Method to my madness!! Building Journal Pages:

Questions: How do you create a journal page or foldable? Where do you start? How do you come up with it?

I'm not sure if I've written about this yet, but it is definitely on my mind quite a bit. My second year co-teacher always asked, "How do you come up with this?"

The answer to that question has been on my mind all through my third year of teaching. So let me see if I can lay it all out.

Step 1: I start with a general objective, select an assignment, and check to see that it aligns with the quiz and unit assessment.

This strategy evolved from the curriculum director at my previous school. "Keep the end in mind." When planning you want to continually loop through and keep the assignment, quiz, and assessment in mind as you plan a journal page, lesson, activity, etc.

I have several EOC prep books that I use for quizzes and the CSCOPE curriculum for unit assessments. I always start by taking the quiz or assessment myself. I work each problem in as many different ways as I can and note each strategy used. The hardest strategy for me to see is always the logical approach. Usually, this method comes out during the lessons from my students. I know that this idea looks and feels like teaching towards a test, and it probably is, but I do what I can.

Step 2: Now that I know what we're working towards, I take the concept, topic, or objective and begin my research. I look online mostly, reference CSCOPE curriculum, Glencoe textbooks, EOC prep guides, colleagues, etc. I try to reference a minimum of four to make sure I have confirmed my findings.

Step 3: Time to organize. I look at the information that I want to convey to my students and begin to think about the method that would best fit this lesson.

• Are we defining something?
• Is this too much at one time?
• Do I need to break this into mini lessons with guided and independent practice loops? (That's what I did for special right triangles this past year and it worked out great.)
• What will this journal page or foldable contain?
• Will it define and organize the concept, contain a reusable manipulative, be the result of a paper folding activity or lesson, a reference of guided practice, or all of the above?
• What is the point of this journal page and how will it benefit my students?

Once I decide the purpose, I then begin to look for or create a foldable that will organize the information and lesson into sections.This is important to me. I like information to be organized, sectionalized, bolded, boxed, highlighted, etc. Kids tend to remember things like that. A lot of times, we'll end up with glued attachments here and there to accomodate new information or make a little more room.

I can't really explain how I come up with my lesson. I've been told that my wacky brain is hard to follow. Sometimes, the lessons are from colleagues, workshops, or previous experiences that I tweak to fit my agenda. My goal on each journal page is to take an overload of information, organize it, and make it relatable to my students. If you've read previous posts, you'll see where I ask for suggestions on how to make a journal page better.

I'll admit, I am not always this on top of my lessons. Sometimes, I walk in knowing what I need to teach, but not how. My go to "don't know where to start" strategy is to go with a blank white sheet of paper. My students know to use my go to short fold half page foldabable. It's boring but I can expand this, glue attachments, glue it like a pocket for additional stuff, and initially this simple foldable provides three sections for attempting to organize. I use this foldable alot, even if we're not writing much. I don't want to run out of room. (Occasionally, I come up with nothing. I turn to a printed paper lesson. We glue together like a book and then into our journals.)

During the past year, my geometry class actually wrote on a lined page in the journal.... twice maybe. There's never enough room and I like to contain a concept to one page. We actually used 90 of the 100 sheets in the composition book. I did only use the front side, but hope to use the back/opposing side as a reflection, sentence stem, summarizing, something page.

Step 4: Once I know how I want to organize and relate, I create a quick disposable mock up of what I plan the journal page to look like. I scribble an outline and notes to self. This is usually something that I use as a guide to keep me on track and throw away later.

Step 5: (optional) Sometimes, I create a pre fab printable foldable template. This makes journaling go much faster and students are less likely to fall behind or make mistakes. I usually have one foldable completed to show students what we're trying to make. Some students are quick to figure it out and begin to help others. I use solid lines to indicate folds and dotted lines to indicate 'cut here'. This strategy can save time by having the students write less and provides structure to help them better organize the information. However, I am a huge advocate of students writing! I think my students have learned more this past year than the previous two because they wrote everything. I rarely printed definitions, diagrams, illustrations, proofs, etc. It was sometimes hard, but my students were better off. Watching them draw platonic solids and cross sections was entertaining, but extremely difficult. I did give in in the end and printed them off. However, anytime I print something off, I still require students to participate by highlighting, fill in the blank, notating, etc.

Step 6: I teach the lesson. I try to make every step of the process engaging and mathematical. I ask open ended guiding questions before, during, and after the creation of the journal page. (I have developed excellent wait time. It was hard, but I'm quite proud of that.)

Even the foldable itself is a mini math lesson. I try to use mathematical language when referencing folds. It took about half a year to come up with new terms for hot dog and hamburger fold. Actually, a student suggested long or short half fold and I've used it ever since.

One time in geometry, I needed the students to fold a blank piece of paper to get sixteen boxes. They recognized a pattern in the words I was using - one half, one fourth, one eighth, one sixteenth. It turned into a mini lesson on exponential functions.

Is this strategy full proof? Absolutely not! I usually change a journal page up year to year, class period to class period. My students are my guiding force, and they let me know what works. Someone once told me that you have to learn to teach students and not just teach a curriculum.

 

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Geometry: Special Right Triangles

Pg 10. Rationalize Square Roots

Before we dived into Special Right Triangles, I though we'd go over rationalizing square roots. This went much smoother this year than in the past because my students were familiar and comfortable with square roots and simplifying them. Surprisingly, most of the students took this very well and rationalized square roots like it was nothing! (Still amazed!) It has been such a struggle in the past.

 

 

Pg 11. Special Right Triangles

This has always been my toughest area to teach to my students, until this year. When it was all said and done, I confessed to my students that this is one of the hardest concepts/lessons for me to teach. Then, they blew my mind. My students told me this was the easiest thing they've done so far and loved it. Throughout the rest of the year they chose to use the special right triangles method to solve most other problems over trigonometry!!

I think that part of reason for this is the method I used to teach this concept. I pulled several resources for notes, guided practice, and independent practice. I worked all problems myself to identify a pattern to the differing levelss of questioning. After this, I taught each question type as a lesson by itself.

For 45-45-90, I focused on finding the legs first and then the hypotenuse.

For 30-60-90, I began with the questions that required simple mathematical relationships in order to solve and then we worked up to the questions involving rationalizing.

We would work out an example with extensive explanations, then complete a student let guided practice. For the independent practice, I encouraged them to work as a team and I graded them immediately. I actively monitored for independent and collaborative work and I made sure to intervene when I saw attempted cheating.

Special Right Triangles

Cover:

Deriving the formulas:

Lesson examples:

Guided Practices: These were folded and tucked behind the above notes that were glued down like a pocket.

For each question, you'll notice a select number of homework problems. I assigned what my students thought was randomly selected problems. I would assign a small two to three problem practice and then the next day come back and do one to two more or the same. In the end, we completed the worksheet.

Honestly this whole journal page probably took us four or five days to complete. We looped through lesson, guided practice, and independent practice for each type of question. I felt that this was an important tool needed later for properties and measurement of two and three dimensional shapes.

Usually, the lesson using trigonometry to solve right triangles is introduced here. However, this lesson hit right before Christmas break. I looked through upcoming units and decided that I could make up the lessons and concept in Unit 8 Measurement of Two Dimensional Figures. It turned out great! Not sure if I will keep it this way next year or not. I guess it depends on timing.

This is a page from my second year journal.

Optional Pg. Right Triangle Solving Strategies

This foldable was used after the lessons on Trigonometry to summarize the strategies used to solve right triangles.

 

 

 

 

 

 

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Supplies... Key to Journaling!

SUGGESTIONS?!? Anyone?

For some reason, I cannot type in the reply comment box through my iPad and my iPad is all I have to work with.

A fellow expert in her field added a comment:

Jessica MonahanJune 26, 2013 at 5:42 PM

"I decided to try journals with my kids this year. It lasted about two weeks before all of the scissors, glue, markers, etc that I had bought for the "supply" baskets disappeared. I had spent hundreds of dollars and wasn't replacing it so the journals went away. I explained to the kids that these weren't for the taking but they disregarded me. Any ideas for solving this problem? I am an old teacher. I'm very comfortable being the sage on the stage so out of the box thinking is very new for me and everything I try, blows up. I work with VERY inner city kids who do not bring their own supplies...ever."

I wish that I had all the answers. All I can do is share some thoughts and reflections.

I purchased supply 'caddies' from Dollar Tree for $1 EACH. I have seen them elsewhere such as K-mart, Wal-mart, Target, etc. These helped me to organize and quickly count supplies before dismissing class.

Each caddy consists of three

• bottles of glue (always liquid, it's cheaper and holds better)
• small safety scissors (They may be highschool students, but I found that the smaller the scissors, the less time the scissors spend in their hands.)
• highlighters
• ultraflex rulers
• safety compass
• mini protractors

The following images are ones that I pulled from a google image search and do not reflect what my baskets consist of. My baskets remain on my classroom tables where the students sit.

Thought the above image was a neat idea for storing the baskets. The teacher used 3m plastic hooks.

IDEAS:

My second year students purchased one supply of their choice to contribute. This sort of brought out some ownership from them and they didn't disappear.

STAPLES: My first year, Staples had amazing sales and as a teacher they would let you get 15 to 30 of penny/quarter items instead of a limit of one. (Must have evidence that you are a teacher.)

The caddies made a difference in organization and counting of supplies.

I am extremely particular when it comes to objects in my class. My saying: "Don't jack with my stuff!" I watch students like hawk. Supplies stay in the basket until needed. If I see one out or used without need, I tell the student to put it back and continue teaching without pause.

Modifying behavior: I start day one with what is supposed to be in the basket and before they leave each day we make sure everything is put up and accounted for.

For middle school and freshmen, a colleague of mine assigned supply managers every other week. The supply manager was in charge of getting the basket and accounting for the supplies for each table when class was dismissed.

Journaling is a daily event of my class. The only day the journals are not used is on testing days. The journals are turned in for a major grade.

 

If anyone has strategies, advice, and/or success stories, please share!

 

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Geometry: Angle Basics, Protractor, Compass, and Types of Angles

Pg 10. Compass: What, How, and Use

It was important to diagram (trace) and label the components of a compass. We took a few minutes and practiced constructing circles with the compass on scratch paper to discuss the essential task of a compass.

I felt that it was critical to have students write out the steps for each concept. By writing the notation and terminology, students used them when teaching and working with others. Even though arcs haven't been officially introduced, I still used the term and notation for the diagram. This was a good experience for them. They began to observe and identify arcs as they came up throughout the year.

The independent practice problems that they store behind the notes previously completed by glueing the notes down 'like a pocket'.

FAVORITE: One of my perfered methods of teaching is to introduce the concept, complete a guided example together, and finish with one independent practice problem that day. Then on a seperate day, I have them go back and do one more. When they finish four days later, students either have it down, or we complete another set every other day. This helps them retain the skill over a period of time. There are some days when my students are independently mastering a series of concepts. I enjoy those days.

 

Pg 11. I begin angles with a page called Angle Basics. This page focuses on the components of an angle. I feel that in geometry it is very important to know and continually recognize angles.

 

Pg 12. How To Measure an Angle

For this page, my students are given a regular plastic protractor an angle, and together they are to build a set of three to four step instructions on how to measure and angle.

Then we take an envelope, cut it half and use it as a pocket for their own personal protractor that I print off on a transparency.

EXCELLENT IDEA: Print reusable tools like rulers, protractors, and grids on transparencies. Templates can be found through google. I use the grids for transformations of shapes and functions, and I also discovered that they are a great tool for layering and comparing systems of equations (especially those with infinite solutions because students then understand when we say the two equations are the same line - one over the other) from a list of four to five equations.

Pg 13. Angle Construction

Each student constructed their own angle and completed a set of sentence stems.

I really like the idea of students individualizing their experience-creating diagrams, writing problems for given information, etc. This encourages students to collaborate with others about their findings and allows them to teach each other without cheating tendencies.

Next year I plan on inserting a page of Angle Construction using the compass to copy angles, bisect angles, etc.

 

Pg 14. Types of Angles

This page is a half fold consisting of five flaps.

 

BETTER IDEA:

I pulled this diagram from a SmartPal template book. Using a push brad and straw, we created a reusable took for types of angles. We used the straw to physically demonstrate each type of angle and then we defined them under the 'area' for that angle.

LESSON SEQUENCE:

1. Engaging: Read Sir Cumference and the Great Knights of Angleland to my high school students. (They actually enjoyed it!) As I read they were given post-its and asked to write down any words or phrases they thought were important to the world of Geometry. From here, I knew that they caught the cute geometry references along with the important vocabulary. They demonstrated a significant prior knowledge for angle types (which I should expect). They then posted and organized the class post-its into some form of organization. Discussion ensues.

2. Exploring and Explaining: We complete the foldable.

3. Evaluating: I would ask them questions that required them to demonstrate a certain angle measure and type using their foldable and hold up their journals when asked. (Surprise(Elaborating): Disscussion of the two angles that actually exist each time came up!)

It just so happened that I ended up with a unannounced evaluation that day. It couldn't have gone better. I will never forget that lesson.

 

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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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Box and Whiskers Plot

So, today I had the opportunity to do something different. I got to work with 8th grade students on Box and Whiskers Plot. Now, I know I am not an expert and I know I missed identifying an outlier, but our goal for this tutorial session was to teach a basic understanding of Box and Whiskers Plot. Their teacher liked my lesson and the kids loved it, so I thought I would share.

My principal asked me if i knew much about Box and Whiskers Plots? I said that I knew a little bit and I have an idea to make it slightly more hands on.

I pulled some data from a textbook and put it on individual pieces of paper creating eight sets.

Here's what I did...

Each table received a sheet of poster paper and a stack of cards with numbers written on them.

My example was taped to a write board with the cards taped in a scattered unorganized manner. I worked through the first data set with them.

Teacher: "What do you call a set of values randomly given?"

I was looking for the word "data". After I guided them there...

Teacher: "What should be the first thing we do with data?"

Students: "Put the data in order from least to greatest."

Teacher: "What are the four measures of central tendency or variability?"

Students: "Mean, Median, Mode, and Range."

I then proceeded to ask the students to define and explain the process used to determine each.

Teacher: "Median is the essential tool in creating a Box and Whiskers Plot."

I then had them find the median of the data.

Teacher: "What is the minimum and maximum value of the data?"

Student: "28 and 67."

Teacher: "Understanding the information in a Box and Whisker Plot is determined by a number line placed below indicating the values used. What would be an appropriate range and scaling for a number line here? ... Another words, what would be a pretty minimum and maximum value that we could use?"

Students: "From 20 to 70 and go by fives."

Each table constructed a number line with the appropriate values and scaling.

Teacher: "Now, let's go back to our data. We need to determine the lower and upper quartile."

I explained the process (similar to median) and why it's called upper, lower, and quartile.

Teacher: "How many significant values have we identified?"

Students: "Five."

Teacher: "Using a short vertical line, let's identify the location of each value along our number line. You then connect the lower quartile to the upper quartile using two parallel lines. What did this create?"

Students: "Two boxes."

Teacher: "Then you connect the minimum to the lower quartile and the upper quartile to the maximum using a single horizontal line. What do you think we call these?"

Students: "Whiskers!"

Teacher: "What do you think is the significance of this type of graph?"

We spent several minutes discussing this before I gave them a new set cards.

I wanted to share this because it was well received. I don't know if it was because I'm not their usual teacher or they were really into it, but this lesson was refreshingly engaging and fun. It was one of those lessons that just worked, flowed, and the kids really connected. If you're a teacher, I'm sure you know what I mean.

Thank you.

 

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My Tool for Finding Slope & Slope Scrabble

Before our test, I decided to review finding slope with the two methods we had studied.

1. Counting Slope on a Graph

2. Slope Formula

Several of my Geometry students used a method earlier in the year that I thought Algebra 1 might appreciate.

• Positive: rise over run
• Negative: fall over crawl

 

We also discussed the staircase within a staircase.

Then we moved over to the slope formula. We also discussed the relationship between coordinate values and slope values of horizontal and vertical lines.

 

SLOPE SCRABBLE! Not as exciting as it sounds right now. We tried this but it was difficult to get the idea across to my students.

They had an excellent time finding slope for all of the problems cards I gave them. I even set up a table with all the solutions laid out so that they could match them.

The idea of slope scrabble is to begin at the origin and, using slope, make your way to the far blue dot in the corner to win. All of the other dots are things like double your slope, draw again, etc. There was some success with my students that have to patience to solve puzzles. Other students wanted to match slope again.

My students have an excellent understanding of slope.

I just wish I could troubleshoot the process and get this game going for them.

 

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Solving Equations is Like Wrapping Presents!

For my first year of teaching Algebra 1, I have made a lot of mistakes. These mistakes all revolve around an assumption. I assume that my students already know this and that. This comes from my experience in state testing remediation for 11th graders for the past three years. I now have realized that I have a chance to teach students to understand Algebra 1 from the beginning. I decided to review solving equations with my students, since this was a nightmare at the beginning of the year. I decided to teach them to understand each component of the process and what solving meant.

Step 1: "Unwrapping Your Solution"

I love reading educational material and Danika McKellar is one of my preferred authors. I remember her referencing gift-wrapping as a metaphor for solving equations. The idea of operations applied to a solution is similar to wrapping an object to hide its identity. To reveal the item, one has to reverse the process of wrapping, which is similar to finding a solution by reversing the applied operations.

It didn't turn out as spectacular as I would have preferred. However, this was a day well spent because my students no longer feared equations (for the most part).

First we started with x=3. Next, the students selected different operations and values to "wrap it up". Then in order to solve we reversed to process. When finished, we a concluded that solving is reversing the original operations. Hooray!!

 

Step 2: Properties Used to Solve

We identified the most common properties used in solving equations. Within the notes, we used the same equation to demonstrate how similar operations can be applied to acquire the desired result.

Step 3: How to Solve Those Equations

With the use of multi-door flap foldables, students identified each step in solving an equation by technical property and then by general vocabulary accumulated by the class. This step was critical in building their fluency in solving equations. Even lower level students that were hesitant in the process could solve.

Example1: We always started with the inside process.

Then finish by summing up with general words to help them identify the steps.

Example 2:

Step 4:

We moved from the in-depth process to identifying the general steps. By now, my students were using the vocabulary-properties, names of terms, quick steps, etc.

Step 5:

We reviewed with the giant Sorry board game. During this step, students started with a given equation including the solution and focused on the solving process.

Step 6:

TEST: I gave them a test in standardized format and received outstanding results! :)

 

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