# Engaging students: Finding the area of a right triangle

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 again comes from my former student Trenton Hicks. His topic, from Geometry: finding the area of a right triangle.

As an engagement activity, give students the following problem: “A rectangle has dimensions of base: b and height: h. How many different ways can you cut this rectangle in half with a straight line? How many shapes can you make from the different ways you cut the rectangle in half? Now out of those, which shapes are not rectangles?”

This will leave only two different ways to cut the rectangle in half, yielding identical triangles on either side of the line. Now, ask the students, “From what we’ve already learned about rectangles, what would be the area of this rectangle?” After confirming the area is base times height, wait a few moments before saying anything else. Now that the students are thinking about the base, they will now start to make predictions about the triangles that we’ve just made and their areas. Have them write their guesses for the formula of the triangle down on a piece of paper, and keep them to the side through the lesson. From here, we can break them up into groups and give them 3 right triangles to solve for the area, and one equilateral triangle to solve for the area. Go through the answers together and compare groups’ answers, as well as their predictions on what the area of a triangle is.  The odds are, many groups will be stuck once they get to the equilateral triangle. If so, you may want to send them back to their groups to try and find the area, giving them the hint, that they may have to make new shapes, just as they did with our rectangle at the beginning. This lesson assumes that the students understand the pythagorean theorem so they can solve for the height of an equilateral triangle by making a new triangle. This way, the students can explore the phenomena of triangles’ area, and see if they can recognize that the height isn’t always a side of the triangle, but rather something they may have to solve for.

The students should be able to use similar techniques to find the area of a parallelogram, trapezoids, and other shapes, as these shapes are partially composed of triangles. As students progress to more complex 2-dimensional shapes, you can derive formulas as you go. As you move onto 3-dimensional shapes, we actually see lots of different triangles appear in the shapes’ respective nets. For instance, when computing the surface area of a triangular prism, we need to know how to compute the area of the base. We also see this same idea in computing volumes of triangular prisms, where we need to know the area of the triangular base. This is also applicable to pyramids, tetrahedrons, and octahedrons. Finally, these ideas are brought up again later in trigonometry where we can determine different parts of the formula with trigonometric ratios and functions and whenever the students learn Heron’s formula.

This concept of finding the area of a triangle expands many things that the students may already know. This won’t be the students’ first time seeing a triangle, nor will it be the first time they compute the area. Overall, this content should be a refresher and not new to the students. However, this may be the first time that the students are presented a rectangle and told to make a triangle out of it. From that point, they are told to make conclusions about the triangle’s area based on the rectangles area. As students think through this, they are using logic and reasoning to argue what makes geometric sense to one another. This further develops their mathematical reasoning skills, which may be a bit rusty since we far too often focus on the “what” and not the “why” and “how.”

# 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 Austin Stone. His topic, from Geometry: finding the area of a square or rectangle.

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

There are many applications to the real world that involves geometry and specifically area of squares and rectangles. Students could use this topic to find the cheapest cost of tiling the floor of a bathroom. Giving them the dimensions of the different tiles and the cost of each tile, students would have to find the area of the bathroom floor and then be able to pick the set of tiles that would be the most efficient and cheapest. This gives students a real world application to what they are learning while also giving them practice in finding the area given dimensions of a square and/or rectangle. This project also calls back to prior knowledge such as perimeter of rectangles and multiplying cost of one tile with the number of tiles used to get to total price. This project could also be a small part of a bigger PBL using area and perimeter of multiple polygons.

How does this topic extend what your students should have learned in previous courses?

The obvious prior knowledge to finding the area of a square of rectangle is being able multiply two numbers which is learned back in grade school. If the students are given the area of the square or rectangle and labeling the sides with a variable, the students would have to be able to solve for the variable. By doing this they would have to be able to multiply binomials (or polynomials if you want students to have more of a challenge). Once they multiply the two binomials and set the equation equal to the area given, they would then have to use the quadratic formula or factor which is learned in Algebra I. If students are given one side and the area, then they would have to solve for a variable with degree one which is used continually in all math classes. Depending on what information is given in the area problem, students will have to use prior knowledge to determine the answer.

How have different cultures throughout time used this topic in their society?

In East Asian mathematics during the 1st-7th centuries, a book called The Nine Chapters gives formulas for solid figures including squares and rectangles. The formulas are given as series of operations to get the result, called algorithms. Instead of variable and symbols, the formulas are given in sentences as in, “multiply the length of the rectangle by the width.” This puts the regular A=lw into words so that if someone who had no idea how to compute the area, they would be able to understand by the sentence given. This undoubtably was much more difficult to follow and became too long of descriptions for more complex figures, as this way of mathematics ended in Eastern Asian in the 7th century. That does not mean that this way of math was not important. This put words into formulas instead of symbols which made it easier to understand for those that are learning it for the first time.

References

https://www.britannica.com/science/East-Asian-mathematics/The-great-early-period-1st-7th-centuries

# Engaging students: Finding the area of a right triangle

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 again comes from my former student Andrew Cory. His topic, from Geometry: finding the area of a right triangle.

How can this topic be used in your students’ future courses in mathematics or science?

Finding the area of a right triangle opens up the door to all sorts of applications in the future. The next step is the Pythagorean theorem which is used constantly throughout many math courses. The study of right triangles also opens up the world of trigonometry with students will be using in nearly every math course they go on to take. Once knowledge is learned of right triangles, other triangles can be manipulated to look like right triangles, or to create right triangles within normal triangles. Triangles are even utilized when determining things about other shapes as well, such as dividing rectangles into 2 triangles and other manipulations. If they go on to pursue geometry further, the Pythagorean theorem is one of the first couple of theorems proved and used in book 1 of Euclid.

What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

Pythagoras was a Greek philosopher that contributed to right triangles. He is credited with discovering possibly one of the most important right triangle properties. A legend says that after he discovered the Pythagorean theorem, he sacrificed an ox, or possibly an entire hecatomb, or 100 cattle, to the gods. The legitimacy of this legend is questioned because there is a widely held belief that he was against blood sacrifices. The Pythagorean theorem was known and used by Babylonians and Indians centuries before Pythagoras, but it is believed he was the first to introduce it to the Greeks. Some suggest that he was also the first to introduce a mathematical proof, however, some say this is implausible since he was never credited with proving any theorem in antiquity.

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

Applications such as Geogebra can be used for any type of geometry activity. It is a great way to help kids visualize what is happening with shapes in geometry, something that is usually a struggle for students. For helping students understand how to find the area of a right triangle, it can easily be shown that if you take a rectangle, or a square, and cut it in half diagonally, you get two right triangles. And since the area of a right triangle is half of the area of a rectangle or square. The various ways that shapes can be manipulated virtually can be a big help for students that learn in different ways. Being able to view shapes in different ways opens doors for students who traditionally struggle seeing a shape in their head, and using it to solve their problems.

Sources

https://en.wikipedia.org/wiki/Pythagoras#In_mathematics

# Engaging students: Area of a trapezoid

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 again comes from my former student Lissette Molina. Her topic, from Geometry: finding the area of a trapezoid.

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

I believe most students in America all discovered finding the area of a trapezoid with one very easy and simple activity. Students are to receive a trapezoid of some different sizes. They are then asked to find area by cutting off the triangular sides. The student then finds that all trapezoids are composed of triangles and a rectangle. This is a very quick activity that requires students to come up with a formula that works across all trapezoids. Learning about finding the area of a shape with hands-on discoveries keeps the formula and how it became embedded into students’ memories. This activity may also work with most polygons.

How does this topic extend what your students should have learned in previous courses?

Find the area of a trapezoid does not require much information from previous courses. One major topic the student should be able to have learned before coming into a geometry class should be area. However, very rarely, students do not know what area is already. So, the student should be able to apply what they know about area into finding the area of a trapezoid. This involves finding the area of a rectangle and a triangle. It is important that a student understands exactly where a formula is derived, so it is also important that students know that the trapezoid contains two shapes and that finding the area of those two shapes will help them find the area of the resultant trapezoid.

How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

One helpful website or program is Desmos (desmos.com). There are usually modules made for students often made by teachers. I have not yet come across one already made, but here is what I have in mind. Desmos is primarily made for graphing, but there are so many functions in this website that it can be manipulated to perform other things such as the unit circle. One very helpful idea would be to make a shape of a trapezoid by combining two triangles of different sizes off each of a rectangle’s sides. Since these shapes are placed on top of a graph, students would be able to calculate the area by counting the square units. WIth triangles, students can count the number of half, quarter, etc. square units. This way, students can find the area of a trapezoid by counting the squares, and realize that it would be easiest to find the area of those two triangles and one rectangle and combine them.

# 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 Christian Oropeza. His topic, from Geometry: finding the area of a square or rectangle.

How can this topic be used in your students’ future courses in mathematics or science?

Finding the area of a square or rectangle comes up again later in Geometry when solving for the surface area of a prism. The reason behind this is because any n-sided prism, where n is the number of sides the base of the prism has, will have n many squares or rectangles. Therefore, in order to calculate the surface area of any prism, the use of finding the area of a square or rectangle is required (Reference 1). Another course that involves this topic is Calculus. When approximating the area under a curve, one strategy is to use left or right endpoint approximation which is just the sum of the areas of the rectangles under or over the curve (Reference 2). This topic is also used in physics when covering measurements. The idea of finding the area of a square or rectangle in the measurements section is to precisely and accurately find the area.

How has this topic appeared in the news?

Steiner Ranch is a hair studio that just recently added 1600 square feet, thus bringing their total to 3468 square feet. With the addition of more space the studio now holds: 19 stylist chairs, 8 shampoo bowls, 3 restrooms, and a color mixing room. All in all, this could not have been done without the use of finding the area of a square or rectangle because then the owner, Brian Charles, would not know how much of each studio equipment would be able to fit in a way that was fitting for him (Reference 3). In other news, state deputies of the Legislative Assembly of Rondonia decided to try creating 11 new protected area in the Brazilian Amazon, which amounted to a total of 2,316 square miles. Therefore, the use of the area of a square was used to determine how much area would go to the new protected areas. However, the bacanda ruralista agribusiness lobby opposed this decision and passed a bill that did not allow the process of making the protected areas (Reference 4).

How have different cultures throughout time used this topic in their society?

During 570-495 BC, the use of finding the area of a square impacted math in Greek culture. More specifically, a man by the name of Pythagoras created what is known now to be the Pythagorean Theorem. He discovered this theorem by noticing that the area of the square created by the hypotenuse of a right triangle is equal to the sum of the area of the squares created by the other two sides of the same right triangle (Reference 5). Also, there were different cultures who had discovered the same formula as the Pythagorean Theorem, but were not the first to publish their findings. These different cultures include: Mesopotamian, Indian, and Chinese (Reference 6). Finding the area of a square or a rectangle comes up immensely in computing the cost for installation of hardwood floors. The cost is computed by charging the customer for the price of each square foot of wood used and the labor for each square foot of wood installed (Reference 7).

References:

# 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 Trent Pope. His topic, from Geometry: finding the area of a square or rectangle.

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

On this website I saw that the Kelso High School GIC students went out and built a home as a class project. They were able to get a \$13,000 grant from Lowe’s Home Improvement and blueprints from Fleetwood Homes to go out and build a physical house. I like the idea of having students use geometry in a real world application, as a teacher I would bring this idea to paper. Students would design and create blueprints for their dream house using squares and rectangles. I would start by giving them the total area their house will be. For example, I would tell them to make the blueprints for a 400 square foot house. They could have anywhere from 5 rooms to 20 rooms in their house. They will be responsible for showing the measurements for each room. After creating the layout of the house and calculating the areas of each room, students will be given a set amount of money to spend on flooring. They will then calculate the cost to put either carpet, wood, or tile in each room. This is to have students decide if they would have enough money to have a large room and if so what flooring would be best. There are other aspects you can add to this project to make it more personalized, but as teachers we just want to make sure we are having students find the area of square and rectangles.

http://tdn.com/news/local/geometry-in-construction-class-finishes-building-first-home/article_74143492-d7a9-11e2-995a-001a4bcf887a.html

How has this topic appeared in the news?

There are many instances of where area made the news. I found multiple websites that talk about how schools are having building projects for geometry and construction classes. These students are building homes from 128 square feet to 400 square feet. Teachers are having students make these homes so that they can see that geometry is in the real world. By having a range of sizes, students have to adjust their calculations. When creating a house or mobile home you need to accommodate for walking space in each room. In order for students to know if there is enough space, they must find the area of each room. Teachers are using this project because blueprints for houses only use squares and rectangles, making it easier for students to practice solving for area of these shapes. This is just the start of teachers making the concept of area more applicable.

http://design.northwestern.edu/projects/profiles/tiny-house.html

How have different cultures throughout time used this topic in their society?

The topic of finding area of squares and rectangles is used throughout many cultures. In the Native American culture along with todays, we see it in growing crops. A farmer must know how big their crop is so they can figure out how much food they will have at harvest. An instance used by many cultures is creating monuments in the shape of square pyramids. In order to build it the right way, you must know the area of the bottom base to build on top of that. A final use of it in our culture is in construction, when we decide how we want to build a building. The concept of area is something that many cultures use today because of how easy it is to calculate. This creates a great way for cultures that are less educated to become familiar with the same concepts as other cultures.

References

Geometry in Construction class finishes building first home. n.d. <http://tdn.com/news/local/geometry-in-construction-class-finishes-building-first-home/article_74143492-d7a9-11e2-995a-001a4bcf887a.html&gt;.
Tiny House Project. n.d. 6 10 2017. <http://design.northwestern.edu/projects/profiles/tiny-house.html&gt;.

# Engaging students: Area of a triangle

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 again comes from my former student Kelly Bui. Her topic, from Geometry: finding the area of a triangle.

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

As an activity, possibly the “exploration” part of the lesson, students will be paired in partners and the instructor will provide each pair with a different rectangle or square. The goal is to find the area of half of a rectangle.

The condition they must follow is that they cannot “draw” a straight line across the shape, they must “draw” a straight line starting from a corner. At some point, it should be evident that you can only draw a straight line from a corner to another corner. By drawing a diagonal line across the rectangle, they will now have two triangles (if that isn’t clear to them at this point, let them realize it on their own or go over it as a class at the end of the activity). Using rulers or meter sticks, they will have to discover on their own what the area of half of the rectangle is along with what the formula for that looks like. Most students will probably take the area of the entire rectangle and divide by 2. Once they come up with a formula for the area of half of a rectangle, it should look like A=1/2 bh, tell each student to raise half of the rectangle they cut, and announce: “congratulations, you have found the formula for the area of a triangle.”

How can this topic be used in your students’ future courses in mathematics or sciences?

Students begin to see the formula for the area of a triangle in 6th or 7th grade. They know the formula, but often times they don’t understand where it comes from. It can be useful for future homework/test problems that ask for the area of an irregular shape as well as in algebra with unknown lengths. These types of problems require students to think “outside of the box” in order to find the area of an irregular shape. It is not always evident that the irregular shape is simply made out of polygons.

Additionally, this topic will be useful when students are in algebra and they must solve for the area of a polygon that doesn’t have specific dimensions. For example, the trapezoid below has an unknown height as well as an unknown base. It is good for students to know how to apply the area formula of a triangle to solve for the dimensions as well as the area of the entire trapezoid itself. One important thing that should be stressed in the classroom is that formulas are extremely helpful on their own, but they’re even more helpful when they can be applied to different applications.

What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

Most students know the formula A=1/2 bh for the area of a triangle, but many students don’t remember the formula used to find the area when all three side lengths are known. Heron’s Formula: √[s(s-a)(s-b)(s-c)] is briefly mentioned in geometry and is often not used in other math courses in high school. Along with his derivation of Heron’s formula, he contributed greatly to ancient society.
Heron of Alexandria was a Greek engineer and mathematician who was known mostly for his work with geometry. He was also a lecturer at the Library/Museum of Alexandria where he would meet with other scholars and discuss work. Additionally, he wrote Metrica, a series of three books which included his work on area and volumes of different types of figures.
It is no secret that Heron had a brilliant mind, and with his engineering and mathematics background, he was actually ahead of the industrial revolution that would take place centuries later. He invented the “Hero Engine, also known as the “aeolipile,” which was powered by steam. Essentially, Heron was the first inventor of the steam engine.
Another one of Heron’s inventions was the “wind wheel,” which is very similar to the modern windmill.

Students will already know that there were many breakthroughs during the industrial revolution, but some of the machines and inventions implemented in the 1800s were actually ideas that were invented centuries before.

Irregular Shape Image: http://www.softschools.com/math/geometry/topics/the_area_of_irregular_figures/

Heron of Alexandria: https://www.britannica.com/biography/Heron-of-Alexandria

# Engaging students: The area of a circle

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 Deetria Bowser. Her topic, from Geometry: the area of a circle.

How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic? Note: It’s not enough to say “such-and-such is a great website”; you need to explain in some detail why it’s a great website.

An example of a helpful and engaging website for students is aaamath.com. On the left side of the webpage, there are a list of subjects. To find the Area of a circle lesson, select geometry and then area of a circle. The lesson is color coded with green being the “learn” part of the lesson, and blue being the “practice.”In the “learn” part of the lesson it explains briefly how to find the area of a circle. While I believe that and actually lesson should be taught before using this website, I think that the “learn” part provided by this lesson would be a great way to quickly review how to find the area of a circle. The next section (“practice”) gives a radius and the student is expected to calculate the area of the circle using said radius. I think this aspect of the lesson will help students gain speed and accuracy in computing the area of a circle. Although I do not think that this website can be used as a complete lesson on finding the area of a circle, on its own, I do believe that it could serve as a great review tool for students.

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

Hands on activities are easier to find for geometry topics, and finding the area of a circle is no exception. An example activity can be found in the YouTube video “Proof Without Words: The Circle.” In this video, the area of a circle is proved using beads and a ruler. The demonstrator creates a circle with silver beads, and shows that the radius of the circle can be measured using the ruler, and the circumference of the circle can be measured by unraveling the outermost part of the circle and measuring it (or by plugging the radius into the equation 2πr). The demonstrator then deconstructs the circle and traces the triangle created by it. From this he shows that $A=0.5bh = 0.5(2\pir)r = \pi r^2$. Instead of just using symbols to show this idea, I would create a guided explore activity where the students need to actually measure the radius and circumference of the circle they created as well at the base and height of the triangle created by deconstructing the circle they created. I would ask how the circumference and radius of the circle relate to the base and the height of the triangle. Once students recognize that the base of the triangle correlates with the circumference of the circle, and the radius correlates with the height, it will be easier to see why the area of a circle is calculated using the formula $A=\pi r^2$

What interesting (i.e., uncontrived) word problems using this topic can your students do now? (You may find resources such as http://www.spacemath.nasa.gov to be very helpful in this regard; feel free to suggest others.)

Practical uses for finding the area of a circle proved to be quite difficult. For example, most questions contain unrealistic examples such as “making a card with three semi-circles” (Glencoe). Although, many of these impractical exist, I found two example problems that could actually be used in the real world. The first example states “The Cole family owns an above-ground circular
swimming pool that has walls made of aluminum. Find the length of aluminum surrounding the pool as shown if the radius is 15 feet. Round to the nearest tenth” (Glencoe). This example is practical because when constructing a pool, one needs to know the surface area which can be found by using $\pi r^2$. The final example states “A rug is made up of a quadrant and two semicircles. Find the area of the rug. Use 3.14 for $\pi$and round to the nearest tenth!” (Glencoe). Although this seems less practical than the pool example, it is still related to real life because finding the area of a rug will help when deciding which rug to choose for a room.

References
M. (2012, May 29). Proof Without Words: The Circle. Retrieved October 06, 2017, from

(n.d.). Retrieved October 06, 2017, from http://www.aaamath.com/geo612x2.htm#pgtp
(n.d.). Retrieved October 06, 2017, from

# Engaging students: Finding the area of a right triangle

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 again comes from my former student Deanna Cravens. Her topic, from Geometry: finding the area of a right triangle.

How could you as a teacher create an activity or project that involves your topic?
One of the most common questions students ask when working with the area of a triangle is: “Why do I multiply by ½ in the formula?” It is a rather simple explanation for working with right triangles. Students could either do an explore activity where they discover the formula for the area of a right triangle, or a teacher could show this short two minute video in class.

So why do we multiply by ½? If we look at the formula ignoring the ½, you will see that it is the same formula for the area of a rectangle. Each angle in a rectangle forms 90 degrees and if we cut the rectangle along one of the diagonals, we will see that it creates a right triangle. Not only that, but it is exactly one half of the area of the rectangle since it was cut along the diagonal. Another way of showing this is doing the opposite by taking two congruent right triangles and rearranging them to create a rectangle. Either way shows how the ½ in the formula for the area of a right triangle appears and would be a great conceptual explore for students to complete.

How can this topic be used in your students’ future courses in mathematics or science?

Students are first introduced to finding the area of right triangle in their sixth grade mathematics class. One way that the topic is advanced in a high school geometry class is by throwing the Pythagorean Theorem into the mix. Students will know that formula for the area of a right triangle is A=½ bh. The way the topic is advanced is by giving the students the length of the hypotenuse and either the length of the base or the height, but not both. Students must use a^2 +b^2=c^2 in order to solve for the missing side length. The side lengths will not always be an integer, so students should be comfortable with working with square roots. Once students utilize the Pythagorean Theorem, they can then continue to solve for the area of the right triangle as they previously learned in sixth grade.

How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

In this short music video young students at Builth Wells High School did a parody of Meghan Trainor’s “All About that Bass.” They take the chorus and put the lyrics in “multiply the base, by the height, then half it.” This music video can help several different types of learners in the classroom. Some need a visual aid which is done by specific dance movements by the students in the video. Others will remember it by having the catchy chorus stuck in their head. The parody lyrics are also put on the video to help students who might struggle with English, such as ELL students. Plus, it is a good visual cue to have the lyrics on the screen so it makes it easier to learn. No doubt with this catchy song, students will leave the classroom humming the song to themselves and have connected it to finding the area of a triangle.