Finding the Area of Rectangles, Triangles, and Squares

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Objective

SWBAT recognize and use the area formulas for rectangles, triangles, and squares.

Big Idea

Rectangles, Triangles, and Squares… Oh My! Figuring out how much territory these shapes cover.

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.

Engagement

10 minutes

For the opening exercise, I will provide each of my students with one rectangle. The rectangles will be of varying sizes. While passing out the rectangles, I will ask if there is anyone who knows the formula for the area of a rectangle. Once I receive the correct answer or provide the correct answer, I will then ask if anyone knows the formula for the area of a triangle. Once I receive the correct answer or provide the correct answer, I will then write the formulas on the board. I will then ask if there is a way to demonstrate how to get the formula for the area of a triangle using the rectangle that I have provided. In this exercise, I am looking to see if the students are able to make the connection between the ½ presented in the formula for a triangle and the action of cutting a rectangle in half. Questions that I may use to prompt the students to come to this conclusion are:

  • How can I create two congruent triangles using a rectangle?
  • How is cutting a rectangle in half significant when we look at the formula for the area of a triangle?

 

The ultimate goal is for students to see that the formula for a triangle is created by taking half of the formula for a rectangle… just like cutting a rectangle in half to create two congruent triangles. I will also emphasize the fact that when cutting a rectangle in half that we are creating two CONGRUENT triangles which speaks to the fact that we are cutting the rectangle in half. If the triangles weren’t congruent then we wouldn’t be cutting the rectangle in half and therefore the formula wouldn’t work. Furthermore, the reason for differing sizes and dimensions is to demonstrate that this is true for ALL rectangles.

Instruction & Teacher Modeling

10 minutes

During the instructional piece, I will first provide each group of students with a sheet of chart paper and 2 minutes to discuss, compile, and write a list of observations concerning the physical properties of rectangles and triangles and how these properties are related to their corresponding mathematical formulas for area. After the allotted time has expired, each group of students will share their observations with the class. I will ensure to fill in gaps in reasoning as the students are presenting their observations.

Examples of the types of observations that I would expect to see on my students' chart papers are as follows:

  • The height of a rectangle is the same all the way down the length of it (This is the reason we are able to multiply the length times the height).
  • Triangles are always half of some type of parallelogram (This is why we are able to use the formula for area of a parallelogram and then divide it in half to find the area of a triangle).
  • All sides of a square are equal (This is the reason that you can square the length of one side of a rectangle and get the entire area of the square).

 

As the students are working on their lists, to ensure that the list is comprehensive, I will aide in the activation of critical thinking by using strategic questioning to cultivate the connections between the characteristics of each shape with its formula.

Then, using the students' lists, I will fill in gaps in understanding by using a discussion style instructional strategy that invites students to interject their thoughts, ideas, and questions.

Next, I will demonstrate how to use the formulas for area of rectangles, triangles, and squares. I will do this by finding the area of each type of shape mentioned above. I will also show how the ability to use a formula relates to standard EE.2c which is from Unit 3. I want my students to be able to see how everything that they are learning this school year is related. It is my hope that if they are able to see the relationships between different concepts that they will retain more information.

Try It Out

5 minutes

In today’s, "Try It Out," I will have my students practice finding the area of a rectangle, triangle, and square using the formulas presented in the instructional portion of this lesson.

During this time, I will be traveling the room to observe the students as they are working, answer any questions that any of the students might have. Ultimately, I am looking for ways to determine whether or not any of my students need additional support when it comes to finding the area of these basic polygons.

Should I find any students who need additional support, I will pull them into a teacher led group and aid them in solving the problems that will be presented to them during the independent practice.

Independent Exploration

20 minutes

So that my students can explore and practice finding area of basic polygons, I will have complete a worksheet that requires them to solve problems in real-world context. This worksheet will contain 6 word problems; 2 involving the area of rectangles, 2 involving the area of triangles, and 2 involving the area of squares. 

What I am looking for my students to be able to do in this instance is apply what they have learned about the area of basic shapes to real-world situations without explicit instruction that breaks down these types of problems for them. I want to see that they are able to successfully demonstrate Mathematical Practice Standard 1- Make sense of problems and persevere in solving them. Ultimately, I am looking for students to answer the questions, "Can my students solve problems involving area, that are put in a real-world context, by simply using what they know about area?"

It is important that students be able to transfer basic knowledge about a particular concept and transfer that knowledge to a situation that will allow them to demonstrate a deeper understanding of that concept.

Closing

15 minutes

We will close this lesson by presenting the problems that were completed during the independent practice. To do this, I will select 6 students (one for each of the six problems) to present their work to the rest of the class using the document camera. During the presentation, the students should be able to tell me all of the following:

What in the problem lead them to know which shape they were dealing with?

What formula did they use?

Tell the class step by step how they used the formula to solve the problem?

Provide a complete answer to each problem.

Provide a visual of the shape and its dimensions.

 

Homework: The students will complete six more problems similar to the problems that they completed for independent practice.