Engaging students: Finding the Area of a Square or Rectangle

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Tracy Leeper. Her topic, from Geometry:finding the area of a square or rectangle.

How could you as a teacher create an activity of project that involves your topic?

I would start off my lesson by allowing the students to use block manipulatives, and worksheets with different squares and rectangles printed on them, and ask the students to find out how many blocks each square or rectangle takes to fill the space. I would then tell them the space covered by the blocks is called the area, and see if they could find the relationship of $A = l \times w$. By having the students use the blocks, they can easily see that a square would use 9 blocks. The “hidden” block in the middle of the square would become visible. By doing this, I would allow the students to discover the algorithm for the area of a rectangle / square on their own. This would enable them to remember it better. Using the blocks would also give them a better visual memory of the activity, so later, it should be easier for the students to recall the appropriate formula. Using various sizes of rectangles and squares would also illustrate that the algorithm works every time, regardless of the size of the rectangle or square.

How can technology be used to effectively engage students with this topic.

LearnZillion.com has a great lesson on finding the area of a rectangle. The video starts out by reviewing what a perimeter is, and uses scaffolding to build to finding the area. After the area has been determined to be $A = l \times w$, the video then goes on to ask questions for finding area on a different rectangle, and then shows that given the area, and one side, by using inverse operations, we can solve for the missing side. The next question is, given a rectangle with a perimeter of 24, what might the area be? Again, the video not only reinforces using the inverse operation, but continues to show the importance of the word “might” by showing that there are multiple solutions. After teaching what mathematical reasoning should be used for this problem, the video then moves to applying the knowledge to a word problem. The video uses proper mathematical terminology, and demonstrates how to apply prior knowledge to help in gaining new knowledge. The video does seem a little dry, and the students might want something flashier to catch their attention, but I feel this video would be a very good tool to use, to reinforce new concepts for students.

How has this topic appeared in the news?

1n 2006, the San Alfonso del Mar resort in Algarrobo, Chile opened the “world’s largest swimming pool” as dubbed by Guinness World Records. It is measured to cover approximately 20 acres, which is 871,200. I would use this as a lead in to an activity for my students. I would show them a picture of the pool and challenge them to find out how many Olympic size pools it would take to cover the same surface area. Since this lesson is on area and not volume, I would give them the measurements of an Olympic Size pool, which are 164 ft. in length and 82 ft. in width. The students would then have to find the total surface area of one Olympic-size pool, which is 13,448. Then the students would have to divide to find out how many Olympic-size pools it would take to cover the same surface area of the San Alfonso del Mar resort pool, which calculates to be approximately 65 Olympic-size pools. I think this would be a good elaborate for the lesson on area of a rectangle or square.

http://twistedsifter.com/2012/05/worlds-largest-swimming-pool-san-alfonso-del-mar/