# How to Teach Area of Quadrilaterals and Triangles in the Upper Elementary Classroom

Are your students finding themselves in a maze of confusion when trying to find the area of quadrilaterals and triangles? I’ve got an exciting and effective solution waiting just for you! In this post, I’m unveiling my approach to teaching how to find the area for these shapes using the Math Wheel tool for guided notes. This interactive graphic organizer is set to turn the complex task of finding the area into an enjoyable journey for your students.

If you’re on the lookout for a new and engaging way to master the essentials of area calculations, you’ve come to the right place. Stick around until the end for some additional resources that are ready to be used in your classroom. They’ll make learning about area an approachable and dare I say fun experience for your students!

## Guided Notes Math Wheel for Area of Quadrilaterals and Triangles

Energize your classroom as you learn about quadrilaterals and triangles using the Area Math Wheel!

This dynamic tool is ideal for introducing and instructing the computation of area. It doubles as a fantastic resource for later review within the unit. Whether used for initial learning or as a reinforcement tool, the math wheel ensures an understanding of these important geometric concepts. Serving as both a graphic organizer and a study aid, students can tuck this interactive resource into their notebooks for reference.

Let’s dive into each of the five sections of this math wheel. With this math tool, you can watch as your students embrace the exploration of area with enthusiasm!

Let’s take a look at how I introduce the area of quadrilaterals and triangles before I start explaining the first section of the math wheel! I always like to see what my students already know, so we review what we know about area, quadrilaterals, and triangles. We might also take some time to use graph paper or unit blocks to create squares and rectangles and show how the inside of a shape is composed of square units. This helps make the concept a little more concrete before we jump into formulas.

### 1. Squares

Once we have refreshed our memories, it’s time to take a look at the first section on our math wheel, which is how to find the area of a square!

Before diving into the example, we write down a few notes to keep in mind. On the left side of this section, I have my students write down that area = side x side. On the right side of the section, we write down another note about how side x side is the same as length x width to find the area of the square. And. . . we can’t tackle the area of a square without remembering that all four sides of a square are the same.

We then turn our attention to the example in the section. One side is labeled 7 m. I have my students write an “s” underneath this measurement to help my students remember side also refers to length or width. Where it says A = ____, we write s2 because we need to multiply two sides to find the area of the square, and since both sides are the same length we can write that as s2. Underneath, we write out how this formula plays out in our example. I add another equal sign and write = 72 and then on the following line I multiply 7 x 7, which equals 49, and add this as the answer. The area of this square is 49m2.

### 2. Rectangles

Moving to the next section of our guided notes for the area of quadrilaterals and triangles, we turn our focus to rectangles. In this section, I explain the formula to my students for how to find the area of the rectangle.

The first thing we write down is the formula for area, which is area = length x width. Students can shorten that to A = l x w. Looking at our rectangle example, we notice that the shape has two measurements (11 in and 5 in).

We don’t jump right into solving just yet. We first need to identify which is the length and which one is the width. The side with 11 in. is labeled with a “L” for length, and the side with 5 in. is labeled with a “W” for width. When labeling, I use two different colors. Length is in green and width is in purple. I will write the number in the formula with the matching color to help my students see easier where the numbers are coming from.

Now that the sides are labeled, my students are ready to solve! We remind ourselves about the formula, and then we plug in the numbers so it reads A = 11 x 5. This equals 55, so our area for this rectangle is 55 in2.

### 3. Parallelograms

In the third section of our math wheel, I review two new terms, base and height, which are used within the area formula for parallelograms. We talk about how the base is the length of one side, while the height is the perpendicular segment between the base and the opposite side.

The first thing we write down is the formula for finding the area of a parallelogram. Area = base x height is written out along the side of this math wheel section.

Next, we take a look at the parallelogram example. It has two measurements, 12 ft. and 4 ft. I have my students pull out their two different colors once again. We color code our numbers on our parallelogram and also in our equation to solve for area. I take my blue marker, and we label 12 ft. with a b for base. Then I take my orange marker, trace the dotted line, and write a h for height next to 4 ft.

Once we have our labels written down, we are ready to solve the area! Following the formula, A = b x h, we fill in the length of the base and height (12 and 4). When we multiply 12 x 4, we get 48. So, the area of this parallelogram is 48 ft.2.

### It’s Not So Complicated

In the trapezoids section, I give a heads-up to my students that there are more numbers in this formula. We talk about how it looks trickier than the other formulas, but in reality, we are going to break it down into small steps just like the others. Throwing in a fraction throws off students, so I like to add reassurance to ease their nerves.

We start by writing out the formula in words. We look at it and see what’s familiar to us and what is new. Then we write Area = 1/2 height (base1 + base2). Together, the class and I point out that we know what height and base mean. We also know that using the order of operations, when there is a number next to a set of parenthesis, we need to solve what’s in the parenthesis before multiplying the inside number by the number on the outside.

Before we begin our trapezoid example, we have our two colors ready to help us see the different parts. Then we find the three measurements on the trapezoid, which are 9 cm, 6 cm, and 11 cm. First things first, we must determine which of these numbers represents the height and which represents the 2 bases. I have students look back at the parallelogram example to make this determination.

Then using the first color, we trace the dotted line and label 6 cm with a “h” for height. Then we pick up our second color and we trace the top line and the bottom line of the trapezoid. We label 9 cm with a b1 and 11 cm with a b2.

### Applying the Formula to Our Example

Now it is time to plug our numbers into the formula! I remind my students that the formula is A = 1/2h (b1 + b2). This becomes A = 1/2 (6) (9 + 11). We begin working through the equation one step at a time. I make sure that after each small step we start a new line. This really helps students see how simple it is to use this formula.

First, we add 9 and 11 to get 20. Our equation now looks like A = 1/2 (6) (20). Next, we find one-half of 6. When 6 is multiplied by 1/2, it becomes 3. Then we multiply 3 and 20, which equals 60. The area of this trapezoid is 60 cm2!

I love that when we finish this example there are lots of smiles and eyes gleaming with confidence. It’s one of those ah-ha moments for students when they realize that just because something looks complicated doesn’t mean that it is.

### 5. Triangles

In the final section of our area of quadrilaterals and triangles math wheel, we discuss how to find the area of a triangle.

### Breaking Down the Formula

To one side in the section, we write out the formula: area = 1/2 x base x height or A = 1/2b x h. Despite this being another “complicated” formula students generally see this one as a fun challenge because they have learned the power of breaking it down into small steps.

I check in with my students to see what they notice and to identify any similarities from previous sections. They’ll point out that there is a fraction involved, we are still using base and height, and how we are now multiplying 1/2 by the base, not by the height.

Once we have analyzed the formula, we turn our attention to our triangle example! We grab our markers, and we take note that there are three measurements on the triangle, even though we only need 2. So the first order of business is identifying the base, the height, and the extra information.

### Finding the Area of a Triangle

Taking my green marker, I guide my students in labeling 10 m with a “b” for the base. Then we take our next color, mine is blue, and we trace the line that is cutting down through the middle of the triangle. In the same color, we label 12 m with a “h” for height.

We are ready to plug in our numbers and solve! First, we write out the equation with the numbers: A = 1/2 (10) (12). We put the order of operations into play and know that we are going to do the multiplication from left to right. So we multiply 1/2 and 10 first, which equals 5. Then we multiply the 5 and 12, which equals 60. The area of this triangle is 60 m2!

## What’s Next?

Once we complete the math wheel, my students engage in practice problems placed around the math wheel. This allows for either guided or independent practice based on their understanding. My students have the option to add a personal touch by coloring the background pattern or adding doodles that will help them remember the different formulas or steps.

Once finished, these math wheels find a permanent home in my students’ math notebooks. They serve as a valuable point of reference throughout the area of quadrilaterals and triangles unit and beyond. These guided notes help to break down complex concepts into smaller chunks of information. This makes the concept easily accessible through this visual aid.

## Teaching Area of Quadrilaterals and Triangles Simplified!

By navigating through the five sections of the Area Math Wheel, your students will develop a strong understanding of how to solve for the area of quadrilaterals and triangles. Whether you use them as lesson notes, a practice activity, or review before a test, they are sure to help your students gain a better understanding of these skills and concepts.

If you’re ready to incorporate the Area of Quadrilaterals and Triangles Math Wheel into your teaching toolkit for this topic, visit the Cognitive Cardio Math store on TPT. This resource is readily available for download, printing, and immediate use in your classroom.

## More Resouces for Area of Quadrilaterals and Triangles

On the hunt for resources to simplify the teaching and learning process for finding the area of quadrilaterals and triangles? Be sure to explore the following materials designed to assist you in teaching these concepts.

## Save for Later

Remember to save this post to your favorite math Pinterest board for when you teach students how to find the area of quadrilaterals and triangles.

## Ellie

### How to Use Math Small Groups in Middle School

Welcome to Cognitive Cardio Math! I’m Ellie, a wife, mom, grandma, and dog ‘mom,’ and I’ve spent just about my whole life in school! With nearly 30 years in education, I’ve taught:

• All subject areas in 4th and 5th grades
• Math, ELA, and science in 6th grade (middle school)

I’ve been creating resources for teachers since 2012 and have worked in the elearning industry for about five years as well!

If you’re looking for ideas and resources to help you teach math (and a little ELA), I can help you out!

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