Week 1 Reflection!

I loved my first week even with all the imperfections.  My students are awesome!  I wish I had asked them for feedback on the first week (maybe next week??) but so far, I think we are clicking :)  I know I have a few students who are not as enthused as I am; I hope to win them over completely!

So you say, what imperfections??  Most of the imperfections boil down to time.  OK, so this is where my current placement is different than other places I have worked.  We have a curriculum calendar published by the district that says Unit 1A covers certain standards, and takes 7 days.  There is an expectation that we will test on that seventh day (or be prepared to make up the difference in one of the next units because they are all outlined down to the day!)

1. So we planned too much curriculum for Day 1.  That in itself wouldn't be too bad, except my team and I planned every day of the 7 day unit ... built upon the mastery of the previous day.  The morning classes on Day 1 were cut short by a 1/3 (60 minutes instead of 90 minutes).  So every day this week I've been trying to make up time ... within reason ... while still ensuring thorough understanding of our content.  In the future, I want to recommend to my team that we plan for the shorter class, or allow one whole first day for "getting to know you" opportunities.
2. I talked too much.  High on my list of 3 goals is to talk less.  I'm already planning for it for next week.  This week each day had too much note-giving, note taking!  We used a flip book, Venn Diagram, Cornell style notes, and a webbing to help make the notes have meaning.  But still it seemed I did most of the talking.

I felt like some things went well.  I loved the conversation, noticing and wondering, on the first day around the vertex forms of equations.  On most days, I asked students to experience a math activity before labeling it ... trying to activate their prior knowledge, using the activity for my own informal observational assessment of students. 

We are on a block schedule (A/B days) ... so I saw 3 classes 3 times this past week.  In those 3 classes we discussed these topics:  

...  Defined a function
...  Introduced the seven parent functions we study this year
...  Defined the difference between discrete and continuous functions
...  Illustrated how to notate domain and range using three methods      (inequalities, set builder, and interval notation)

...  Defined transformations and took notes on the effects of a, h, and k.

Next week we spend time exploring transformations and define inverse functions.

If you are interested in following along day by day, I have a 180 blog.  My goal in that blog is to take one photo a day, to make teaching and learning visual ... and to share my work.  I hope you'll check it out!

Our first noticing and wondering!

I am excited about our first day!  I know students will need more time going over procedures, but I'm glad we jumped right into our curriculum.

We spent a few minutes noticing and wondering today.  It felt a bit awkward and students were slow to respond ... but I know that as we practice, we will be able to build their curiosity!

Here are my students noticing and wondering today:

I notice …

• 4 variables in each equation
• They all have f(x)
• Each equation seems to get more complex
• There is x-h in every one
• The last equation does not have “plus k”
• The last one is the only one with a v
• They all have the same layout

I wonder …

• Why does the last one have a v and none of the others do?
• Does the form help us find the maximum or minimum of the functions?
• How would the last equation look when it is graphed?
• What does “log” mean?
• What do the letters (a, h, k) mean?
• Where are these equations used?

I am posting these questions in our classroom so we can refer to them during our unit of study!

Beth

PS ... follow along with our daily snapshots!
PSS ... here are photos of some of today's noticings and wonderings!

Lesson plan template ... the simpler the better!

Today I created a simple template for lesson plans.  Our administrators don't require a specific plan.  Our math department uses what I think is a convoluted and complicated plan.  When I am assigned lesson plans to contribute, I use their form.  But for my daily purposes, I like a simple listing ...

• Date
• Standards
• Criteria for Success
• Materials
• Activities
• Formative Assessments

I created my template in Excel.  I embedded all of our standards for the year in drop down menus - so I can just select from the menus to insert the standards.

In class activities I try to outline as much as possible the details I want to include.  This year I'm trying to be very conscious of asking better questions and allowing time for noticing/wondering.

Our administrators specifically look for our criteria for success and how we measure those criteria during a lesson.  So in class tomorrow, I want students to know how to recognize a function in a table, mapping or graph.  I need to build in a short activity to measure their success.  Then as we move on to representing parent functions, quizzing students as we build our foldable, making sure they note key characteristics, various restrictions on domain or range, etc is essential ... and expected.

What do you write down in your lesson plans?

PS ... Check out my daily blog ... http://180snaps.blogspot.com/ ... to see what we capture on day one of school!

Learning new tricks! New Faves!

OK ... so if old dogs can learn new tricks, this older than most teachers can learn them too!  This week I've learned two new tricks that I already love!  

The first new trick is creating online quizzes using Google forms.  I know - we all use Google forms to collect information ... but did you know that Flubaroo, a script, will grade those quizzes for you?  It's so awesome!  Simply create your quiz (and yes you can embed pictures like graphs and tables).  Choose a new spreadsheet as your response destination.  Take your quiz yourself.  When you are ready to grade, open the spreadsheet, and select Tools ... Script Gallery.  Search for Flubaroo.  Install it.  (It installs in just that one spreadsheet).  You have to have more than 2 responses to your quiz to test it out.  Flubaroo will ask questions ... what key do you want to use (you'll choose your answers) and how many points to give each question.  When you hit your next button, you'll have graded quizzes!  It's really quite simple!

The second trick I learned this week is how to make my own instructional videos using my laptop and document camera.  I uploaded my first and only today to Youtube ... my own channel, woohoo!  This first video is very basic - just defining a function using the Frayer model.  In the coming days, I plan to work classwork and homework problems - typically just one per video.  That keeps the videos short, and to the point.  Near the end of a unit, I'll work a set of review problems.  Students will be able to hear my voice, see me working out problems and writing notes.  And it was soooo easy!  I used movie maker because it is installed on my school computer.  I used my document camera.  The only extra cord I needed was a USB cord that went from my laptop to the camera.  After making choosing only a couple of pertinent settings, I was ready to record.  I like that this method simply captures my hands and the paper on which I am working.

These are my new faves!

Error Analysis Function or Not a Function

On our first day we will review the definition of functions.  Before we delve into the details of the definition, students will visit posters of graphs on the walls with a partner and determine if the graph represents a function or not.  After experiencing the math for themselves, we will spell out the specifics of the definition as we check the work.

To make sure students understand the definition I have an "error analysis" exercise for them.  The error analysis exercise is a one-page worksheet  (8 problems) that already has answers.  Some answers are correct, some are incorrect.  Students need to rework the page, identify the incorrect solutions, and explain the error in thinking.  Here is a link to the activity.  If you modify it, share your changes so I can learn from you!

MSSunFun: Goals!

Last week when I read the topic for this Sunday, I thought to myself ... great idea!  Then my brain seized up ... and no goals came to mind!  Last year, my goal was to survive!  Returning to the classroom after several years was more difficult than I expected it to be.  And if you had asked me about mid-November how I was doing, I would have told you I was definitely not going to make it.  I experienced many of the same feelings that new teachers feel - as documented by research.  Fortunately by the end of the first semester I determined that I could at least finish out the year :) ... and surprisingly by May, I was ready to sign on for the next year!

So this year I want a different goal or two.

Goal 1:  I want to talk less.  I have a tendency to talk too much, to explain too much, to demonstrate too many times.  Instead, I want to give students more time for inquiry work, more time for problem solving, more time for cooperative work.

Goal 2:  I want to promote and develop student curiosity. 

My first step is to ask students what they notice, what they wonder.  And not just pose those two questions, but to record their responses, and invite students to explore them in class and on their own.  This means I need to start with better "problems" ... problems without questions already posed, problems in context that allow for noticing and wondering.

I know more goals are too many but a third goal is to do more with student mistakes.  One strategy will be to use the "favorite no" activity - especially in short review activities.


So ... I was impressed by Mary's measurable SMART goal.  This is the first year in a very long time that I am not teaching a tested course.  So I won't have formal state testing data to examine.  Since my goals go together, talking less, posing better questions, the hard work will be in planning my lessons.  And then ... I must, must use a timer!  I often use a timer for student work, but now I must apply that same strategy to my talking!

I am in that anticipation phase ... excited about the possibilities for this new year!  What goals do you have???

My Fav Friday: Google sites, apps, extensions!

One of my favorite tools for the past few days have been Google and Google Chrome Apps/Extensions!  Last year our district used TeacherWeb for class websites.  This year we have the choice of SharpSchool or Google sites.  I decided to go with Google sites and I'm loving it.  It is sooooo easy to update assignments, announcements, and handouts!  Here is the link to my class website.  It's a work in progress ... but I'm pleased with the way it is coming together!

I'm also learning more about Chrome extensions and apps.  I attended a workshop a week or so ago, and received this handout.  The ones with asterisks came highly recommended.  If you are a Chrome user, check them out!

180 Snaps ... coming soon!

Starting tomorrow, our first day back to school, I'm going to capture a snapshot a day to chronicle the next 180 days.  Check out my classroom at http://180snaps.blogspot.com/.

Families of Functions Day 1

I'm working on Day 1 plans ... they keep evolving as I talk with new team members.  Here is the outline of my Day 1 this morning :)

August 26/27 ... Lesson Plan 

• Enroll:  As students enter, invite them to complete the Fixed vs Growth Mindset survey.  
• As students complete the survey, ask them to put a sticky note on the board (number line) to get an overview of our class.  
• Briefly explain our class emphasis on growth!
• Experience:  In pairs, students will sort a set of cards into two groups – function, not a function – with no teacher direction – only questions.  (I am borrowing from Math Tales from the Spring and adding a few sorting cards from VA DOE.)
• Label:  Use Frayer model to define a function. 
• Ask students to use the definition and discussion to assess their card sorts.    
• Assign 8 Error Analysis problems.  Topic:  is it a function or not.  Answers are provided but some are incorrect.  Which ones are incorrect and why.
• Demonstrate:  Introduce 7 functions to students.  
• Students will take notes on family, equation, graph, domain, range, and characteristics.  
• Students will enter parent functions in calculator to assist in exploration.  
• Use guiding questions.
• Review:  Introduce notebook expectations … use unit overview to review briefly today’s goals.  Assign setting up notebook as homework.
• Celebrate!  (Think about how best to do this on first day )

(By the way, this is my favorite Lesson Plan outline ... for students to experience math before we label it!  The outline is called EELDRC out of Quantum Learning Training).

Here are pictures of our flip chart for families of functions ... it's a quick put-together ... individual cards taped in succession so that they flip up.



If you want the full pdf, click here.

Looking forward to seeing everyone's Day 1 plans!

Digital Frames - Exploring Color

I have begun to play around with creating borders.  I see the elementary folks on TpT create so many intricate designs.  I don't print much in color; I don't have a color printer at home or work.  So it is cost prohibitive.  

Here is a set of borders representing typical math manipulatives in the elementary years ... linking cubes, pattern blocks, and cuisenaire rods.  

Do you "decorate" stations?  Do you use color?  Art?  How do you use digital frames?

Ice Breaker - Pipe Cleaner Structures!

In our TAG/Pre-AP Algebra 2 classes we will jump into curriculum activities on the very first day of school.  I've debated about how many and which "getting to know you" activities to do and how much time to spend on specific math content.

I haven't decided for sure what icebreaker to do, but I found this one online.  It looks interesting to me. I borrowed it from this website.

• Provide each student with three pipe cleaners.
• Give students about five minutes to use the pipe cleaners to create a structure or symbol that represents something about themselves. 
• At the end of the five minutes, set up a sequence of 60-second "speed dates" during which each student tells the other what their symbol is and why they made it. (Sound a bell to indicate when they should switch chairs.)

Alternately, students could create structures, then share them in groups, ask each group to select a "winner" - their favorite and give a reason.

Another alternate idea is for students to work in groups to create a structure ... that represents something that all the students in the group have in common.  Groups share out after 5 - 10 minutes of building.

I would love to hear if you have tried this and how it worked ... or if you have ideas for how to strengthen this idea!

Countin' down the days ... 18 days until our students arrive!

Made4Math ... First Pages of Notebook Plan

I've been inspired by several bloggers who are sharing their notebook plans and outlines for the first day of school.

I have decided to use a 3-ring binder this year for our math notebook.  I discovered last year that I really don't like tape and glue.  And we have a print shop in our school district that does most of our printing for us ... they will print on hole-punch paper.  So ... I'm going to give this a go!

The first pages of my notebook plan are posted here.  If you have ideas or suggestions please post your thoughts in the comments!  

Primary Dicey Numbers!

I had fun tutoring elementary students this summer.  We used tiles, cards, pattern blocks, dice, and poker chips to build number sense.

One of the activities we did was to roll 3, 4, or 5 dice to create the largest possible number, then the smallest possible number.  We added them, subtracted them, graphed them on a number line, and talked about the patterns we saw.

Do you need extra practice for your young mathematicians?  If so, check out this free center activity, Dicey Numbers!

MakeOverMonday Week 8: Ferris Wheel

Dan Meyer says there are only 4 more makeover Mondays.  I have enjoyed participating and learning from others!  I report to school in the middle of this month ... I may not get to participate beyond this week.  I definitely want to take this idea of transforming textbook problems to my team.  I'll be working with different teachers this year - some I know from a distance last year, and some new faces.  I'm hoping we can put our heads together to create rich, worthwhile tasks for our students!  (I'm curious about the professional development they did as well ... it will be fun to put all of our new learning together!)

This week's problem is about a periodic graph.

So, #1 is all about proportional calculations.  #2 requires creating a graph; I can imagine students using the points from #1 as the basis of their sketch.  #3 is about the circumference of a circle.  So this problem is accessible to middle school students.  Students don't have to know anything about the sine curve or equation to approach this problem.  But if this problem is introduced after we have studied linear equations and transformations of those lines, I would start with enrichment stations ... from this desmos file.




The desmos file is an amazing collecting of applets and interactive spreadsheets.  Students manipulate a, b, and c (period, amplitude, and vertical shift) in the sine equation to match the movement of an engine, roller coaster, and scientific data (daylight hours).  The website says it is for upper math students and that students should be familiar with sinusoidal curves.  For this lesson, I don't think students need that understanding.  In our studying of linear functions, we would have noted that there are other functions that make other shapes or designs.  And that playing around with the parent equations of those functions you can transform them.

So ... first I would show a picture of a ferris wheel and/or a video of a ride on one.  I will invite students make notes about what they notice and what they wonder.  In groups, students would share, and then we would share out in class ... making a list of their thoughts.  I will invite students again to continue thinking about their ideas as we do some exploration activities.


Next, I would set up exploration stations (at least the engine and the ferris wheel).  I would invite students to explore, discuss, and develop ideas about what is happening.  I would have some guiding questions.

Then ... when we would go back to the textbook problem, just the picture and the seconds needed for a revolution.  "What are questions we might ask and answer from this picture?  Work with your group to develop 3 questions.  At least one must include a graph.  Answer your questions on a separate sheet.  Be sure to label you work carefully."


When groups are finished creating and answering their questions, I would collect those and sort them by types of questions.  I may create a few question cards myself depending on the groups' response to the task.  In our next class we would work through some of the student developed questions.  Last we would return to their noticing/wondering to discuss any ideas we had not yet explored.

http://www.mathdemos.org/mathdemos/sinusoidapp/sinusoidapp.html

How to Learn Math #5: Number Sense!

I worked on Session 5 of How to Learn Math yesterday.  This course both affirms my knowledge and practice ... AND it challenges me to grow and learn!  I have long believed that building number sense is huge and that we don't do enough of it in schools.  I have been tutoring young students this summer - students going into grades 2, 3, and 5.  These students in particular needed help with composing and decomposing numbers and in using "friendly" numbers to assist in problem solving.



As I thought about number sense I was remembered that I posted about that topic several months ago.  I am repeating the post below because it has some useful links in it!

~~

Usually when I think of building number sense, I think about primary math education.  I know, though, number sense is something we all must work on all the time!  So I did some Internet research to find resources and ideas for middle and high school.

1. Knowing how precisely a high school freshman can estimate the number of objects in a group gives you a good idea how well he has done in math as far back as kindergarten, researchers at The Johns Hopkins University found.  This Science Daily article is quite interesting.


2. One of my first "hits" in my search revealed this book, Building Powerful Numeracy for Middle and High School Students written by Harris, published by Heinemann.  The Heinemann website has a brief description.  I plan to put this book on my summer reading list!


3. If you are looking for number sense strategies and tricks, this website looks awesome!


4. The state of Texas has a well-developed academic competition developed by the University of Texas - one of which is number sense.  Practice tests are available online here.


5. NCTM has published several number sense tasks - with explanation in their Reasoning and Sense Making Task Library


6. The state of Washington has posted sample number sense writing prompts for all grade levels.


7. San Diego school system has posted ideas for number sense routines.


8. University of California also published a workbook on number sense.


9. Minnesota has published an interesting paper showing the progession of number sense through primary years to high school.

I enjoyed this research ... now ... how shall I build the recommendations and examples into my daily practice?  My students would definitely benefit!

I'm working on a plan for warm-ups ... for when students first enter.  I know I want to incorporate number sense activities, as well as problem solving and review of the daily curriculum topics.  Once a week I want to use Math Munch in some way.  There are so many ways to go ... so much to do ... How do you structure those first 5 - 10 minutes of your class?

I look forward to hearing about what others do to build number sense!