Intro to Conics with Rice Krispies!

My colleague uses play-dough to explore conics.  And that was what I had planned to do until I read in Twitter one day that Julie was making rice krispy cones.  And I decided I wanted to do THAT!  After all, a bit of sugar helps the medicine go down!  (Not that I think conics is medicine ... it's one of my favorite units!)

But as Julie tells us in her blog about this activity, she has only one class of Algebra 2.  I have SIX!  Yes, 149 students.  And making 149 cones sounded daunting!

I purchased 3 big boxes of HEB crispy rice ... and 7 bags of HEB miniature marshmallows.  I was tired last night ... but I persevered in making 50 cones ... using about half of those ingredients (4 recipes of 6 cups cereal, 10 oz marshmallows, and 3 Tbls butter).  I had purchased 4 oz cone water cups ... I found mine at Amazon.  I bought one sleeve of 200 cups for about $6.

I see my 149 students over two days ... we are on a block schedule.  I decided to give one cone per pair of students today.  I used 39 cones ... I have 13 left.  Tonight I need to make 21 more cones.

So why all of that detail ... and all of that work, you ask???  For the smiles, the engagement, the joy of finding hidden shapes in our treats ... and the great give and take math talk all around the room!  "Can we eat these?" they asked.  Well, of course, you can!  

So the lesson:  

1.  Students did a quick web hunt for homework before class today to provide some understanding of conics.

2.  When students arrived in class, they shared their homework responses with their partners for just a few minutes. Then I asked a few questions about conics in general and about cutting a cone in particular, using an illustration on the board.

3.  I gave each pair some wax paper, a plastic knife and a cone.  I asked them to cut the cone to illustrate the four conic sections.  At the same time I asked them to discuss these 12 questions.

4.  To wrap up this section of our lesson I showed just a short clip (out-dated) of a teacher and student cutting a cone with a band saw to emphasize the relationships between the sections and the central axis and edge of the cone.

We continued by learning how to identify a conic section when its equation is given in general form.  We also practiced completing the square to rewrite from general form to standard form.  In our next classes we will tackle each of the sections one by one ... using Cindy Johnson's conic cards!  Conic cards are now online ... find them here!

Other blogs about Rice Krispy conics ... here and here.

Conics Unit Day 2: Circles

In planning our Conics unit we started with the toughest task first ... completing the square. This means we can practice that skill all throughout the unit! Students seemed pleased last week when I told them they tackled the hardest part first.

We are going to work through each conic section ... circles first. Students will start by working in groups, defining a circle, and listing everything they already know about them.  We will consolidate their lists to make a class list.

Then we will make a connection between the general form of the equation and the standard form. Using the standard form we will identify key attributes (center and radius) and graph circles.

Next we will sort conic cards. Students will sort cards in each class ... first in groups, then in pairs, then individually. On the first day the sort was rough, more of a detective activity. Students had to deduce quite a bit of information. In this sort, we will "check" their work on circles.

Because students have had geometry I want to spend some time making connections. We will explore tangents to circles using Desmos. I've already built folders for each problem on Desmos so that I'm ready to illustrate.  I plan to ask students to work with partners for a few minutes to see what they can discover.  And then we will discuss the problems. 

Last we will explore an application problem about radio stations that I found online from the Atlanta Public Schools. 

I notice that colleagues in the MTBOS are blogging daily this month ... count me in a few days late! #MTBOS30

Planning our Conics Unit ... Day 1

We are testing tomorrow on our Rational Functions unit. It will be interesting to see the results. My formative data indicates we could use more time on this unit. But our calendar says we must move on. I offered tutoring review several mornings last week, and again this morning, tomorrow morning.  Several students have taken advantage of the opportunity for extra instruction.  But those few ... you know who they are ... haven't visited ... yet!

In the meanwhile, I am pulling together our next unit.  I could just do one worksheet after another as that is what is in our school's files.  But I'm trying to mix in technology that will enhance student learning, hands-on activities that will promote critical thinking, and problem solving - applications that make sense.

Here is my plan so far ...

On test day, the homework will be an invitation to read background information on conics, to tweet something they learned, to try to find 3 interesting facts about conic sections and to begin exploring the equations in Desmos. Already some of my sophmores are whining ... "What?!? We are going to tweet math stuff?  I'll have to create a math Twitter account!"  Oh my!

Then on Day 1 of the unit ... students will have some background IF they do they homework.  As students come in, I'll have their tweets on the screen ... and invite them to work in teams to create "top ten" lists of interesting facts they learned about conics in their homework.

Next, I'm using Cindy Johnson's conic cards.  Students will sort cards ... carefully looking for patterns, key attributes to sort the cards.  In this first round of sorting, students will work with partners, and will try to sort one whole deck into four piles - and explain why.  The extension would be to organize those four piles into sets of 3 cards representing specific conic sections.

To follow up with the sorting, I'll use Discovery Education 10 minute video from the series, Math Factor: Physical Properties of Conic Sections.  The video will provide students with a clear picture of how the conic sections are sliced from a double-napped cone.  I thought about having students slice the sections from play dough but decided against it.

We'll use the work students did with sorting cards and the video to start filling out a graphic organizer about the four sections.  The graphic organizer doesn't have to have all the details on this day - we will revisit it daily to add notes.

Last we will spend a few minutes in direct instruction reteaching completing the square.  Since we have spent time on this skill, I'm hoping that a short review will be enough for students to work with conic equations.

For homework, students will practice using completing the square, and I'm asking them to find an example of a conic section in their home, capture a pic, and tweet it!

On Day 2, we explore circles.