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First Day

Anyone have some good opening lessons for the first days of geometry?

I know a lot of people do activities related to definitions in their first days. I was thinking of launching straight into the opening activities in Henri Piccotto's Geometry Labs book. I was also thinking of starting with some of the activities in the New Visions Geometry course.

What are you doing? I'd be really appreciative for some help figuring out my first couple days! (I've been teaching geometry for seven years and I still feel like there's huge parts of the course I need to work on.

I started with one of the Pattern Block labs from Geometry Labs last year. It went fine, but this year I plan to have a discussion about sandwiches. I haven't worked out the details, so why not start here?

My first class is only 25 minutes long. Students will start by learning my group organization system - they draw a card that sends them to a particular table, simple. Question on the board:

Is a hamburger a sandwich? Discuss.

Walk around and listen for good comments. Write them down if I remember to (I probably won't). After 1-2 minutes, next slide.

Is an Oreo a sandwich?

Then...

Is a hot dog a sandwich?

Then...

Is a burrito a sandwich?

Then...

Is a "falafel sandwich" a sandwich?

Then...

(A picture of me lying on the couch with my kids, one on each side) Is this a sandwich?

...

Then 'll transition into some set of questions asking them to define the word "sandwich" so that some or all of these things are included or excluded in various ways.

 

I just created a foldable today giving a bunch of definitions and symbols that students will need to know for Geometry. I'm planning on doing this toward the end of the first week of school - I'm going to give them the foldable, show them how to cut and put it together, and then have them do an activity to practice recognizing and using the symbols. I have NOT yet written an activity or found one that I particularly like. Not sure what I'm going to do about that yet, but when I come up with something I'll try to provide an update.

Click here to access the Word document.

Printing instructions: copy the first 2 pages back-to-back, and pages 3-4 back-to-back. Each student needs one copy of pages 1-2, and two students will split one copy of pages 3-4. It will look really cool if you do two different colors of paper for the two sheets.

Students should cut on the dotted lines and fold on the solid lines. This foldable is a little complicated to fold if you've never done one like this. Click here for a slideshow with folding instructions. When the book is complete, it should have the title "Naming Things in Geometry" on the front. I STRONGLY recommend that you try one yourself before doing it with a class.

The link above goes to a Word doc in my Google Drive account. Feel free to customize as needed.

 

Here are my assumptions:

- The geometry course is primarily about geometry, and only secondarily about vocabulary, notation, and logic

- The geometry course should be interesting

The implications for the start of the course are especially to avoid boring crap like "Prove that the midpoint of AB divides it into segments of llength AB/2", or as you pointed out the other day, the Ruler Postulate.

Here are three options that fit with those assumptions.

1. I started my geometry course with not just the pattern blocks activity from Geometry Lab, but much of that Angles unit. The reason was that I had to bridge the gap between students who had only the shakiest understanding of what an angle even is, and students who are ready for some engaging reasoning about figures. That unit accomplishes that goal. Note that the inscribed angle theorem has few prerequisites, so it lends itself to early treatment.

2. Another option is to open with a tiling unit, especially if you have my Geometry Labs template. That too leads to interesting angle work, including angles in a regular polygon. Moreover, early on, some scalene triangle tilings can be used to discover and discuss many important basic ideas: sum of angles in a triangle, vertical angles, parallels and transversals... Tilings are also a good way to introduce rigid motions and symmetry.

3. I've gotten good reviews about the intro to transformations material on my Transformations page. You might check that out, especially if you're interested in exploring transformational proof later in the course.

You could do any of these, or any combination of them. Or something else, but definitely think about your assumptions about the course, as they should dictate the opening.

Oh, one more idea: Chakerian, Stein and Crabill open their classic Geometry: A Guided Inquiry with the so-called "burning tent" problem. I guess that fits my assumptions, but I stopped doing because it was too much of a hodge-podge in geometric content. (My suggestions above are more focused.) But I guess one could argue the hodge-podge thing makes it a good intro to the variety of coming topics. 

In any case, good luck!

-- Henri

I like to talk about the specificity of definitions by doing categorization activities. I usually have a handful of cut out shapes that I provide groups with, and ask them to categorize them. The first time, I say to create however many groups they want. After that we usually do another round or two with a specific number of groups they are tasked to create. 

I do really like the idea of starting with "is a hot dog a sandwich?" though as well, and am considering making "which of the following is a sandwich and why?" the first day warm-up. 

There are two sets of talking points that I've accumulated from somewhere on points/lines/planes and names of angles that I'll be doing during the first unit, unsure of when exactly yet. 

Heh. I think my assumptions about geometry are the reverse of Henri's.  

Another thing I have done with success in the past is start with one or two Which One Doesn't Belong then have the students in their groups make one of their own with themselves - come up with ways each one of them is unique in their group. It is a pretty fun ice breaker and if you like using WODBs throughout the year it is a nice intro.

I really like the sandwich activity and will need to think about how to incorporate that somehow. Two things that I did to begin my Geometry classes last year:

1) With my regular Geometry classes, I began with some visualization exercises. Last year, I gave groups of 4 all of the 8 questions and that did not go well. I think that I would be more likely to use this in the future as a jigsaw type activity, where they are in groups with all of the same question and then have the responsibility to be able to explain their question and the way that they thought about it to others. 

2) With my Honors Geometry classes, I began with this mobius strip exploration, modeled heavily after a similar activity in the CPM Geometry Connections book. I like the activity because of its connections to the scientific method and that it gets students excited on the first day of school about things that are mathematical that they may not previously have considered to be mathematical. (If you have not read Sara Van Der Werf's recent post about "what is math?"  you really should and it also includes some beginning of the year ideas.)   

I am still several weeks out from the start of school and haven't made any decisions for this year yet. 🙂 

I have had some success the past few years starting off with the handshake problem on day one in Geometry. Our school schedule has us with about a 35 minute class on day one. My students can have a meaningful conversation, we usually have a couple of different ideas about how to generalize, and we can revisit the problem in a number of different contexts during the year in Geometry. 

Michael,

Since I use the New Visions curriculum for geometry I will often do the instructional routine, contemplate then calculate, 2-3 days in a row right at the beginning of the year. My focus is always on building a community in the room first where the students and myself get to learn names and get comfortable communicating in both small groups and with the entire class. I focus much more on the kiddos getting to know each other, getting comfortable with the classroom space and the instructional routine than the math content itself in the first few days. I do pick tasks where I can assess the kids' use of structural thinking without it getting to geometry heavy.

I started with the task below last year and I will probably do the same this year as I really liked the access level and the creativity that emerged from my kids!

https://docs.google.com/document/d/1jnZeFbMi4mgEcxJ7PufRDSiSnMdX69uST9yg1lh1Zqs/edit

 

I've use this lesson for the last few years and I love it! https://betterlesson.com/lesson/434560/dig-in-day-1 Our first day is really short (about 2o minutes) so this is really the second day of class. I love this lesson because it is accessible to everyone in the class but has a high ceiling once you start thinking about area and perimeter. You can really get a feel about what students know; I usually keeps of list of geometric vocabulary that I hear while circulating around the room. After this lesson we prove the Pythagorean Theorem (using an accessible method) as a class (since that is needed to find the perimeter of the figures) as students likely don't have too much experience with proof. After Pythagorean Theorem we will move on to Midpoint Formula, and angles. It's kind of a hodgepodge for the first unit but it's a good intro to geometric thinking (proof, defining, generalizing relationships).

I try to avoid the points, lines, and planes lesson that most geometry books start with because it's like you are assuming students have never learned anything about geometry in their life. We do a quick recap but otherwise I feel like students are bored out of their minds.

A lot of good ideas above. Or below 

I like starting geometry with on the bus/off the bus game because to me geometry starts with noticing attributes. I always think about van Hiele levels, and that move to analytic can usually start right away because of learners' overwhelming visual experience.

  • I think I'm going to launch with this: Conditional Statements Introduction Its a slight adjustment to Sam Shah's post on conditional statements. I used it a few years ago in the middle of the year and loved the student response. I think I'll adjust it slightly again since it will be early in the course, but I figured its a good way to refresh things students should know but might forget, gets students thinking about order/word choice, and introduces things we'll prove later in the course and it gets students working in groups, providing feedback and debating really early in the course which sets the groundwork for how much of my class runs.
  • Sam also has an introduction (linked in post) on having students draw a picture following directions, but I was recently talking to someone (I forgot who 🙁 ) who does something similar but in pairs, with students sitting back to back. One student tries to get the other to recreate a picture that has been provided. It could be used to show why something like "triangle" might lead to multiple different results and is another fun way to get at word choice and review of some terms students will use in the course.
  • Two years ago I launched with a definition writing activity. After a warm up from a Discovering Geometry textbook about "widgets," Students were handed cards with examples and non examples and had to write definitions and then groups switched and had to attempt to break them. I think I have files with my task cards on my work computer so I can update with those files if anyone is interested the next time I'm in the classroom along with a few more launches. 

I have done something like the below with computer science and physical science students. Fun! 

 
Posted by: Altmath
  • Sam also has an introduction (linked in post) on having students draw a picture following directions, but I was recently talking to someone (I forgot who 🙁 ) who does something similar but in pairs, with students sitting back to back. One student tries to get the other to recreate a picture that has been provided. It could be used to show why something like "triangle" might lead to multiple different results and is another fun way to get at word choice and review of some terms students will use in the course.

 

Thanks for the ideas, everybody! Keep them coming. This is really helpful for me.

I use the attached sheet and have the students group the quadrilaterals based on similar characteristics. I ask them to create a title for their grouping and which letters belong. I want to see what type of vocabulary they use, misconceptions they may have, as well as what they were looking at for each shape (angles, sides, etc). I have them create 3-4 groupings and then share out as a class to discuss.

Uploaded files:

@ahpettit This sounds awesome! Yay for doing geometry on day one! Plus you get a non-threatening formative assessment out of it. (Alas, my computer seems unable to download the PDF.)

Henri, can you see this?