Area in Real Life With Irregular Polygons

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SWBAT calculate the area of an irregular polygon using multiplication strategies with arrays.

Big Idea

Dividing an irregular shape into rectangles helps students find the area of an irregular shape.

Warm Up

5 minutes

To begin this lesson I review area models of different types of rectangles found in classroom.  This includes the area of the student desktop, a book, tissue box, or math geoboard.  I keep the focus on finding the area of squares and rectangles. Using these everyday items gives students a real life connection to the purpose of determining area that we are working on in this lesson.  To support students during the warm up, I also review strategies for modeling multiplication for students using diagrams, arrays, and if necessary hands on manipulatives.   

Why do I use additional teaching time to review multiplication strategies? Both area and the understanding of multiplication and division strategies are Grade 3 Critical Areas. Critical Areas in the Common Core focus teaching and learning of the entire grade level math content. Within the description of Critical Area 3. Developing understanding of the structure of rectangular arrays and of area, the explanation specifically states "students connect area to multiplication, and justify using multiplication to determine the area of a rectangle". 

Student compare their area results and make sure the information includes square measurement labels such as 30 square inches or 120 square centimeters.  These labels are critical to their understanding of area. 

This lesson also gives students the opportunity to practice using measuring tools, including rulers and tape measures (MP5).  

Mini Lesson

20 minutes

The purpose of this lesson is to apply finding the area of a real world setting using spaces familiar to the students. Because the Common Core requires students to make a connection between math and its application in the "real world", this lesson provides students with this type of experience.

The focus of this lesson is finding the area of irregular shaped polygons in real life.  To find these areas I take the students to the hallway in our school at locations where they intersect with other hallways and exits to the playground area.  We continue the tour of the school to include focusing on doorway entrances into the cafeteria and library where the doorways are set back from the main wall.  During this time the students draw some of these models on whiteboards, and I take digital pictures to capture these shapes so that they can be shown once we return to the classroom.  These visual models support all students, and they are especially important to the ELL students in my classroom. The shapes we discover include T and L shapes. Students record the shapes on grid paper by matching the grid to the number of square tiles on the floor.  If your school does not have a tiled floor, students could use tape measures or meter sticks to measure these areas, or you can assign a numerical value to these spaces. 

Returning to the classroom, I ask the students to look at the shapes on their whiteboards and ask them to think about how we can find the area of these different types of shapes.  With some discussion, the students begin to realize that each area that has been diagramed includes different types of rectangles and squares.   I include in the discussion which measurements would be used for these real life areas and determine if it would be meters or yards compared to inches, feet, and centimeters. 

I model for the students how to decompose the irregular polygons into separate rectangles and squares.  Once students can see the different rectangles and squares in these shapes, determining the area of each individual polygon is determined, and then added together.

These types of problems require the students to perform multiple steps to determine the solution.  It is important to show students how different lines can be drawn to find different size rectangles in the same figure, but the area does not change.  These examples from the school are completed together with the students.

Try It On Your Own

25 minutes

Practicing on their own, students work together to find the area of a polygon with the outline of stair steps. Students work together to find the length of the lines drawn in to create the separate rectangles.  This requires the student to add and subtract from the known lengths.  I chose to support students by providing grid paper to find unknown lengths and to check their work.  Once students practice with the grid paper, most are able to move to unlined paper to find the area of irregular polygons.  

The shape below is the one provided to the students to compute area. However, I also allow choice, giving students the option of challenging themselves with creating their own shapes by combining rectangles.  


5 minutes

To close this lesson, I share with the class some of the students made ShowMe videos which demonstrate strategies used to determine the area of a shape.   I ask the students to draw their model, as well as to write their solution in their math journal. I also make sure to include in the discussions a variety of ways to "see" these shapes. Using the example in the video, this would be to think of real world shapes besides stairs.  The students identify doors, windows, buildings, and Legos as additional examples.