## 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 andrew.rsmas.miami.edu/bmcnoldy/Humidity.html .  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.

Updated Note: Since I wrote this blog Texas Instruments has started posting STEM activities and even offers kits for teachers on their website.

## 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 courses 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.

## Blended Learning with CAS

I have been reading about more classrooms using blended learning as technology becomes a natural part of education.  One article stressed that it doesn’t always have to be students 1:1 on computers.  It could be a YouTube video, a teacher made video, Twitter chats using personal devices, etc.  Of course I immediately thought, “What about CAS?”  Although there are CAS applications on computers, there are CAS apps on tablets and of course the TI calculators.  I have yet to come across a teacher in middle school or high school that did not have access to a calculator.  The key is asking for the correct device.

Blended learning according to Google is “a formal education program in which a student learns at least in part through delivery of content and instruction via digital and online media with some element of student control over time, place, path, or pace.”  This definition varies with different sources but all have the same basics:  The student is not sitting and listening to a teacher talk for the whole class and some part of the learning is digital.  Most sources state there is a student-controlled path and pace also.  Using CAS covers all of these things.  TI has activities for their devices that allows students to learn by just using the device and following instructions.  Teachers can create lessons ahead of time and send to the device for students to use.  CAS apps allow for downloading pictures from the internet to be used with investigations of skills.  It is not meant to be the ONLY tool in a blended learning environment, but it definitely should be in your toolbox.

This part of the blog post is going on a little tangent, but I get this excuse all the time.  “My school does not have the money for technology.”  Money is always an issue with technology but there is state and federal money allotted to schools for instructional technology.  There are also grants that are fairly easy to get.

• The first step is to let your administrator know that you want new devices.  Be prepared to negotiate.  The word “calculator” is usually easier to sell than “device” or “iPad”.  If you feel your classroom will benefit more from the tablets, agree to 5 or 6 and use in groups but don’t forget the money needed to purchase apps.  If needed suggest stages, i.e. get 3 each year until we have a classroom set.
• The next step is be willing to follow through by finding out when the district orders technology and keep gently reminding your administrator.  Do the leg work and find out the costs of different solutions and have it ready at all times.
• Look for grants!  Donorschoose.org is designed for schools and has companies just waiting to give you money without you having to find them yourself.  A science teacher in our building received TI-Nspires and probes this year by using this website.

Blended learning is the future and has been proven to motivate students.  What we once thought would be impossible is now not only possible but inevitable.  Are educators ready?  Ready or not it is here.

## Can I do CAS?

I promise I am working on another CAS lesson to share (Hint: think proportionality) but I also love to share stories of students’ first impressions of a CAS device.  As most of you know by now for me this is the TI-Nspire CX CAS handheld or the TI-Nspire CAS iPad app.  In this case it was the handheld.

This week my students took a categorical self-assessment on categories such as utilization of  class time, level of effort, learning new skills, staying focused on assignments, etc.  Next the students averaged their rating for an overall percentage.  They had their choice of a TI-84 Plus, a TI-84 Plus CE, their phone, the computer calculator, or the TI-Nspire CX CAS handheld to do the calculations.  Fifty percent of the students chose the CAS handheld.  Now our CAS handhelds are new to all of these students at this time.  I did not give any instruction I promise.  I just handed them out.  Only one student had a question about how to operate and that was because it opened on the setup screen.  The only other question I received was, “Why does it give me a fraction instead of a decimal when I divide?”  Now talk about a teaching moment!  This happened in six different classes, grades 7th-12th, gifted students to students with 504’s and IEP’s.  Merry Christmas to me!

Moral of the story

One of the biggest obstacles I have to getting teachers to use CAS is they claim that students won’t know how to use them and they do not have the time or knowledge to teach them.  I just proved no EXTRA teaching is necessary and the teaching you do need will be math skills and practices that should be in every class.  I also want to add that Texas Instruments has getting started docs and tutorials for all of their devices for anyone willing to look at them.

So can I do CAS?  The answer is YES!  Everyone can do CAS.

## Inspirational Story

This blog post is a story that made me appreciate being a teacher after a long, exasperating month.  This is the story of a student discovering a CAS device for the first time.

Background:  This student is a 9th grader who had me for a class other than his Algebra I class which he took from another teacher.  I have my TI-Nspire CAS handhelds at the back on the room on the chargers.  All students know them as “calculators” and tend to ignore them unless they are closer than the computer or their phone to calculate.

Story:  One day a student was waiting for a group member at the back of the classroom to make a phone call pertaining to a project.  He noticed the CAS handhelds and said, “I always wondered what these were.  Can I play with one?”

Me: “Of course you can but make sure you do not neglect your project.”

The student turns the handheld on and exclaims, “Cool! I wish I had one of these.”

He continues to investigate the functions of the handheld his other project forgotten.  I think to myself, “This is a teachable moment.”

Me: “Do you know those calculators are special?”

Student:  “What do mean?”

Me:  “Type 1 apple + 2 apple and press enter.”

Student:  “Oh my gosh it says 3 apple!  What if I add something else?”

Me:  “Try whatever object you want.”

Student investigates a little more then says, “I need one of these for my math class.  Can I please, please, please do homework?”

Student:  “I promise to work harder tomorrow on my project if you will let me do math homework today! please, please, please.”

Me:  “I guess.” (I really wouldn’t have passed up a chance to teach a student some math but I didn’t want to give in too easy.)

Student gets out math and finds his assignment.

Me:  “What are you working on?”

Student:  “Quadratics with that equation thingy.”

Student:  “Really?  I want to try.”  Student works a few problems and is amazed by the results.  The student even uses it to teach another student who was absent for the lesson.  This went on for a while and I was loving just watching the learning.  The student eventually investigated what the graph looked like and why it isn’t always 2 solutions.  Then the student made me feel wonderful.  He said, “I wish I had you as my math teacher, Mrs. Bonds.”  He probably just wanted the handhelds but it blessed me and made my heart swell.  I need days like that to remind me why I became a teacher.

## CAS with Unit Rates

Using CAS to allow students to investigate unit rates opens up a world of options due to the device recognizing words as variables.  Teachers can actually enter one cup of sugar makes 2 cookies in fraction form on a TI-Nspire CX CAS and get the results shown below.

Asking questions that promote deep thinking about the topic gets students into the discussion.

• Why are these true?
• What stays the same?
• What changes?
• What other ratios would work?
• What other ratios would NOT work?

Asking the right questions is key to starting effective discussions, but what then? Multiple representations help students visually see what the math is doing which in turn leads to better understanding and skill mastery.  Look at the following situation:

Joe can mow 7 lawns in 4 hours.  How many lawns can he mow in 3 days?

Now look how the CAS can investigate this problem using Numerical form, a table, and a graph.

This allows students to see relationships between “doing the math” and “using the math.”  See how long it takes the students to realize that the data is in hours but the problem is in days.  The number 3 is nowhere in the data which will generate questions from students.  This opens up a broad range of “teachable moments” which is what teachers love to see. The students want you to explain instead of you begging them to listen. Now let’s throw in some geometry.

This introduces using the unit rates for unit conversion.  Although unit rates are a 6th grade skill, students can see how solving equations will play a part even though they haven’t mastered that particular skill.  Ask the students to investigate how the device got that answer.  You may never have to teach “cross multiply” again. 🙂

## CAS with Percentages

As I think about important skills for students, percentages stand out to me as an important skill for both elementary and middle school students that is not understood completely.  The students memorize the algorithms we set before them but never really reach the mathematical understanding of why and how we use them.  Using the TI-Nspire CX CAS handheld and some teacher preparation, students can delve into the why’s and how’s of percentages.  For example, start the lesson by putting the following slide on the board or send to student handhelds.

• What stays the same?
• What changes?
• Why do you think the last one is false?

Using a Quick Poll in the TI Navigator system or a cooperative learning strategy, facilitate student discussions on their answers.  The students can use their devices to investigate other percentages to see if their theories hold true. Teachers can use the activity Solving Percent Problems from the TI Math Nspired website as a follow up activity or intro activity for the lesson on using percents to solve problems.  As the unit progresses other investigations and discussion starters could look like this:

Ask questions like, “What do you notice about the numbers?”, “What is the relationship between the numbers?”, “What conclusion can you make based on this pattern?”.  Also show some other percentages such as the slide below asking similar questions.

Of course as in any good unit of study, opportunities for practice and hands-on applications are needed throughout the unit to master the skill but getting students motivated to understand the math is the first step.  Investigations such as these will allow students to delve deeper into the math instead of skimming the surface with algorithms only.

## Use More CAS

When I was first introduced to a CAS device, I thought it was a great tool for my AP Calculus class.  The more I used CAS activities I realized it would be a great tool for all math.  I believe student investigations are key in deeper understanding of mathematics.  CAS devices such as the TI-Nspire CX handheld and iPad app give students the opportunity to investigate the why’s and how’s of math.  If I write the steps on the board, the students only half believe.  If I give them technology and pose a “dilemma” such as why does ½ + ⅓ = ⅚, then the real learning begins.  I created this blog to share my experiences with and thoughts about using CAS in all grade levels.