3D Rendering

Humans are creative creatures. Whether finding ways to turn branches and leaves into shelter, or turning whale oil into candles, or tweaking electrical signals to be able to transmit voice through a telephone. Innovation is often born of necessity, but it can also be the catalyst which transforms innocent curiosity into great discover and growth. Not all of our students are on grade level, or proficient in every subject, but every student in all of our classes is creative, and we should be using that to teach them deeper level thinking and analytical skills. This is where 3D rendering comes in.

In talking with other teachers it seems likely that at most of our schools there is probably at least one classroom with a 3D printer in it. That allows for rendering to be taken to another level, but is hardly a requirement for students to be able to get something substantial out of it. In fact, we have yet to print anything out all year, but my students regularly render objects for an assortment of tasks.

Fifth grade math we get into three dimensional shapes and learn volume. Students can use place values cubes and other manipulatives, or they can draw out 3D shapes on graph paper. These are good ways to gain a conceptual understanding of shape. Though when you have to attend to precision in rendering a rectangular prism, ensuring sides measure out exactly as they are supposed to, students have to access a level of thinking and analyzing their creation deeper than stacking cubed manipulatives.

Image of a student produced 3D bridge renderingScience brings up a variety of ways we can take advantage of 3D rendering. Classes in many grades have students tackle engineering design challenges, and allowing them to create something much more significant than toothpicks in marshmallows allows these challenges to become more meaningful. You also have the ability to add constraints to their builds. If students need to create a bridge, you can give size requirements/limitations and students need to think more analytically to bring their designs to life while following these outlines.

Teaching modern or digital art can offer other uses. There are a variety of free programs or websites available for use, such as Tinkercad, but many require students to make accounts that have to be verified by a parent, so that needs to be done ahead of time. If you are not sure how you may use it, try one for yourself and explore. Your students may amaze you with what they can create. Last year my students designed the keychains we 3D printed and sold at the school carnival!

 

GSuite in the Math Classroom Part II

For the past few years, I have assigned slide presentations and technology based projects as options in semester final projects. In the 18-19 school year I made presentations required since they need to know how to use presentations for not only the SBAC but in college and career.

Each student pair is assigned a topic lesson that is covered on the semester final.  Students are to do a multitude of tasks along with their Google Slides presentation. Students are to create interactive activities using technology such as Kahoot, Quizizz, Quizlet, etc. for the class to do during the couple of weeks right before finals as part of their presentation.  In at least one of the examples that they do on their slideshow, they must use Desmos to create a table, diagram or graph that models the situation.  I created a folder on Google Classroom where their Google Slides will live as they work on them so that other students can look at their work to help them review for the semester final. It becomes an amazing resource for their semester review that they themselves created and can use!

Students were given a couple of months to work on their project. All of my classes had to do this project. At the time of this writing are currently working on semester 2 final projects.  There are some pictures and a video for you to see how the presentations are run. They are definitely engaging and student led. Enjoy!

As I have previously stated in part one, implementing the use of Google Apps and other technology in the math classroom covers at least two topics from the Common Core 8 Mathematical Practice Standards.  Students are engaged by modeling with mathematics and using appropriate tools strategically.

I am a lifelong learner and this year has been quite challenging. Many would say that I am well-versed in technology usage but I disagree. I have much to learn and have enjoyed this journey immensely.  Have a great new school year and I hope to do something innovative this school year!


Below is a gallery of pictures from some of the student presentations.

Some teams of students created an interactive activity using Quizlet. Students also had to create presentations to demonstrate their mastery of concepts.

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In the video below students are participating in a student led interactive activity using Quizlet.

 

GSuite in the Math Classroom Part I

This school year I have given multiple professional development workshops on using Google Suite in the classroom. I had also challenged myself in creating them for my students to use in a few of our units of study.  

In our Algebra 2 course this year, I had created a template for personal budgeting as an introduction into our unit on Exponential and Logarithmic Functions. Students learned how to use the functions on Google Sheets along with inputting data and information.

Here is a link to the all the functions you can use on Google Sheets.

Image of a students budget.After using my template for a basic budgeting activity, students were assigned to do research on a career choice and look up statistics on income, future outlook, education requirements and experience requirements. Students then created their own personal budget on Google Sheets with data on what it would look like for them in the future where they would be making loan payments and other personal financial responsibility payments. All students were highly engaged and thoroughly enjoyed the projects involved in the unit. Most saw the relevance of mathematical concepts in their life.

Implementing the use of Google Apps in the math classroom covers at least two topics from the Common Core 8 Mathematical Practice Standards:

Standard#4: Model with mathematics.

“Math doesn’t end at the classroom door. Learning to model with mathematics means that students will use math skills to problem-solve real world situations. This can range from organizing different types of data to using math to help understand life connections. Using real world situations to show how math can be used in many different aspects of life helps math to be relevant outside of math class.”

Standard#5: Use appropriate tools strategically.

“One of the Common Core’s biggest components is to provide students with the assets they need to navigate the real world. In order for students to learn what tools should be used in problem solving it is important to remember that no one will be guiding students through the real world – telling them which mathematics tool to use. By leaving the problem open ended, students can select which math tools to use and discuss what worked and what didn’t.”

Image of a students budgetEffective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.  

Creating such authentic assessments took time and strategic planning. But the rewards heavily outweighs the work it took to get there.  If you are struggling in using this technology software, here is a link to where you can explore and learn more on your own rather than me posting steps on doing one type of thing when there is massively more you can do! (Or you can attend one of my workshops in the future!)unnamed (3)

 

 

 

 

 

Online Math Resources

I’ve always felt like it was hard to find good math resources online.  Sure, if you want a worksheet, your options are nearly limitless, but when you want a worthwhile, free, standards-based supplement for your curriculum, it’s sometimes hard to find.  I’d like to add a disclaimer before I go on. In the 2019-2020 school year, every SUSD student should receive rigorous tier one instruction that maintains the integrity of our newly adopted curriculum.  Since most of us are new to this material, I believe we should do our best to use what is provided by the publisher. All of the websites I’m including in this post should be considered a teacher resource.  For example, Khan Academy can be used by adults to deepen their understanding. It should not replace instruction.

Recently, someone shared an article with me that I found to be very helpful. In this link are over 60 websites for teaching and learning math.  I’d like to share the ones that are free for teachers and (in my opinion) will be most useful for Stockton Unified School District staff.  I’m also throwing in a few that are not on the list.

My long-time favorite has to be Khan Academy.  With video tutorial content that can be assigned by the teacher to individuals or the entire class that are standards-aligned, this resource works great for a flipped classroom, as an intervention, or for acceleration. Students can access all content (not just what is assigned) at any time, using almost any device. There is even a version for preschoolers now called Khan Academy Kids. Math content goes all the way up through college level courses and can be customized to follow grade level standards or align to PSAT and SAT needs.  Another website that offers something similar is Freckle.  It has a diagnostic and customizes practice to meet student needs.  A third option is Moby Max.  This website has a paid version that provides more features.  Even more sites that deliver something of this type include Math Help and Splash Math.

In the past, I’ve seen how the Chromebooks can become babysitters while kids play on websites like Cool Math Games, Fun Brain, Sheppard Software or Math Game Time. If I’m being honest, even Prodigy Game is more game than it is learning.  That’s not to say that these don’t have a place in the classroom at all.  In my opinion, they should be relegated to rainy day recess activities because they are games.  Another option would be to tell students to play these games for homework. If we assign specific practice that students actually need, they’d get more out of these programs and they’d probably be more likely to do their homework if it involved playing a game instead of completing a worksheet. One website that goes a little bit further than just providing games is Math Playground. In addition to having games, it also has logic puzzles, instructional videos, and a “Story Math” section that models word problems with step-by-step solutions.

If you’re interested in playing math-themed music videos for your students, Flocabulary and Numberock have free songs that kids enjoy.  If you want a neat site for online fluency practice, Xtramath might be what you are looking for.  Many of the websites I’ve listed provide a variety of resources in addition to the pieces I’ve mentioned and I encourage you to click on the links and explore the features to see what might be beneficial.  The next few links provide what I think are great activities to get your students thinking about math in new and different ways. At  Which One Doesn’t Belong, classes can get into some amazing math dialogue about which one doesn’t belong.  KenKen puzzles are what I would call the next level of Sudoku, and require students to use number sense and mathematical operations to solve a puzzle. It doesn’t have the strongest math problems, but Free rice does give students the chance to fight hunger while they practice math facts because it donates rice with every correct answer.

This section is dedicated to middle and high school math teachers.  I haven’t recently met a single subject math teacher who didn’t already know about Desmos, but if you’re new to the profession, or you somehow missed it, Desmos provides a free online graphing calculator with many features.  In addition, at Teacher Desmos you can find a myriad of activities to use with students.  You’ll want to get comfortable with Desmos if you’re teaching high school math in SUSD next year because it is embedded in many of the Pearson enVision lessons.  A different website that also has a graphing calculator is Geogebra. This site also has 3-D math features and worksheets.  A third reference for high school teachers is Shodor.  This site provides interactive activities for students in grades 3 through undergraduate level.

More resources for teachers can be found at Illuminations.  This is the National Council of Teachers of Mathematics page, and it contains lesson plans, games, activities, and brain teasers from a very reputable source.  The same organization has another site, Figure This, with games, family practice, and challenges in English and Spanish for the middle grades.  Another source for middle grades is PBS Learning Media.  Here, you can find culturally relevant video logs that are added to regularly.  The website Greg Tang Math is helpful because it offers a variety of resources for both student and teacher learning.  Like many other pages, it has games, worksheets, and student lessons, but unlike others, it also provides teacher professional development and center activities (be aware that some are not free).

Finally, one last resource that I have found to be helpful over the years, is Natural Library of Virtual Manipulatives.  Here, you will find virtual manipulatives for just about every math concept from pre-K through twelfth grade.  The site is clearly organized by math strand and by grade. Unfortunately, there may be issues with Java, depending on which device you are using to access the website.  However, if you are able to use these virtual manipulatives with students, they can be very powerful and are a free alternative to purchasing physical manipulatives for your class.  If you’ve read this far, I hope you came across at least one resource that will support student learning.

The Argument for using Google Classroom with Digital Immigrants, Digital Natives

Digital Native? Digital Immigrant? What is that? As teachers, we often tell our students to break down the words we don’t know and to piece together using context clues. Most of us educators will look at the digital and understand that it refers to a technology in some capacity or more likely the computer. But how does being a native or immigrant fit into this picture? Great question! Natives are people who are residents who live in a certain area. Immigrants as we know travel from one place to another. This is also in the very true in the world of technology we live in today. In Marc Prensky’s article “Digital Native, Digital Immigrant”, he discusses the world we live in through the lens of digital literacy and knowledge of technology.

Prensky talks of “digital natives” today as the net generation or digital generation – Kindergartners through college who have grown up with everything digital – Internet, TV, computers, computer applications, digital music players, video games, etc. “Our students today are all “native speakers” of the digital language of computers, video games, and the Internet” (Prensky, p. 1). Prenksy discusses how technology has infiltrated all aspects of our lives and instead of purposely leaving out technology or having it become a baby sitter, using it to deepen and further learning is essential for students to be prepared for 21st-century learning.

Prensky goes on to discuss who are we that did not grow up with this digital technology? As time has passed, people who have seen technology come into our everyday lives and have seen it take over our daily life are known as digital Immigrants. Prensky says “Those of us who were not born into the digital world but have, at some later point in our lives,  become fascinated by and adopted many or most aspects of the new technology“ (Prensky, p. 1-2). Our students feel the same way about technology. The fascination of what the possibilities are boundless when our students enter the cyber world. We as immigrants have to be more understanding that technology is here to stay and to keep our kids engaged and prepared we have to mold and adapt to our students, not for them to mold and adapt to us.

As we move into and through the early parts of the 21st century, it is essential that we as teachers bring technology into the classroom and give our students opportunities for them to use technology the correct way and how it correlates with college and career readiness.

Starting a new school year is the perfect time to implement Google Classroom into your classroom. It allows you to cover the importance of routines and expectations around technology in your classroom and to stress the importance of how to become responsible digital citizens. With that being said, here are five easy ways to implement Google Classroom into your daily teaching assignments and activities to improve your classroom instruction and engagement when starting the new school year.

 

  • Posting questions for simple quick writes

 

unnamed1This is an essential first for the digital immigrant. By posting questions or simple prompts through the question tool, it gives your classroom a chance to open the door to technology and see what amazing opportunities can happen through learning through this media. By posting a simple question or prompt online, students can: practice typing, get familiar with the keys, learn to navigate the computer to go to google classroom, and finally, how to post something that positively contributes to a learning environment.

As students get comfortable posting their answers, you can then allow them to respond to other students in the classroom to promote the sharing of ideas and learning how to give proper feedback to their peers.Untitled 3

This is important because students then feel their work has value and has meaning and purpose. This will take time to practice with norms and expectations, but students do enjoy responding and learning how to engage in discourse on a digital platform. It is a great opportunity to teach them real work life skills on how to communicate with peers in acting in a professional setting. This will transfer to other forms as they grow and mature (or at least we can hope).

 

  • Posting math word problems and students explaining thinking

 

unnamed 4This is another great introductory tool for teachers to have students use math with technology. This is also great support around SBAC (hint hint)! Post a general word problem and have students explain their thinking about how they solved it. Start off simple with number sense or easy addition or subtraction problems that students can generally explain with their words. Not only will students feel confident in answering questions, but they will learn how to use proper vocabulary in explaining their thinking. With the shift in math being more explanatory rather wrote notation, it’s important to build in simple activities to show students and have them practice how to explain their thinking, which translates into college and career applications later.

 

  • Announcements – links and general news

 

We all get sent links throughout the year to give our students and or parents to take for feedback. Google Classroom is a great way to push these links instead of writing them on the board or trying to type the right link!

To do this, click on the giant plus sign in the lower right corner.unnamed 5

Click on the announcement option, and then you may type your instructions or note for what you want your students to do.unnamed 7

From there, copy the link you need to use and insert into the link option in classroom. By doing so, it will automatically take students to the survey/website/video you need them to go to without worrying about typing the wrong link in the URL bar. Plus, this saves time in making sure all students can get to the right website quickly and effectively. This also helps with instruction if you want students to read online articles or go to a certain website like ST math, Starfall, etc.

These are just a few ways teachers who are digital immigrants can acclimate to the 21st century in the classroom. As always, make technology work for you, not the other way around!

Teaching Math In the Digital Age: The Debate and More Resources (Part 2)

My experience with intertwining technology into my Math curriculum has been a roller coaster. Initially, 5 years ago, the attempt to combine the two knocked me down and out more than Mike Tyson in his prime. Once the initial problems occurred I felt like throwing in the towel but I knew if I could use tech with Math my lessons, student engagement, time management, and data collection would all be improved if I stuck with it.

Now, five years later, I have a system that is working for me and my population of students. I know that there are naysayers out there that are totally against anything tech in a math class besides a calculator, but I can say from my experience that student growth and achievement have gone up in my classes since I introduced tech into the game. My students are not always locked into a screen and there is always a time to put pencil to paper, or expos to whiteboards. What I am trying to get across is that there are powerful tools that technology can provide educators and I believe it is our duty to teach our students how to use them correctly so they can implement them in their college or career choices.

There have been many studies regarding tech with math and the overall consensus is that technology should be used to bolster learning. Researchers have stated that the key to being successful is to get accustomed to the programs and be educated on what you are exposing your math students to, so they can have success with the tech. There are downsides to using tech like distracted students and cheating, but the benefits far outweigh the cons according to research.

Picture of student working on a computer.

Students use Tinkercad to design 3D objects and models.

On that note, I am going to give you, the reader, a few more programs that are extremely effective when it comes to student engagement and technological skill. The first being Tinkercad, which is a student friendly version of Autodesk (design program). This program allows students to create 3 dimensional objects and can be used for geometry but also for engineering purposes. Tinkercad is used best when the teacher has a 3d printer because student ideas can come to forwishen over the course of a day of printing. I have used Tinkercad to teach area, angles, and volume for different shapes.Perfect cubes, cube roots and finding square roots could also be taught with the program as long as you take the time to create an assignment that includes Tinkercad. If the students have a google account they can save their designs in the cloud and upload them into google classroom with a few clicks of a button because it is a cloud based program. There are tutorials for the students and teachers on the site, and the best part of the program is that it is another free resource. The skills that students learn in Tinkercad can be used for jobs of the future and enable students to creatively engineer.


The next program is mainly for students to obtain vocabulary terms in a fun and creative way. It is called Flocabulary. Flocabulary is a website that creates rap music based on many different subjects and topics. My students enjoy the music and seem to retain more of the terms than traditional ways of teaching vocabulary in Math and any other subject. The students will usually watch a music video, do a few exercises based on the video, take a quiz, and then create their own rap using the vocabulary they used. This program is also synced with Google Classroom, so adding students and classes is as simple as a few clicks of the mouse. The only issue with this program is that it is not free. There are individual, school, and district plans that can be bought and are definitely worth the price.

Implementing these two programs will get your students more engaged and subsequently give them tools that can be used for their entire lives. Whether it be designing a new logo, car, a shape, or making music with a program, the students will definitely be better off going forward in their education with skills that are applicable to the real world. In this day and age being creative and collaborative are highly valuable in the work world and I believe we as educators should use the tools that will enable students to attain these skills rather than stifling their creativity with the same old curriculum.

Teaching Math In the Digital Age: The Resources (Part 1)

Teaching Math in this age requires a lot of technical skills when it comes to creating and implementing curriculum. Luckily there are many programs out there that can guide you on your path to teaching Math in this day and age. In this blog I will give you a quick rundown of the tools I use with my students as we go from paper and pencil to stylus and screen.

The first and most interesting website to me, which is incredibly interactive, is Desmos. Desmos is geared towards most standards from 6th grade to college calculus. It can double as a graphing calculator and the best part is that it is totally free.There are interactive activities that students can give feedback in anonymity, manipulate graphs, and even play games with. You as the teacher, can easily connect this program and activities through google classroom or many other mediums by creating a class code, copying it, and pasting it into a link in Google Classroom.

This leads me into the next program/programs that I use daily which are Gsuite, (formerly known as Google Apps For Education). The main program that I use to give access to websites and information to my students is Google Classroom. It is very easy to set up and can generate class lists for all of the programs I am mentioning in these blogs. To assess my students I use Google Forms which can allow teachers to insert answer keys into the assessments so students can get instant feedback. It also frees up time for teachers because Forms will do the grading for you. There are always new features coming out, most recently the screen lock feature which will lock the screen as seen in Smarter Balanced and MAP assessments. You can also import grades from Forms into your Google Classroom if you do chose to use Google Classroom’s grading system.

This leads me into Google Sheets which can be used as grade sheets all the way to creating graphs of students’ data. Students and teachers should get familiar with Sheets because it can save massive amounts of time for teachers and gives students a tool to use in their future endeavors. I mainly use it for data analysis of assessments and to post grades in Google Classroom. The students use it to collect, organize, and display data with graphs and tables. I will introduce Sheets to them once we have gone over general statistical analysis tools and how we derive them. Once they know how they work, I will show them that they can compute what would take them 20 minutes into 1 minute. This saves time for the students and allows them to get a better grasp on the story the statistics are displaying.

The beautiful part about Gsuite is that a student can create a spreadsheet and insert it into Google Docs or Google Slides with a few clicks of the mouse. The student can display data in a presentation with a pie, bar, and many other types of graphs of their choosing. The students can all work on these platforms together through sharing them with other classmates, which allows collaboration to be done anywhere, anytime, very easily. Once the students are done with their assignments or presentations all it takes is a couple clicks of the mouse to turn them in to me in Google Classroom.

In part two of my blog I will go over more online platforms that go deeper into Math and Science which can easily be posted into Google Classroom for easy access. If you start with a few of these programs mentioned above, it will not only save you, the teacher time, but it will save the students frustration by making collaboration and access to materials extremely easy.