Exponential & Log Functions Scavenger Hunt

Has post-Spring Break, end-of-year craziness hit anyone else yet?  Holy Cow! All I can say about this week is "thank goodness it's over and we all survived"!!  The first day back from Spring Break we spent about 45 minutes in the hallway with our kids sitting out a tornado warning (can I just say that when you put a few hundred teenagers in a hallway with no AC vents and no windows it gets rather stifling pretty quickly) and Wednesday was an un-planned day out due to the threat of severe tornadoes across the area (thank goodness all we wound up with was a little bit of rain - definitely an answer to prayer).   Let's hope that things settle down for the next two weeks before we start standardized testing.  Yep, testing season is almost upon us.  The only good thing I can say about that is it means summer is just around the corner.

Since the weather did not cooperate with me this week and completely messed up my plans to test Friday I was scrambling to come up with an activity for my Honors Advanced Algebra classes that wasn't a waste of a day, but would give 7th pd the opportunity to get caught back up with my other two classes (did I mention that we completely missed 7th pd Monday due to the tornado warning and that my entire 7th pd class was out the day before Spring Break due to a field trip).  Scavenger hunt to the rescue.  What teenager doesn't love the opportunity to wander the hallway for 45 minutes?  On my hallway we love hallway work.  At least once a week you will find someone with their class in the hallway doing some kind of activity.  If you haven't tried it, you should.  It gives the kids a chance to get up and moving without tripping over desks and bookbags (in a classroom the size of mine that is definitely a hazard).  I can stand in the middle of the hall and see both directions and keep an eye on my kids, and (here's the awesome thing) THE KIDS WORK.  There is definitely something to be said for getting the kids out of their desks and getting them moving.  In my opinion they spend way too much of their day sitting passively rather than engaging actively.  Don't get me wrong, I'm not anti-lecture.  I have been know to lecture for a full class period when the need arises, and sometimes it does.  I'm just saying that sitting in a desk from 7:45 to 2:45 5 days a week is a bit ridiculous.

Off my soapbox and back to the scavenger hunt.  Advanced Algebra is in the middle of our Exponential & Logarithmic Functions unit, and we have been working with graphing and comparing functions and their characteristics.  I put together a 13 question scavenger hunt with multiple choice questions related to these topics.  Some of the questions are easier than others, but the goal was to make them think about the graphs and characteristics without completely sketching the graph.  Here are a few sample questions.

Question 1 - Finding the domain of a logarithmic function

Question 7 - Determining the inverse of a logarithmic function

Question 9 - Identifying the correct graph of a logarithmic function

Question 11 - Analyzing and comparing a function and a transformation

I have my kids take a piece of notebook paper with them to write down the question number, answer, and any work they need to show.  If they make a mistake they quickly get stuck in a loop and wind up back at a question they've already done.  I take a copy of the answer key out with me so I can quickly check their work, identify where they made their mistake, and send them back to where they went wrong.  The discussions my kids have while working through this kind of activity are great to hear.  They will argue their reasoning with their classmates, justifying their answers and finding flaws in each other's logic.  It's also not unusual to hear "Ms. M - tell them I'm right because....".  I find activities like this are very effective in making students really think about what the question is asking.  Unlike a multiple choice practice worksheet where they will just circle an answer and hope it's right, in an activity like this they know if they answer wrong it is going to mess them up so they put a lot more thought into what they are doing.  

The set-up is not too difficult either.  Once you have the questions written start with #1 and assign the correct answer the question you want them to go to next.  After each correct answer has a question number assigned to it, then I go through and randomly assign another question number to each of the incorrect answers.  I highly recommend that you write down the correct question sequence along with the correct answers as you are doing this.  It will save you a LOT of time later.  

If you are interested in this activity, or any of my others, please visit my Teachers Pay Teachers Store.  

https://www.teacherspayteachers.com/Product/Exponential-Logarithmic-Functions-Scavenger-Hunt-3095851

Volume of 3-D Figures

Volume of 3-D figures is not a new concept for Geometry students (at least it shouldn't be), but in middle school they focused on finding volume of prisms (square, rectangular and triangular).  The high school standards focus on calculating volume of cylinders, cones, spheres and pyramids, as well as composite figures.  Students also need to be able to identify the cross-sections that are created by slicing these 3-D figures, as well as identify the 3-D shape created by rotating specific 2-D figures about an axis.

For the last week we have been focusing on these concepts, and as a part of this section I had my students create 3-D 'juice containers' that met certain requirements.  I grouped my students based on their performance on the last test (high performer with high performer and so on), and assigned each pair of students a shape with specific requirements.  Some groups were assigned a cylinder and given the total volume and diameter while others were given the total volume and height of the cylinder.  My highest performing students were assigned a cone and given the volume and its height.  Students had to take their information and construct a 'juice container' that met the given specifications.  They were also asked to come up with a brand name and to decorate their containers.

I went into this activity expecting my students to sail through it with no issues, however I quickly realized that was not going to be the case.  They quickly moved through the calculations required to determine the missing dimension, but then slowed down significantly.  Physically constructing a 3-dimensional object is something that my technology focused students do not have much experience with.  While they may be able to manipulate objects using technology, physically constructing them requires an entirely different thought process.  It took many of my students lots of discussion and a few false starts to figure out the best way to build their figure and to make sure they had all of the information necessary in order to do so.  With a few exceptions their final results looked good, and they were able to take from it valuable experience in creating something that fit within specific constraints.  This is definitely a mini-project that I will hang onto for next year.

Arc & Angles in Circles Activity

So we are currently in our circles unit in Geometry.  We started this semester with the basic definitions related to circles, and for the past week and a half we have been working with the relationships between the arcs and angles created by intersecting diameters, chords, secants, and tangents.  Getting the kids to recognize the relationship and figure an arc or angle measure when there is only one thing going on isn't too bad, but when the figures get more complicated and there are multiple segments and lines intersecting in various places things get a whole lot more difficult.  We spent some time working on these types of figures this week and I found that being able to mark on a figure, erase, then mark again was helpful for many of my students, so I designed an activity that allowed them to do this.

I separated my students into groups of four and each group got a supply basket with dry erase markers and erasers (washcloths), as well as four copies of each of three figures.  The copies of these figures were each in a page protector.   Also in their supply baskets they got a page protector with multiple copies of the answer document.

Each student got a copy of the answer document, and they could choose which of the three figures they wanted to start with.  The figures were all in page protectors so students could mark on them with the dry erase markers as they figured various angle and arc measurements about the circle and their answers for specific arc and angle measures were recorded on the answer documents.  My students seemed to like being able to draw on the figures and erase things easily if they made a mistake or no longer needed a specific piece of information.  I also heard a lot of great math conversations as I circulated about the room checking on progress and answering questions.  Any activity that sparks good math discussion is a winner in my book.

Here are the figures that I had my students working with.

FIGURE 1

FIGURE 2

FIGURE 3

Answer Document
Note:  I had students add in the arc markings on the questions asking for arc measures.  

 When attempting an activity like this I highly recommend having group supply baskets pre-made.  I invested in a half a dozen shower caddies from Dollar Tree a couple years ago and they have been great to have for any kind of group project that requires supplies.  Sorting into the baskets is easy and they keep the kids from wandering the classroom in search of things they need. Clean up at the end of each period is also easy as the students just need to put everything back into the basket at each group of desks.