The intent of this mathematical activity is to have the students apply the Pythagorean Theorem and to show off their creative sides. By this time, students would have discovered the Pythagorean Theorem (a^2 + b^2 = c^2) and that the theorem only works for right triangles.

The students will be using this knowledge to draw and label a nautilus-looking wheel titled the Wheel of Theodorus. Explanation is in the link to the activity below. While students are drawing their right triangles and thinking of what they want to draw using their wheel, they are applying the Pythagorean Theorem by labeling the sides of the triangles (legs and hypotenuse ← they have to use the theorem to find this guy) and labeling the right angles in each triangle.

That’s about it. Short and Simple. Why not give it a try? Click on the link below to see the instructions to start making a Wheel of Theodorus of your own. Have fun!!

Daaaaaaaaaaaaaaaang Daniel! Back at it again with the blog posts!

Today we’re discussing flipped lessons. (See what I did there with the featured image? I literally used powerpoint and flipped the slide upside down. Funny, huh? Laugh. It’s funny)

SWBAT: Every good teacher should know this acronym. It describes the learning objective, or target, that the class should have reached by the end of the lesson. The learning target for this lesson would be dividing fractions.

Students Will Be Able To: Divide Fractions

The digital resources that would be particularly useful would be the Khan Academy lessons on dividing fractions as well as a program where students will be able to play with digital manipulatives that will help them visualize how fractions and operations performed on those fractions can be modeled and . This will be especially helpful for students who are more visually inclined than others. These lessons would be done at home.
“What would you do in class with all that free time?”

Well, for this particular lesson, it would be amazing to set up different math stations that deal with the most common fractions: 1/2, 1/3, 1/4, etc. These stations would have these fractions represented in different ways, and the students would be asked to perform the different operations on the fractions as well as describe what is happening to the models of the fractions with each operation in their own words.

The digital resource (Khan Academy) would be available at each station as a review, or as a way for students who may not have that much access to technology to engage in the lesson and do the assigned lessons at the same time the class is working at the stations.

This lesson would benefit greatly from being flipped because of all the misconceptions students often have about fractions. This would allow them to work with the concepts in the comfort of their own home and come up with their own conclusions about what the lesson was trying to teach them, without any influence from their peers.

Then when the students show up to class, they will be able to compare conclusions and how they might have gotten to those conclusions. They will also feel confident going through the various stations because they had a taste of the material the night before. Any misconceptions they have about the material will be made clear by their classmates or the available media; or, of course, the presiding teacher.

I think this is a fun and engaging way for students to understand how fractions work and how to divide them.

My main objective is to assess where my students are in terms of their mathematical skills since students coming into the classroom are on a variety of levels when it comes to their academic skills.

I want the students to be able to gauge themselves on their academic capabilities and learn that it is okay to make mistakes and that sometimes asking for help from a peer or teacher will always be the best choice to make in my class.

I need to free up class time so I can register students onto WordPress (or some equivalent like Edmodo) accounts so we can do online help forums on the various units we will be covering in the year.

Digital Resource(s) I will be using for the lesson:

I will be using a WordPress blog post with a multitude of links titled with mathematical concepts that will lead students to online worksheets to practice on.

Examples: Addition and Subtraction, Multiplication and Division, Long Division, and so on. *I just underlined them so they are not actual links*

The list will go on up until the last concept we will be covering in the year. A lot of the students may give up before that point since they have yet to learn these concepts, but some will give it a try.

Each “worksheet” will contain around 5 – 10 problems each. 3 – 5 if they are word problems.

Active Learning Strategies

Students will be gauging themselves on how well they are able to do the following concepts. The quicker, the farther. They will have a huge confidence boost at the beginning since the work will be “easy” for them, but the challenge will slowly rise as they continue.

Students will be able to work with fellow peers on problems they are unable to get passed, establishing that teamwork and group work strategies will be used in the classroom.

Once I have finished with setting up the WordPress accounts with the students individually, I am then able to walk around the classroom and interact with the students. Getting to know and/or answering any of their lesson specific questions.

How the digital resource integrates into other instructional elements of lesson – what’s the flow of the lesson?

The flow of the lesson is quite free form. On my WordPress blog post, all the students will see is a bunch of math concept titles that they are able to click on that will send them to a worksheet with problems related to the title. They do not necessarily have to go in order (top to bottom), though I feel like some students will do that. If students are comfortable enough with the concept/skill, they are allowed to “skip” on clicking that link and move onto another that perhaps will provide a challenge to them or that will allow them to revisit a concept/skill they are not strong in and practice. Students are allowed to ask others for help, but only after they have given the problem an honest-to-God attempt.

Benefits for student content mastery, collaboration or learning workflow – Why is it worth it flip / blend some of the content?

I believe it is worth it to doing this because the students (most of them at least) will see that they have learned many things in their academic journey and that they are able to do them all and are going to learn more concepts to add to that repertoire of theirs.

Hopefully, the students will see that math skills build upon themselves and what they are doing is adding tips and tricks to those skills. It is an important skill to be able to do math problems on pen and paper since the work will be saved “eternally”, or until one throws it away, that can be used to check back in and refresh oneself, to have others check your work more visually and easily, and as physical evidence to the teacher that one is doing the work.

I also see this lesson as a practical lesson on the expectations of the class surrounding teamwork, behavior, and conduct in my classroom.

For this project, I chose to use the My Maps feature of Google Maps to chart Odysseus’ journey home after the Trojan War. With this tool, I was able to place points at important locations, and in another layer, I included the pathways in the order that Odysseus visited them. This tool allows students not only to visualize the distance he traveled, but also to actually add up the approximate distance with the tool’s included distance measurements.

This tool also allows you to add images and descriptions to the location points, further enriching the experience. I have added an image and description to the first point on the map as an example. If there was a way to have students editing this, it might be a good group or individual activity to have the students create descriptions, or identify important information to create a more complete representation of Odysseus’ (or any literary or historical) journey.

Featured Image Source: “The illustration for the humorous book The General History Edited by Satyricon” by Alexander Yevgenievich Yakovlev accessed from Wikimedia Commons

Students are always going to have a favorite subject or a classroom that they look forward to going into everyday. When you are a teacher you have to learn to not take things personally and often your classroom will not be that safe haven for every single student. However I still want to know every single know of my students feelings about science and school in general. You cannot truly teach your students well until you understand them as a person. Because of this I explored using the google tool Google Forms. I created a survey that I would have my students take within the first couple days of a new school year.

I created a brief version of what I wanted, outlining the different topics I would want to cover. If they like science, if they think they are “good” at science, do they feel like they are a smart as they are ever going to be and what do they want to learn this year. These are the different topics that I would want to learn about from my students.

Understanding where your students frame of minds are when entering a science classroom can be key to running a successful classroom. If students are not interested in science I need to plan super engaging lesson initially to make sure to grab their attention. If students have specific requests about what they want to learn and I can incorporate them great! If I can’t maybe I can point them in the right direction to learn more about it. I need to know whether my students have growth mindset or whether that is something I need to incorporate into my teaching. These are all important elements that I can gain from a survey and Google Forms makes it even easier to manage!

Today we’re going to follow the path of a medieval Spanish guy who was known as El Cid, or the Lord. You can think of El Cid as the Odysseus of Spain: legendary, super-heroic, courageous, indispensable. This was a real man, an admired military commander and nobleman of medieval Spain who went on to become a mythical giant through the renowned Spanish epic poem entitled El Cantar del Mio Cid. What lingers and continues to inspire about this man was his unstoppable resolve, his ability to act fearlessly in the face of obstacles, and his ability to gain the support of even some of his enemies.

Our activity revolves around the Cid’s journey throughout his military campaigns. Using Google My Maps, we can create a map charting Cid’s stops along what has become the modern Camino del Cid, a trail that draws tourists to traverse the path of Cid and see many historic sights along the way. After reading some of the epic poem in class, we can go on to visualize the journey by creating this map, which allows us to add pictures and notes at different points along the way. Maybe some will be inspired to one day hike the route as well!

I made a customized map showing all the places that Alexander Supertramp went as he ventured across the USA. I would use this as an actual lesson in the class I am hypothetically teaching. I think this program would be extremely useful for students that learn more through visuals, rather than me just talking directly to them. The benefits of using “My Maps” is that there can be a wide range of media included into each map: a picture, description, or even a video. This application has many uses– it can teach kids about the March to Washington, or where in the West settlers migrated to, or outline wars from a specific ancient dynasty. There are an endless amount of uses for “My Maps”.

I will definitely keep using this app. Out of all the things I’ve learned in this class, this is what I’ll take home the most. I think “My Maps” is essential to use when going on road trips or any big trip abroad. As for teaching, I think “My Maps” is a perfect way to show students the history of movement. It simply shows the entire world, which encompasses all that we ever learned from. However, this app will not help Astronomers. That is the only downside…Maybe in a couple hundred years Google will have a “My Maps” that is compatible with the universe? Just a thought.

Featured Image by: Christiano Mere, entitled “Alexander Supertramp

I used Google Forms to create the following self-assessment for students in a pre-calculus class.

Students would complete this form at the end of a semester/quarter. The intent of this activity is twofold:

In order to receive some feedback about my teaching performance, I ask students to tell me one thing that they thought I did well and one thing they thought I could do better to help them be successful in class. I can use the student feedback to help myself improve as a teacher. Initially, I had a field for students to enter their names, but I chose to delete this question so students could answer more candidly. I also devoted one question to finding out whether or not students think the material they learned will be useful in their lives. I always try to make math lessons applicable to the real world, and this question tells me how well I did this.

Students are given an opportunity to reflect on their own performance throughout the semester. They might consider if they need to stay more organized, put forth more effort, or ask more questions. The intent is that students reflect on their performance and then improve in following semesters.

Since I am already pretty familiar with many of Google’s most used features, I thought I would try and create something that I have wanted to set up for my class in the future – a blog! Unfortunately, Google hasn’t progressed that far yet, and they don’t have an option for a class blog that can be built into Google Classroom. I decided to play around with Google Sites, and I created a relatively simple class website that I could share with parents and students to give them access to what is going on in school, and to get easier access to a calendar where students can see what is going to be due soon. I also envision having a place where students can download copies of homework assignments so that if they lose them, they can print them at home or submit them to me online. I feel that this website could contain many features, such as a place for students to post or to comment on things, but I did not see anywhere that that could be an option.

The other thing that I found that I want my students to install on their Chromebooks is this app called “Google Cast for Education” which allows students to cast whatever is on their screen to my computer so that I can display it on the Smartboard which is connected to my computer through a wireless AppleTV connection. Often students will be researching something, or will want to display something on their screen to the class, and rather than sharing it with me or having me find it on my computer, it would be useful for students to have this installed on their Chromebooks.

I see a future where there are no more desks or pens and paper in a classroom, and all there is are places for students to sit and work on their Chromebooks, and all the learning and assessment is done on their computers. I see furniture that is flexible and easy to move to make space for collaboration between students and the teacher, and I think Google is the leader in getting us towards this future.

The other thing that I found super cool while exploring some of the “Hipster Google” apps was the Google Trends app. It allows you to see in real-time what people all over the world are googling, and what popular Google searches are happening in countries all over the world. I’m not sure how it would be beneficial in an Educational context, I just thought it was a cool feature, and a cool way to see what people are interested in in this specific moment in time. I also set it as my screensaver.

How much did that title trigger you? I’m not a shill, I swear!

If you understood any of those words, good on you! If you didn’t, chances are you stopped reading and went to Google to look up the definition to try and understand what I was trying to say.

These slang words are everywhere. Even the word “slang” is slang for shortened language. You hear it all the time: on the radio, in your home, from your friends, if you’re a teacher definitely in your classrooms.

Let me tell you a thing, man. If you want to do a rad math lesson that not only introduces trends but gets your kids engaged because it’ll relate to them in the best way possible: they speak that language. Not only will they be super excited to be speaking their hipster tongue, you’ll also (hopefully) get them super excited about speaking your language: math.

Here’s a really cool site that you can use for the lesson:

It’s a card on Google Trends and it is amazing. This particular card shows you the top rising definitions of last year (2016) and how it is ranked based on how often they were searched in Google.

Click on the image to go straight to the card. You can scroll down to see different representations of the same data Google has been collecting over the past couple of years; even the top rising definitions of words from previous years.

But how would I use this in a lesson? And why would I ever encourage my students to use language that I don’t understand in the classroom?

Let’s face it. Students are more and more distracted every day by the various forms of technology they are exposed to; I am not an exception to this because just now I checked my phone to see if I had a message from anyone….

Why not use this distracting quality of technology, and the students’ overuse of slang, and at least attempt to make it educational? They’re going to do it on their own at home anyway; might as well make it relevant to the subject matter you’re teaching.

With this Google Trends card, you can prompt students to think critically about:

How these words got popular

Why some words might have died out

Predictions about how much longer they’ll stay popular based on their own personal experiences/uses of the words as well as the data on the site.

Plus, the site is really interactive, so even kids that aren’t usually engaged will want to play with the cool colorful things they see on the site, or explore any of the other Google Trends cards that are available.

Trending word definitions are not the only things you can look up on Google Trends. There are sections about everything and anything that somebody has put in their search bar and pressed enter.

Here’s what their card on Global Warming/Climate Change looks like (click on the picture to go to the website):

You can see how each major city/country ranks regarding the frequency of searching those words on that list on the left. It’s incredible. Google Trends is one of many leaps Google has taken to visualize data to make it easier for educators to present and analyze information they have been collecting. You would also be doing your part as a citizen by spreading awareness and making sure your students, or anyone who would listen to your lesson, are able to make well-informed decisions.

They will also avoid sounding like know-it-alls who have no concrete information to back their claims up. They could just pull out the notes from your lesson and the activity they did and present the same information, thus increasing the number of people who are aware and are able to make informed decisions.

What is groovier than using the word groovy? Answer: Being able to use tech tools to realize the relative usage of the word “groovy” throughout time and thus conclude that perhaps your smooth colloquialisms might not be so smooth or hip after all. Good news: There is an abundance of alternative adjectives; maybe with some more research you can identify your optimal adjective of choice.

Which brings us to the reason for thinking about word optimization after all – as a slightly more creative method of learning about rates of change, critical points, and optimization in a Calculus class. I’ve designed a lesson that involves students researching word usage to apply the information they will have learned just prior.

After this lesson, students will be able to:

Identify on which intervals a function is increasing or decreasing.

Identify whether slope over an interval is increasing or decreasing at an increasing rate (accelerating) or a decreasing rate (decelerating).

Label critical points and make conjectures about the cause of these points.

Identify local and global maxima and minima (ie. extrema).

Apply the Extreme Values Theorem to a graph and explain why, when the conditions of the theorem are satisfied, it assures that the given point is a global maximum or minimum.

Basically, students will use Google Ngram to look up word usage over time and select a few of the resulting graphs to analyze to practice applying what they will have just learned about the topic in a fun way.

For example, students might look up the word “groovy” – yes, I said it again… I’m just helping the search rankings for this poor antiquated word to go up a tiny percentage (I should know better than this) – and the following result will appear:

I particularly like this example because of its graphical qualities – it has a clear increase and decrease and is not very choppy.

Once students have found a “nice” graph, they will then identify a given list of qualities such as maxima, minima, extrema, signs of the slope (derivative) within intervals, and signs of the derivative of the derivative (acceleration) within intervals.

Next, in order to connect this activity to real life, I will ask students to make predictions about why a word gained or lost popularity over a given time period. To make an informed prediction, they might research relevant events that occurred in the given time period and how this might then have affected common word usage. In essence, I want them to realize that graphs tell stories and that math is a tool that we can also use to communicate, illustrate, and explain these stories.

One data visualization tool that would be helpful for students to use in a math classroom is Desmos graphing calculator. I could use Desmos in a lesson about graphing sinusoidal functions. I might begin the lesson by instructing my students to log on to Desmos and simply modify the equation in any way that they wish. I would instruct them write down what they observe as they do so. After they have had some time to explore, I might provide a worksheet for some more guided practice. The worksheet might ask them to do things such as add a constant to the equation and observe what happens. Students should notice that the graph is moved up by whatever constant they added, like in the image below.

The worksheet might also ask them to multiply the sine curve by a constant. When doing so, students should notice that the sine curve gets taller.

The use of Desmos graphing calculator allows students to quickly and easily see how modifying the equation changes the graph. Once students have any idea of different modifications change the graph, I would introduce formal vocabulary for the modifications. For example, adding a constant creates a vertical shift and multiplying by a constant changes the amplitude of the sine curve.