the vocabulary words edge, sides, vertices and so forth.  I have also found that the more I can tie vocabulary into different math concepts and have my students "see" them in different context the better they retain it. 

I pass out the blocks and the students begin building their simple shapes.  I walk around the room making sure everyone is creating a shape that can be measured along its perimeter easily. I believe in starting with simplicity, and then building complexity.  I want my students to remember the basic formula of P = L + W + L + W.  It will get more complex. 

I also build complexity to create a classroom environment where every student feels comfortable (there are 4th and 5th graders in my class). I'll take this beginning lesson from simple perimeter to area and volume.  This reinforcement or review lesson for the fifth graders is simple, but I've seen amazing" ahha" moments and incredible student leaders helping each other.  

As I am walking around I tell the students to write a number on their papers.  This is the number their model will be on a list from one to 28 - the number of students I have currently.  After the models are built the students will be walking around to each model and figuring out the perimeter  writing the answer down.  It is very important that each student has an assigned number because when you go to review the answers everyone needs to know which model belongs to number 1 or 2....

This is an exciting time for the students because they are up moving around, discussing and analyzing another students' work.  I find that I have to "front load" appropriate behavior.  As great teachers we always have rules or procedures to do this.  In my classroom I use a process called Tribes and it focuses around the four Tribes Agreements of Attentive Listening, Appreciations/ No Put-Downs, the Right to Pass (not check out but needing some extra time) and Mutual Respect.  I review these by asking my students to tell me what will Attentive Listening look like, sound like and feel like.  Then what will Appreciations look like sound like and feel like.  I have learned if I don't take my time to review this important classroom expectations before I have the kids move around the room there will be more discipline problems.  This one three minute activity set the stage for better behavior and more time on task, deeper learning and greater retention. 

Wrapping It Up

10 minutes

I finish every lesson with reflection questions because when a student reflects on their learning they have double the retention rate.  I also include social skill reflection questions because when a student reflects on their behavior their collaborative skills increase.  For this lesson I asked my students to write answers to three reflection questions.

1.  What did you learn about perimeter?  I ask this question so I can assess what the students took away from this activity and if they are ready to move on and compare perimeter and area. 

2.  What did you learn about your own thinking? Metacognition is important for everyone.  The more the students reflect on their own thinking they become aware of how they learn and process information. 

3.  How did you help another student? With this question I am able to reinforce being helpful to others when you are working in a group setting. 

Reflection is a step that I used to forget, or pass up because I run out of time.  One year I made a goal of including reflection in every lesson, and now it is part of my lessons, whether it is a written reflection like this one or a quick verbal reflection in their table groups.  As a reminder, I put up a symbol in different places in my room.  For me the symbol is the pelican named Reflection.