Which is the best deal? Gatorade Introduction to Algebra Problem

Here is a Grocery Store problem.  I went to the store and video taped all the different Gatorade options.  (And yes, I did get some looks at the store)  My student's will have to decide which is the best deal.  I want my students to try to use problem solving skills to get at the best deal.  I want them to struggle a little bit with the complexity of the problem.  They will somehow need to get all of the 5 different options on the same unit measure playing field.   I have given a couple of answers below.  I was looking for students to justify their work with equations, diagrams or graphs.  They are not bound by any particular method.  However, they must show their work and give their answer in complete sentences.  In the video their is an example of what kind of work I expect.  I debated on whether to include this.  My end thinking was that I wanted them to see that their needed to be some work shown and a complete sentence answer. So I showed them a couple of solutions in the video.  But the exemplar solutions are NOT in the worksheet.

Click Here to Get the PDF Worksheet  (see below)

Of course I loved the traditional approach of figuring out the price per oz.  However, if you notice she also write that the Large Can was equal to 3 of the Smaller cans.  (24qts = 3(8qrts))  I love it.

This was a different student's paper.  This was another favorite answer because she wrote a diagram of two of the smaller bottles equaling the larger bottle.



All this really makes me realize how different we think.  I have to get myself out of teaching a certain method and saying that is the only way to do it.  It just is not right.  Think of your choice of cars.  Why are there so many cars choices out there?  It is because we all are different and like different things.  In math, it is the same way.  The plain and simple truth is that understanding our method of choice thoroughly first, then branching out to understanding other answer methods will benefit us.  I know I will forever be learning how to teach better.  This is exciting and daunting at the same time.  I will keep on trying to get better.

Let me know your thoughts?
Dave

Will Froggy get to the other side of the Lake? Solving Trig Equations.

WILL FROGGY GET ACROSS THE LAKE?

Froggy is a mechanical toy Frog.  He follows a sine wave path surfacing every 12 feet.  He dives down 7 feet from the surface along his path.  He is trying to get across Lake Tad which is 120 feet wide..  There is one problem, actually two.  There are two shallow places in the lake that if Froggy hits will break.  That's right.  Froggy will not make it if he hits those shallow spots.   The first low spot is 24 feet from the starting spot.  The second low spot is 51.5 feet from the ending spot.  The video actually will tell you a possible way of solving and the answer.  This is definitely not the only way to solve this question.
Click Here to get the Frogger Worksheet

This activity helps students put a few skills and concepts together.  They need to know how to build a trig equation.  They need to know how to graph a trig equation.  They need to recognize the periodic nature of the trig equation to spot the answer farther out on the graph.  

I had my students make a video of their answer.  I checked out the iPad cart for the day and had students make their videos on the app called DOCERI.  We then uploaded them to our content management system called CANVAS.  At the bottom of this blog, I am giving you an example of one of the solutions.

STUDENT SOLUTION

All the best,
Dave

Attitude

I came across this yesterday and I really liked it.  I forget this all the time.  I tend to dwell on things I can't change rather than the things I can.  I am going to give this to my students and get their response.  What are your thoughts?

Dave

Choose Your Attitude
 

This may shock you, but I believe the single most significant decision I can make on a day-to-day basis is my choice of attitude. 

It is more important than my past, my education, my bankroll, my successes or failures, fame or pain, what other people think of me or say about me, my circumstances, or my position. 

Attitude . . . keeps me going or cripples my progress. It alone fuels my fire or assaults my hope. 

When my attitudes are right, there's no barrier too high, no valley too deep, no dream too extreme, no challenge too great for me.

Yet, we must admit that we spend more of our time concentrating and fretting over the things that can't be changed in life than we do giving attention to the one thing that can, our choice of attitude.

by Charles R. Swindoll

How can you Measure Student Engagement?

Have you ever wondered if your students are engaged in their learning?  I have often wondered this and wondered how I could measure it.  So, some colleagues and I have come up with what is called the "ENGAGEMENT WHEEL."   It is a way to reflect on an hour of your day that you have taught and try to give it an ENGAGEMENT score.  The higher the score the more engaged your class was.  The engagement wheel measures what your students are doing.

 The engagement wheel score is most accurate when looking at the same class repeatedly over a number of days.  This will insure the score's validity.

I have an example for you.  Tuesday during 4th period I received a score of 5.  I filled in the categories that were true for that hour.  I would take samples from a few days in a row to determine where I stand.  Also, from this activity it will become obvious which pie slices you are not doing regularly.

PDF Color and B/W are available with the purchase of  Engaging Teaching Tools Book

THE ENGAGEMENT WHEEL IS FULLY EXPLAINED IN THE BOOK Engaging Teaching Tools  

GET THE BOOK Engaging Teaching Tools The book covers the Engagement Wheel in detail and many more Teaching Tools.    To purchase the book please go to to a website   Amazon  Corwin Publishing  Barnes and Noble

Let me know what you think and how you have used this.  I would really appreciate the feedback.

My Very Best,

Dave

Energizing Teaching Tools

I just finished this book. I'm excited about this book because it will help students participate with you in their learning.  It is a call to student action in the classroom.  The first section of the book deals with measuring student engagement.  The second part of the book deals with specific tools to build student engagement.  You can view the table of contents below for the topics that will be covered.  ENERGIZING TEACHING TOOLS is an easy reading book that any teacher can open to find some valuable tools.  It is a spiral bound flip book that is full of quick, practical ideas to increase your class participation.  It has a laminated front and back cover with 75 card stock pages.  Pictured on the front cover is the Engagement Wheel which is a self-evaluation tool to help measure the engagement level of your students.  There are also 50 teaching tools to help build a positive classroom environment and to involve your students.  Energizing Teaching Tools includes sections on the Engagement Wheel, Questioning, Classroom Climate, Classroom Activities, Physical Changes in your Room, Attitude Adjustments and Dealing with Parents.  50% of the author’s profit will go to a Chicago Public School.  To purchase the book please go to to the website  To purchase the book please go to to a website   Amazon  Corwin Publishing  Barnes and Noble 

Other Resources by David Sladkey

Energizing Brain Breaks Book

Energizing Brain Breaks Blog

Engaging Teaching Tools

Reflections of a High School Math Teacher Blog

Having Your Students Set Goals

Today was a good day.  I really enjoyed talking with my students about the goals that they have set for my class.  I was proud of the things that they wrote down.  I was encouraged with their vision of what they want to do.  It just affirms to me that the more we INVOLVE our students in their education, the more they will OWN it.

Here is what I did.
1.  I gave my students a page of questions to answer regarding goals. (see below)  One of the questions was what was their word for the semester.  It was their homework assignment.  There was no other assignment besides this.  That was yesterday the first day of the semester.
2.  Next, I met with my students individually and talked about their goals. I first asked them what their word for the semester was and why.  Then that started them talking and I just scanned the rest of the goals and asked them to elaborate on a few.  That was today, the second day of the semester.  For your information, I had the rest of my students working on a technology assignment with a school set of iPads.

POSITIVES:  I had One on One contact with each of my students.   I could affirm some of my students directly instead of through assignments or assessments.  Grades were not a focus of our meeting.  I gained a deeper appreciation for my students.  I addressed some issues with students like a lack of homework completion or low test scores.

DRAWBACK:  It used a full day of class.

SOME WORDS FOR THE SEMESTER THAT MY STUDENTS CHOSE:  Focus, Tests, Determined, Study,  Finish, Consistent...

I'd love to hear how you have used goals to help your students stretch towards excellence.
Best,
Dave


Here is what I handed out.

Goals for Precalculus Semester 2    Name_____________

Homework Completion

I hope to complete what percent of all the assignments in the course.    _______%

I am planning on doing my homework in this location.   _________________________________

I plan on spending this much time per night working on homework:  ________

Other Homework Goals?

Homework Questions

I plan on taking these steps when I’m frustrated and can’t complete my homework:

Procedural and Conceptual

Math Teachers try to get a balance of 50% procedural understanding and 50% conceptual understanding. 

Where are you now?  Where do you hope to be?

Trigonometry

The first 2 chapters of this course are extremely difficult.  (High Dive and Chapter 6 Trig functions)  However, once through these two chapters, the remainder of the course uses these concepts over and over.  How do you plan on mastering the first two chapters? 

Tests

Studying for math tests is difficult.  Besides studying the review homework, I plan on doing: 

Only for Seniors

Inevitably, seniors lose a little focus and passion for the course as May gets closer.  How do you plan on battling this?

Word for the Semester

Some possible words:  check, effort, preparation, tests, grade, excellence, understanding, believe, thorough…

My Word for the Semester is:  ______________   The reason I chose this word is…

No Easy Roads to Excellence

If you hope to do well in something there are no short cuts.   What are your thoughts on this? 

OPTIONAL:  Comment on your hopes for a overall % in this class

The Aim of Education is ACTION!

Here are some words that I associate with ACTION:

Involved

Engaged

Participating

Helping

Doing

Teaching

Movement

Creating

Judging

Accountability

My goal this year is to have a classroom full of ACTION.

Do you have any words to add to the list?  Please comment.