Area on Geoboards
Lesson 2 of 19
Objective: SWBAT use geoboards to construct polygons when given a specific area.
During the first section of this unit, students will construct a house plan, find the area of the house plan, and calculate flooring costs. While finding the area is the focus of this unit, the first few lessons (where students explore the meaning of a polygon, construct house plans, and decompose rectangles into smaller rectangles to find the area) lay the foundation for finding the area of their home plans later on. This also provides students with a meaningful and purposeful context to find the area.
During the second section of this unit, students will investigate dog pen designs and will primarily focus on finding the perimeter, or amount of fencing needed for different dog pens. Students will also explore odd-shaped polygons by finding the area and perimeter of odd-shaped dog pens.
I pair students strategically for math, taking into consideration student engagement, behavior, math skills, etc. Keeping the same partners for a month cuts back on time wasted assigning partners every math lesson. Also,I often ask one student to be “partner A” and the other to be “partner B." This way, it’s quick and easy to assign tasks!
Finding the Area of a 4 x 4 Square
I invite students to gather together at the front carpet with their math partners, student journal, and a pencil. I ask “partner A” to get a geoboard and rubberbands.
Once everyone is ready, I make a 4 x 4 square on a geoboard and show it to the class. I then ask students to turn and talk with their math partners: What is the area of this polygon? To reinforce the Turn & Talk Guidelines, I insert several reminders: Make sure you are really listening to your partner and trying to understand them! Remember to ask your partner, "Why do you think that?"
I then ask for a few volunteers to explain their thinking. My overall goal is to inspire students to reason with one another and provide evidence to support their thinking (Math Practice 3: Construct viable arguments). I respond with: Hmmmm… I wonder if that’s how area works. Or: I wonder if that’s always true.
As a side note, throughout this lesson, I could have utilized an Interactive Geoboard. This would have been a fun way to integrate technology.
We then develop a simple definition for area as a class, Area: the number of squares on the inside of a polygon.
When I teach vocabulary, I try to use TPR (Total Physical Response). As a class, we will develop a simple definition for a vocabulary word as well as hand movements. TPR activates multiple parts of the brain and promotes a stronger memory connection. Often, students are able to recall the meaning of vocabulary words by recalling the hand movements.
Today, we discuss and come up with the following definition and hand movements: Area! The number of squares on the inside (students form a rectangle with one flat hand while they act like they are counting squares on the inside of the rectangle with the other hand.)
Next, we practice the new vocabulary word several times. To review the meaning of area, throughout the unit I say, Turn and Talk: How do you find the area of a polygon? Students will use the hand movements to recall the definition!
Next, I introduce students to a fun Area song, Project GLAD Area, Perimeter, & Volume Song, to the tune of the Wheels on the Bus. We only sing the first part of this song a couple times, but the mathematics classroom sure comes alive when music is incorporated!
Lesson Introduction & Goal
I write the goal of the lesson on the anchor chart and I ask students to also write the goal in their math journals: I know how to find the area of a polygon. Here's what the completed anchor chart will look like at the end of the lesson: Area Anchor Chart.
I then use the anchor chart to model how to make a 3-column chart with the following headings: Tasks, Examples, and Observations. Students complete the same chart in their journals as well.
I explain: Today I’m going to give you several challenges! I’ll write the task in the task column. Then, I’ll ask for you and your partner to complete the task using your geoboard. Turn & Talk: What will we be doing? I often ask students to review directions to ensure that all students understand the task.
Challenge # 1
I introduce the first task to students: Here's your first challenge! Working with your partner, see if you can make a polygon on your geoboard that has an area of one square unit. I repeat the directions a few times and students go right to work!
During this time, I conference with students to check understanding and to push student thinking. Often, I ask open ended questions, such as Are you sure? How do you know? (one square on the inside)
As students finish, we discuss the multiple ways to construct one square unit. Three volunteers share their thinking in front of the rest of the class: 1st Example: 1 Square Unit, 2nd Example: 1 Square Unit, and 3rd Example: 1 Square Unit. After each student shares, I encourage students to think “outside the box" by asking: Is there another way we can show one square unit?
I model how to draw at least one example in the "Examples" column of our 3-Column Chart and how to write observations in the "Observation" column. Students complete their own charts in their math journals for the first task.
I provide students with continued practice (with less guidance) by introducing the next challenge: construct a polygon with an area of 4 units. Students excitedly began and many wanted to find the most creative approach to the challenge. It is great watching students engage in Math Practice 5: Use appropriate tools strategically. Students were manipulating the tools provided to model their thinking. Some students use several smaller rubber bands to enclose each square unit while others use large rubber bands to enclose an area of 4 squares.
During this time, I monitor student learning, encourage the use of multiple strategies, and ask students to share their thinking with other groups.
Next, student volunteers share their varied arrangements (1st Example: 4 Square Units, 2nd Example: 4 Square Units, and 3rd Example: 4 Square Units) and we complete the anchor chart altogether. Again, students document their learning using the 3-Column Chart in their own journals as well.
Students were especially excited for an even harder challenge: construct a polygon with an area of 12 units. Following the same procedures as above, students work together to create as many solutions to the challenge as possible. Then, we discuss the results as a group and complete the 3-Column Chart. Here are a couple examples of a student work: 1st Example: 12 Square Units and 2nd Example: 12 Square Units.
Again, students document their learning in their journals as well: Student Journal Example.