CAS with Probability

Using CAS with probability lessons can make learning fun and allow students to do experiments on a device instead of gathering data, flipping coins and rolling number cubes the old-fashioned way.  Sorry teachers but the students like the devices, and it will save you money and storage space if you keep it digital.

Let’s start with random samples involving population.  TI has a FREE activity called Interrogating the Data that works great.  The data is a random sampling of 7th grade math scores.  It starts with the question:  “Why might one use a sample instead of collecting data from an entire population?”  The handheld generates a random sampling for the students.  You do not have to come up with the numbers.  Let the technology do the work for you.  Here is a screenshot of the samples:

10-05-2015 Image001You can use the TI-Navigator CX CAS system to capture student handheld screens to display on your screens for discussion and self-checks.  A CAS handheld will allow a student to compare not only the table but different data displays to compare which is the best display to analyze the data.  A dot plot and stem plot is shown below, but you can also look at a histogram.

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You can even compare all of the samples on one page.

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With technology students can customize the color and axis to investigate to their individual style.  Next the CAS will allow students to calculate the mean of the sample and absolute deviation using formulas in the spreadsheet which leads into major discussions on the data.

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Instead of focusing on how to do the calculation at this time you can focus on the following:

1.    What does the formula mean?

2.    Why is it necessary to calculate the absolute value?

3.    What is learned by calculating the Mean Absolute Deviation?

This is applying the mathematics instead of just doing the mathematics.  Students can then make predictions using their analysis of the data instead of a textbook created problem with no meaning.  The CAS handheld will also allow the students to interact with the graphs by hovering over different parts of the graph on the screen to see other important values as shown in the screenshot below: 10-05-2015 Image006

This particular activity gives students other types of population data to study also.

Now let’s look at experimental and theoretical probability.  Using the One and One Equals Win activity from the TI website, the CAS handheld has a basketball player simulation to analyze probability of making a shot and a basic spinner simulation.  Screenshots are shown below.

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The CAS handheld allows students to calculate the theoretical probability then do the experimental probability and compare the two.  This will save time in the classroom and still allow the most important discussion to take place:  Are the experimental outcomes different from the theoretical and why?  Then finally give the students a basketball scenario and let them use the probability experiment to predict the outcome of the game based on the data.  The TI activity provides a scenario but you can create your own if you choose.  A sample table is shown below:Probability TableIt is easy to see that technology is the way to improve motivation for learning probability.  The TI-Nspire CAS handheld comes with pre-made activities and simulations for this purpose and has the calculation and graphing capabilities working together.  Whatever data is put in the table is automatically connected to a graph for manipulation and analysis.  I will never use physical number cubes again.

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Why I Use TI Technology

Although this goes for CAS and nonCAS, I thought it worth sharing and she says it so much better than me.

Easing the Hurry Syndrome

I was asked a few weeks ago why I use TI Technology in my classroom. I have never felt articulate when it comes to extemporaneous speaking, but I agreed to talk with the reporter because my experience has been that it’s good for me to have to justify what I’m doing in the classroom. Why do I continue to use TI Technology in my classroom when other free technologies are available for teachers and students to use?

A Google search of “technology speeds up life” results in about 142 million results in less than half of a second. What I find in my classroom, however, is that using technology actually slows down the pace.

In the midst of my usual rush to cover all of the required standards, when we use TI-Nspire Technology to explore a difficult concept, the questions that students ask slow us down. The platform that we…

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Using More CAS One Teacher at a Time

Wanted to share the good news.  One of our science teachers received a grant today for some TI-Nspire CX CAS’s.  She plans to use them for data analysis and with the activities from the TI Education website.  Hopefully this will catch on in our school and her PLN.  This is one small victory for CAS.  We can change the educational world one teacher at a time.

To Train or Not To Train

We are 6 1/2 weeks into school and it seems we just started.  I have convinced one science and one math teacher to Use More CAS.  Now the issue is training.  With all the webinars, conferences, and of course a regional instructor in the building one would think this an easy task.  I have found that is not the case.  Finding time during the school year for PD seems to be impossible especially if administration prefers it to be only during off hours.  Now I have the dilemma of how to make it easy for teachers to learn more CAS.  I go back to my thought from this Summer:  Don’t do it all at once, but do it bit by bit.  I plan to work on this in the upcoming months.  I also need to start thinking about how Use More CAS can be offered in the standard Summer PD.  How do I be proactive without being pushy?  How do I convince other schools this is worth a day of your time?  Only time will tell.

Thoughts From a Conference

After returning from the USACAS 9 conference, I reflected on the barriers to incorporating CAS into education.  The most common thing I heard was the technology was not available.  I did not have an answer more than if you get a chance to request technology put it on the list.  I was not satisfied with my answer, so I started thinking.  Where is the CAS?  There is a TI-Nspire CAS app for iPads, TI-Nspire software for computers, and of course the handheld.  Easy right?  Not if you have only $500 or less to spend for everything in your classroom.  If you had to choose between a new computer or CAS, what would you choose?  If your school finally were getting wireless slates/iPads with Doceri, would you decline for CAS?  There are no easy answers to these questions, but maybe there is a compromise.  What if we didn’t push for classroom sets but school sets?  What if we asked for the TI-Nspire CAS app to be placed on the school iPad lab?  What if the one iPad with Doceri we got for our classroom had the CAS app on it?  I think we could still change the classroom environment and open doors.  All administrators look at one thing: prove the students are learning.  All we have to do is prove the students are learning with CAS, and I believe doors will open.  I plan to start by sharing my original TI-Nspire CAS set with fellow teachers.  I have upgraded but refused to let the old ones go.  Now I hope to give new meaning to recycling.

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?”

Me:  “This is not study hall.  What about your project?”

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.”

Me:  “Well this particular calculator will allow you to enter your expression and receive and answer in radical form.”

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 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.

0.9 Repeating

This was a precal class but I think would be an awesome activity with Middle Schoolers.

Easing the Hurry Syndrome

I got to teach one of my favorite lessons in a Precalculus class this week, which I developed several years ago from a paper by Thomas Osler, Fun with 0.999…

We started with a Quick Poll. Students could select as many or as few choices as they wanted.

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I shared their responses separated

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and grouped together.

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In the first class, one student selected all three choices.

In the second class, 5 students selected all three choices.

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I set the timer for a few minutes and asked students to think individually about how they could argue their selection(s).

Then I asked them to talk together about their ideas.

I walked around and listened. These are the conversations I heard:

A: 1/3 is 0.3 repeating. 2/3 is 0.6 repeating. If we add 1/3 and 2/3, we get 1. If we add 0.3 repeating and 0.6 repeating, we get 0.9 repeating.

B: 1/9…

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