Blended Learning

Imagine the tardy bell rings, you walk in your classroom, and students are on devices or in groups already working. Think this is impossible? Think again. Now I am not promising that one student who never stays seated will jump right to work, but it is possible to motivate most of your students into starting without you.

Blended learning is where a portion of the traditional face-to-face instruction is replaced by web-based online learning. My last blog talked about online learning. Now I want to tell you how to get there from here. Any teacher can start adding bits of online learning into your day-to-day activities. In fact you can find several resources such as my Why of Math YouTube channel to help you out. Khan Academy is another good resource for video tutorials and practice work. Don’t overwhelm yourself trying to find several things at once. Search for a few things at first and add to them each year.

The key to good blended learning is to keep the traditional discussion/report out time. True online learning does all discussion on forums or social media. Formative assessment must be taken from this or sporadic quizzes. This is not necessarily bad but definitely different. Blended learning can still take advantage of face-to-face round table discussions facilitated by the teacher which you are already used to doing. Students are also used to this as their milestones and accountability. Remember that this change should be a process. As more and more online tasks are added to the day-to-day activities, students will become more accustomed to procedures and what is expected in this type of setting. Trust me. I use this type of learning everyday, and the students adapt to it well. I still have some normal discipline issues, but in the last two years I’ve only had to fail one student.



Online Learning

In case you haven’t noticed, online learning is everywhere. I have experienced it as a student and a teacher. Although there are actually many different types of online learning, there are three I see most often in organized education. One is where the course is laid out and the student just works through the lessons and assessments until proficient. This type has predetermined scores for proficiency, and the computer grades all assessments. Another one is where there is a teacher but the only communication is through email and forums, and the content is released on the teacher’s schedule. For this type the teacher creates the assessments and decides the final grade. A third type involves actual interaction with a teacher through online video conferencing. Like the last type the lessons and assessments are posted by the teacher on a website for students to use, but the students must video conference with the teacher on a certain schedule.

The most common comment I hear about online learning is, “ Students can’t learn without a teacher doing the talking.” Really? I have 5 years experience teaching a class where everything students learn is online. Yes I am in the room, but I am not the key giver of knowledge. The wonderful world wide web is where students get most of the information for their projects. I do believe there should be an adult in the room reminding students of their goals and there should be consequences when goals are not met in a certain amount of time. However, any subject could be learned in this manner…yes even math. Here’s a little secret. Most students would prefer to learn this way. For the past 5 years I have had over 80 students per year and every year I ask them what they prefer. I have not had one student yet that said they would rather sit in a classroom while the teacher talks then do work. All of them say they would like someone available to ask questions if needed but didn’t mind if they needed to email or video conference.

Now for those teachers who think I am trying to do away with their jobs, stop and think about it. Someone has to write the curriculum. Someone has to create the tasks. Someone has to be that person responding to emails or video conferencing. These people should be educated, certified people. We just need to rethink what our roles will be in the future. I hear educators use the phrase “what’s best for the students” all of the time. My question is do you really mean it?

Math the Fun Way

I know it has been awhile since I have posted.  Life happened and I no longer have time to do the nice screenshots and put them together with a lesson plan type post.  However, I do think teachers need support to make their life easier and I want to help.  After some thought and consideration along with much prayer, I want to take this blog in another direction.  My students always bug me about letting others know about my ideas for how to change the way schools work.  I think now is the time to start and I will of course start with math.

I have interacted with hundreds of math teachers over the years and can classify math teachers three ways.  There is the teacher who works so hard to make the students work harder and gets nothing but more stress.  Then there is the teacher who does just enough to keep his/her job and cares little if the students ever get anything.  Finally, there is the teacher that gets it!  This teacher knows math must be interactive to grab students’ attention.  This teacher knows it must be fun.  For this generation it must involve technology whether we like it or not.

Technology is creeping its way into education. Yes creeping!  Teacher’s using it for a gradebook and lesson planning doesn’t count.  Math games as a time filler or even a reward DOESN’T COUNT.  Technology must be incorporated into the classroom completely from the lesson hook to the investigative learning activity to the assessment formative and summative.  I have begged teachers to let me help move their classroom to a more interactive environment and have been refused.  Some of them even commented their students can’t learn “that technology” enough to use it effectively.  Are you kidding?!  I’ve seen 3 year olds work an iPhone!

Some teachers will never get it, but if you are reading this today please consider what I am saying.  There are so many free lessons out there that incorporates technology.  It would not be hard to start.  I have even created a YouTube channel (Why of Math) so teachers can have intro videos for lessons that can be your hook.  I’m not saying to change everything overnight, but once a month would make a big difference.  

CAS with Hydroponics

Real STEM can sometimes be hard to implement in a regular math classroom, but it can be done with a little planning.  It also helps to get a science teacher involved for some topics to consider and help with the scientific concepts that are not covered in math.  One STEM project I use in my class is a hydroponic garden.  

For those die-hard gardeners that are familiar with this method, ours is more aeroponic than aquaponic.  For those teachers who want the plants to actually produce no matter what the students do to it, you may want to purchase an all-in-one kit like Miracle Gro has; but if you want the students to really work for the product, let them start from scratch.  “How does math play into this?” you may ask, but I promise you will be amazed.  I have used both the all-in-one kit and the “from scratch” kit.  The “from scratch” kit is just a rubbermaid container, fish tank pump, small baskets to hold the plants, some purchased growing medium, lights, and seeds.  You can find this setup on the internet along with hundreds of others.  Mine holds 6 baskets so 6 groups of four can work with one set up.

Now for the math!

It seems growing plants in this method takes lots of measurements and applying the right solutions.  First most plants need the temperature to stay between 55°F and 75°F.  How many of your students can read an old-fashioned thermometer?  Think vertical number line.  Here is a real world situation where students can apply the number line.  The thermometer has tick marks between the whole number so the students can study decimals.  It also models inequalities since the red line needs to be between 55 and 75.  You can use these discussion questions:

  • What values work besides 55 and 75?
  • What values would not work?
  • What other things can you think of that would use measurements this way?
  • How can we control the temperature if it goes outside the boundaries?

Using technology like the CAS you can create a table of collected temperatures over a period of time and graph them to predict what the temperature may do at certain times in the classroom.  You can also discuss why it may happen.  The TI-Nspire CAS can also use a Vernier probe to read the temperature in real-time for different places in the classroom.  Is by the window better or close to the door?

Let’s throw in some percents.  The ideal relative humidity for plants is between 30% and 70%.  For real outgoing teachers there is a free relative humidity calculator at .  Or you can get a relative humidity Vernier probe and plug into a computer and use TI-Nspire CAS software to collect the humidity data over time.

How about light spectrums?  Certain light spectrums are better for certain plants and this is tied to Watts and Watts is tied to cost.  Students can calculate the Watts their plants are using with Ohm’s Power Law (Volts * Amps = Watts).  Remember your CAS can manipulate this equation to investigate the different variables.  Your students can then investigate how much your hydroponic garden is costing.  For example, if it cost $0.05 per KWH and the lights needed to be on for 12 hours a day for 4 weeks, what would the total cost be.  Once again tables can be created and graphs plotted to analyze.

Let’s not forget proportions.  Hydroponic gardens no matter what the type need the nutrient solution that feeds the plants.  Different solutions have different instructions but they are all in ratios.  For example, FloraGro uses ¼ tsp/gallon for seedlings.  If the container holds 5 gallons of water, how much solution do you add?  My students had a higher level of difficulty because the measuring cup we had was in milliliters.  The metric ratio was 33 mL/100 L.  They had to convert gallons to liters then do the proportion.  That TI-Nspire CAS came in handy!

Plants grown using hydroponics grow faster than normal methods but they still take weeks to mature.  You can have these in your classroom year around and just use them when ready.  If proportions don’t come until November, no problem.  If you want to use the thermometer for decimals a month before you do proportions, no problem.  The systems can be planted at any time and studied for however long.  


CAS at the T-Cubed Conference

First of all I will apologize that I have not found the exponent feature on this website.  For those of you who don’t know, the conference name should actually have a “3” raised above the “T” instead of typing it out.  It stands for Teachers Teaching with Technology and is one of the best conferences you will ever attend.

This year I did two sessions: One on coding and one on CAS of course.  It is always wonderful to be around like-minded people who believe if we keep doing things the way we have always done them then the results will stay the same or worse.  Also as educators we have to share our new ideas and what has worked in our classrooms so that others can change for the better without repeating the same mistakes.  If I had to choose one “take-away” from this year’s conference, it would be that STEM is our now and future; and if schools including colleges do not start to move in that direction, we are doing our students a disservice.  Now what will I do with this “take-away”?  I plan to start incorporating more STEM in my future blogs.  CAS is perfect for STEM especially with data collection.  You can go from collecting the data to analyzing data all on the same device.  I plan to work on wonderful examples to pass on to my readers during the upcoming months.  Stay tuned!

CAS with Proportions

This lesson deals with teaching not only proportions but proportional reasoning that will have connections from 6th grade through 12th grade.  This is a very important foundational skill for not only future math courses but science course and elective courses as well.  Let’s start with connecting to fractions.  Students will have seen fractions and their equivalents on a basic level so let’s connect with that prior learning.  Place the slide below on the board and ask the students:

  • Why is each one true?
  • What math is being done to the first fraction to get the second fraction?


Now ask if they can share a false example.  Let them use a CAS device and they can investigate before answering which gives them more confidence to answer.

Now let’s look at these fractions in context.  Context is always an important part of a lesson so students can relate to the numbers.  For my example I am using boxes and crates.  This can be modeled easily with blocks and cups, M&M’s on a certain size paper, even real boxes if you can get the different sizes.  The key is nothing fits perfectly.

Discussion Question:

If 6 boxes fit into 4 ½ crates, how many crates will it take for 1 box? for 100 boxes?


Using the CAS students can easily use the words “boxes” and “crate” as variables to do the investigating and keep it contextual.  Students can look at the different representations and make connections between the numbers and the application.  For example the graph below is created from the spreadsheet above without retyping anything.  Create a graph page and SELECT your variables created by the spreadsheet.  It reinforces the relationship between the data, coordinates, and graphing.  All graphs come from data not randomly generated numbers.


After this introduction some good activities to use throughout the unit are TI’s Recipe: Unit Rate, Proportionality in Tables, Graphs, and Equations, and/or Proportions in Stories activities.  I really like the Recipe:  Unit Rate because it ties the previous unit rate knowledge into proportional reasoning and it is contextual.  The other two activities move into the more advanced graphing and equations part of proportionality but still shows the students that slope is just using proportional reasoning for more complex problems.

I feel that we as educators sometimes tend to treat graphing as a separate entity, so the students see it as something completely new.  Actually it really is an extension of proportions and proportional reasoning.  “Slope” is not a new concept it is just a different use for proportions.  If we build on student’s knowledge of equivalent fractions and unit rates to progress into proportional reasoning then proportion calculations and graphing, students will see a natural flow instead of a new beginning.