Geometry: Types of Lines and Relationships

Pg. 7. Lines, Line Segments, and Rules

Original Foldable: Pocket Book

This foldable takes a looooonnnnggg time to complete. I suggest finding another strategy. Suggestions?

QUICK CHECK FOR UNDERSTANDINGS: Book foldables may be time consuming, but they can be reusable. I had my students pull out all cards from the books, mix them up, and match them back to the correct pocket. It is easier to have them compare to a neighbor and monitor their results closely. I really like the disscussions that arise from who's right and wrong.

QUICK AND EASY: 'Types of Lines' foldable:

Line

Segment

 

Ray

Perpendicular

Haven't figured out how to work parallel into this.

This is one of my favorites. I had a student struggling with this concept at Sylvan. We created this foldable in under two minutes, had a one to two minute reteach, and she mastered the concept. She still has this in her folder and enjoys teaching other students that struggle.

This is paired with another trifold foldable in my journal.

 

Pg. 8. Relationships of Segments and Distance

 

Pg. 9. Segment Bisector (this is a trifold)

 

 

 

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Geometry: Undefined Terms, Basic Definitions, and Intersections

Pg. 3. Undefined Terms (Point, Line, Plane):

OR (from year two, printable template)

This is a foldable template I pulled from a Dinah Zikes book.

Pg. 4. Ms. Haley's Example:

I worked a guided example which I had the students copy. Their assignment was to create their own diagram and complete a set of fill in the blank sentences.

NEW IDEA: In a recent workshop, the presenter gave a suggestion: The homework we send home should have students working what they learned in that day's lesson backwards or undoing the process. For example, I gave them a diagram that they identified points, lines, and planes. Then for homework I should provide them with the complete sentences and the student tries to create a diagram that satisfied the statements. I think this would have been a neat way to see the different diagrams and level of creative thinking that each student is working at.

 

Pg. 5. Basic Terms and Definitions: (Not a real big fan of this page... I'm looking to improve it.)

Improved look:

Pg. 6. Basic Intersections:

ORIGINAL

Above images were copied and pasted from CSCOPE curriculum.

Another look:

 

New and Improved look:

When I create a foldable, I am always thinking about how a student will see, study, and use it. Is the foldable defining a concept or to be used a review tool? This usually helps me determine the placement/order of vocabulary, definitions, and diagrams.

 

 

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Geometry: Euclidean and Non-Euclidean Geometry

For my third year, I began with an in depth discussion over the types of Geometry. We had a few debates and lots of illustrations and demonstrations. I couldn't believe how engaging these discussions were and how useful an old basketball could be!

Then we dove into the foundations of Euclidean geometry. Next year, I plan on teaching constructions as a continually developing concept through each unit. I love the vocabulary development that results from these experiences. Constructions became a hands-on collaborative activity for my classes.

I will try to post my Geometry Journal ideas and experiences in the chronological order that I use. I will be sharing differing foldables and information from about three different journals-year two experience, year three experience, and the 'creating an idea' journal.

Pg. 1. Foundations of Geometry: (This is the Unit 1 I have been creating for next year. Information has been pulled from the CSCOPE curriculum mostly. Some have been pulled from older journals.)

Unit Pocket (yes, it is backwards)

Pg. 2. Geometry - "To measure the earth" (These are foldables-mainly half folds, that are glued on a sheet of construction paper folded in half. I use the half fold book alot.)

 

 

My students came up with the real world example for the Non-Euclidean Geometry, and we celebrated with Pringles the next day!

Pg. 3. Structure of Euclidean Geometry

OR (the original from year two)

pg 1

pg 2

 

 

 

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Just the beginning of my Geometry experience...

I have to be boastful; people tell me that I need to be.

I had 100% pass the Geometry End of Course Exam for the State of Texas. Granted the passing rate was probably low being that this is the third year of implementation. However, my students didn't just barely pass. About 92% scored 200 points over the scale passing score. That tells me that it wasn't just luck; I had to have done something right. I would like to share most of what we have done for the past year. This is by far my favorite subject. (I would like to say that about Algebra 1 next year.)

THOUGHT: At a recent workshop, a presenter dissed the use of journals. I almost walked out, but I made my self 'suck it up buttercup' as my students say and finish listening. One tip that I found reasonably useful is that while our students are "wasting their time cutting and glueing" prompt the lesson with guiding questions to spark engaging discussions, complete quick mini oral reviews over recent material, or close your lesson with oral summaries.

Geometry Journal: Finished product of the year.

It is huge; however, this consists of two classes at a time with all of my 'notes to self', assignments, and answer keys. Students that completed everything and placed assessments, quizzes, and assignments in their journals had a journal about half the size of mine.

I let decorating be an optional activity for students on their own time. I go with very little fluff when it comes to journals. Colored paper is extreme for my class. I believe in building an efficient and effective resource first. (It's a work in progress.)

This year in geometry I didn't begin to use journals until Unit 3. I have notes for Units 1 and 2 from my second year which was taught slightly different from my third.

DISCOVERY: Table of Contents-waste of time. We organize by unit and page number.

 

 

 

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A Theory to the Success of Algebra 1

Mathematics is a language all its own, right? So why aren't we teaching it as such? You know summertime; it's the time we teachers spend in workshops soaking in the theoretical views of the 'experienced'. I actually really enjoy workshops, specifically when I'm at that table that just explodes with ideas!

Back to the THEORY: If math is a unique language, then I should be teaching students to listen, write, read, and speak its language.

I realize that I spend so much time focusing on one component-writing the math. I need to teach fluency in math that focuses on all four of these areas.

I have observed several foreign language teachers come and go. The great teachers have their students fluent in these four areas. Students read, write, listen, and speak the language.

As I think back to high school, I was an excellent memorizer. I didn't really know how to read the notation or why solutions were written a specific way, but I could tell you what I needed to put where based on context clues. Then when I got to college, I had one of those professors. He spoke, read, wrote, and listened for the language of mathematics. He expected the same from us. I struggled like you wouldn't believe; however, after I graduated and entered the world of education for mathematics, I noticed the difference in my math language and others. Now, I am not an expert or near perfect, but I notice that my students have a higher level of math skills because I hold myself to high standards when using the language of mathematics.

GOAL: Even though I can read, write, listen, and speak the language of mathematics, I need to expect that from my students.

CONCLUSION: This is all just a theory based on self reflection and observation. We'll see how it unfolds over this next year.

 

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NON-RESPONSIVE TEACHING STRATEGY!!!

CONCEPT: As students are having a 'class congress'-generating the big ideas from a previously completed investigation, the teacher/facilitator monitors their discussion with zero validation.

INITIAL RESPONSE: I watched some videos of a teacher using non responsive techniques, and I was horrified. The kids would be crushed after providing an intensive explanation of their results and the teacher would just turn and walk away. Even if the student was spot on; she would simply turn and walk away. Now, this wasn't the only interaction the teacher had with her students. She would guide them to clarify their math terminology, dismiss outrageous ideas, and reroute their detours to continue working towards the objective. I even know how the students feel because this presenter-Pam Harris has been using this technique on us for the past three days. My colleague and I were very upset and trying to shut down, just like what our students will try to do.

HOWEVER, REALIZATION: As the presenter continued to have us process this method, with the objective question in mind-"How does this benefit the community aspect of your classroom?"; we made some discoveries. I realized that I was looking for that 'teacher pet' validation. When that enthusiastic validation is given, the classroom brainstorm usually stops, and students then try to mirror their inferences to the student that was validated. I also became more open to all inputs from other colleagues. I observed closely and listened intently looking for the correct conclusion since I had become uncertain of my own thoughts. As I heard other's thoughts and realized others agreed with my conclusions, I became self validated and had acquired new understanding from other perspectives.

CONCLUSION: The non-responsive strategy is a method suggested to be used at the beginning of the year to level the playing field for all students. You want the student to be in charge of their learning and looking to get what they need out of the lesson and not what the teacher wants. We all have exceptional teacher pets that know what to say and how to get super enthusiastic validation from us, but what about the quiet student that knows much more than the teacher will ever know because he has assumed from day one that the teacher pet can handle it.

POINT: Something that I will consider using with the objective of building a classroom community that expects all students to respect each others' thoughts and ideas equally.

QUOTE: "Coming together is a beginning, staying together is progress, and working together is success." Henry Ford

 

REFERENCED:

• Class Congress - This is a class discussion strategy based on the International Congress of Mathematics.
• Pam Harris

This is a strategy that I am still unsure of; please let me know of experiences and reflections that you know of. If you have another understanding of this strategy, I would love to hear.

 

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Domain and Range Revised!!!!!!

Due to experience throughout the year, I need to revise my Domain and Range to reflect the more hands on approach that we developed.

This is not what I would call a definable foldable, but an interactive tool used to find domain and range. My original was more of a way to view and define domain and range. If you compare the two I think that you will discover my meaning.

I am going to show you the finished tool and how I used this to find domain and range.

Finished product:

The left and right flaps are used to create the boundaries for domain.

It's hard to demonstrate with photos. This is a very demonstrative and interactive activity that I do as the kids do.

The bottom and top flaps are used to create boundaries for range.

This really helped them understand and see a true maximum and not focus solely on the endpoints.

Now if you have an arrow on the end of a graph indicating an infinite domain or range; I tell my students that this cannot be boxed in and this means infinity.

We discuss discrete and continuous and the types of ways domain and range is written before we do this activity.

We glued multiple graphs in the form of a flip book (instead of post-its, glue lasts longer) so that this foldable became a reusable manipulative in the classroom.

 

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