Area of Parallelograms, Applying the Formula
Lesson 5 of 14
Objective: SWBAT derive and apply the area formula for parallelograms.
Think About It
Students complete the Think About It problem in pairs. Because of the previous lesson, most students will rearrange the parallelograms to make rectangles, and either count the squares or apply the formula for finding the area of the constructed rectangle.
I ask students if they've found a more efficient way to find the area of the parallelogram, as a way to determine if anyone has derived the formula.
Intro to New Material
To start the Intro to New Material section, I fill in the guided notes below the Think About it Problem. After filling in the notes, I will sketch a parallelogram on the board and show students the heights for either base in the parallelogram. If students seem skeptical that the area will be the same, I assign values to my figure - bases of 10 and 5 units, with respective heights of 7 and 14 units.
We then move on to example 1. I ask students to label the lengths of the sides of the parallelogram. We then discuss that the vertical length is easier to identify, because it falls nicely on the grid lines. I ask students to show me on their fingers the value of the height, when using the vertical side as a base. When we label the height, I have students follow the convention of using a dashed line to represent the dimension. Students then find the area of the parallelogram, by applying the formula. I ask students why the formula of A = bh works in this situation - I want students to articulate that the formula for finding the area of a parallelogram is the same as the formula for finding the area of a rectangle because the parallelogram can be rearranged to form a rectangle.
For example 2, I ask students what concept we're applying, and why. Students represent the problem by drawing a picture and labeling the dimensions. I guide students through finding the area of the parallelograms, and then have students complete the application portion of the problem on their own.
Students work in pairs on the Partner Practice problem set. As students work, I circulate around the room and check in with each pair. I am looking for:
- Are students correctly identifying and labeling the base and the height?
- Are students correctly applying the formula to find the area?
- Are students correctly writing units for their answers?
- Are students drawing pictorial representations of problems when necessary?
- How did you find the area of the parallelogram?
- How did you know what is the base and what is the height?
- How did you know that you are calculating the area for this problem?
- How did you find the missing base or height?
In this lesson, there are a number of parallelograms that have lengths that include decimal numbers. The goal of this lesson is for students to master the application of the formula for finding the area of a parallelogram. After 5-7 minutes of work time, I do give students the option of using a calculator as a tool as they work through these problems. Some students will choose not to use them.
After partner work time, we discuss problem #3. I pull two examples from the class on the document camera - one sample that correctly uses the base and height to find area, and one that incorrectly uses the horizontal base and the vertical side as a height. I ask students which work sample is correct (I have an incorrect example ready with my materials, in case no one has made the mistake of using the two sides, rather than a base and a height).
Students work on the Independent Practice problem set.
As students start problem 1, I look to see if students choose to rearrange this parallelogram into a rectangle (rather than apply the formula). If I do see this, I tell students that rearranging is a valid method but applying the formula is more efficient. I then insist that students also apply the formula for this problem.
Problem 4 requires students to identify an unknown dimension, given the area. The numbers in this problem are straightforward. I like this problem, because it gives students a small preview of what we'll work on towards the end of this unit.
Many students are initially thrown by Problem 5, because of the overload of information. A student work sample for this problem is included. Some students will recognize that the top side can be used at the base. Most students, though, will feel the need to identify the length of the bottom side of the base, and will be initially puzzled by the broken up dimensions. I don't offer myself as a resource here; I want students to persevere.
I offer students the option of using calculators with this problem set.
Closing and Exit Ticket
After independent work time, we discuss Problem 4 as a class. I use this opportunity to reinforce my organization expectations with student work. A top-quality solution to Problem 4 will be set up as:
A = l x w
24 sq. cm = (4cm)h
24 sq. cm/4cm = h
6cm = h