Week 2 Sunday Summary #MTBoSchallenge & #made4math

Week 2 is complete.  I am still trying to find my groove with having 1st hour prep.  I am a morning person, so I am ready to interact with students as soon as we arrive.  Sitting down for plan time, I lose my momentum.   Paired with having to be out of our building by 3:00 due to renovations, I have no time to sit and process the day’s events.

3 Things That Happened This Week
I finally got my anchor chart board with sentence starters and questions completed.  I am very pleased with it and have been trying to model/give students opportunities to practice in class discussions.  Here is a link to a file of the starters.

I giggled when I saw Sarah saying she “totally stole” from me…that’s what #MTBoS is all about. Sharing and making our classrooms better for our students!

I am using visualpatterns.org as one of my daily tasks to begin class.  I wanted students to have a page in their INBS to record these…

Here is the file.  Print 2 up and front/back for a booklet for your INBs. 

I shared Thursday how I was a bit hesitant to allow my students to go with their process of locating the midpoint given coordinates of endpoints.  I know.  There are those that say just tell them the midpoint formula.  I could but this is the method they are owning.  Basically, they are finding the distance between the coordinates, then “moving” half the distance will put them at the midpoint. 

But then I got to thinking about the actual standard:

CCSS.MATH.CONTENT.HSG.GPE.B.6
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Midpoint is the most common and yes, we’ll use it in proofs later.  But if I go in Monday and ask them to find 1/3 point which would be a 1:2 ratio, or a 2/5, 2:3? Will their method actually prove more efficient because it is actually the same process for both?

2 Things on My To-do List
I have 3 tubs that still need to be unpacked from our renovation move.  I have my shoe boxes on the shelves, but I need to get those labeled correctly.

Finish an Intro to Matrices Unit, I hope will work as  flipped/blended learning unit.

1 Good Book to Read
Thanks to @mathymeg07 for sharing Wonder by RJ Palacio. 

Megan said it is a book everyone from 9-99 should read!  Right now, the Kindle version is on sale for $2.50.  I am making posters of Mr. Browne’s Precepts for my classroom, such great lessons to live by.

Geometry, Baking & Decorating Cakes…

A colleagues began a new venture last summer…Rich in Blessings, baking cakes.  She sent a link to this post
Perfect Buttercream Stripes to share the math needed to complete the task shown below.

Here are a few images in the post:

There could be some simple, yet nice questions arise in this setting, like:

If Mrs.D wanted 1.5″ stripes on a 10″ cake, approximately what cental angle measure would she need to use? 

If she chose the slanted stripes with 1″ width, what angles would result in the guide strip for an 8″ cake?

If she used a 30º central angle for a 12″ cake, how wide would she need to cut the guiding stripes?

If a batch of buttercream covers ____ 10″ smooth cakes, how many batches would I need to decorate ____ 12″ cakes.

Not sure at what level this is in the standards but I plan to sit down this afternoon and determine how I can use this context during the spring semester…I believe I can make this work for C.A.1, C.A.2 and C.B.5…

From corestandards.org

Understand and apply theorems about circles

CCSS.Math.Content.HSG-C.A.1 Prove that all circles are similar. 

This could easily be done by constructing a “cake map” including 6″, 8″, 10″, 12″.  Allowing students to prove that all of their circles are similar, by showing they are dilations of one another.  Maybe I could even ask, if I wanted to enlarge my diameter 2″, what scale factor would be needed to accomplish this?

CCSS.Math.Content.HSG-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. 
Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. (Thoughts here?)

CCSS.Math.Content.HSG-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

CCSS.Math.Content.HSG-C.A.4 (+) Construct a tangent line from a point outside a given circle to the circle.

Find arc lengths and areas of sectors of circles

CCSS.Math.Content.HSG-C.B.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Maybe play off the idea: use different colors of fondant to create a pattern of the sectors…how many units^2 of each color are needed?

I believe with a bit of work, this could qualify as my Practical Living and Career Studies Program Review submission.  If I plan efficiently, collaborating with my Visual Arts department, I may be able to use it as the Arts/Humanities submission as well.

What ideas, suggestions can you offer that will push my thinking forward…make this a good, quality task?

INB Unit Organizer

I wanted to create a unit organizer than encompassed several aspects but would also be narrowed to one page, fiting in to the INB.  Here’s a list of what I wanted:

vocabulary
unit overview/schedule
learning targets
record of assignments
track their own assessments/learning
place to record questions/big ideas
opportunity for end of unit reflection

Here is what I arrived at for a first attempt, copied front to back and folded in half, this is the order students will see the booklet. 

The vocabulary pre-assess was a great tool.  I saw this idea over at Math = Love earlier in the summer.  It went so well. It only took students a couple of minutes to self-assess their vocabulary knowledge.  As I walked around, I was able to see several terms had 3s & 4s.  We compiled a list of our 1s & 2s words.  I explained, as they learned a word or gained better understanding, they should go back and put a +.  Before the end of class, students were asking if they could go ahead and update their chart.

If possible, maybe completemthis part a day before beginning a unit, in order to make needed adjustments based on student responses.

I included the correlated CCSS # for each target.  Eventually, these may be beneficial when looking online for a resource on a specific standard.

I am not fully satisfied with this chart yet. Assignments made for specific targets can be listed, a note if completed (stamp) and place to monitor their assessment for each.  A second line has been included in case RTI/enrichment is needed.

Finally, the back side has a place to record reflection.  Ideally, I would have them complete the reflection at least 2 days prior to unit assessment, allowing to address any needs the following day, prior to assessment.

As always, this is a work i  progress, suggestions and ideas are welcomed!
PDF:  http://db.tt/DWfJUqLL
Foundations in Geometry doc

Intro to Matrices:

Intro to Matrices pdf
Intro to Matrices doc

Addressing Questions about Formative Assessment Lessons

Rather than go through a gazillion tweets, thought I would share my thoughts here.

The Formaltive Assessment Lessons I have shared I  the past come from the MARS site.  You will find tasks, lessons even sample assessments.

If you are just visiting the site for the first time, I would encourage you to spend a bit of time in the Professional Development modules.

     “Module 1 intoduces the model of formative assessment used in the lessons, its theroetical background and practical      implemention.Modules 2 & 3 look at the two types of Classroom Challenges in detail. Modules 4 & 5 explore two crucial pedagogical features of the lessons: asking probing questions and collaborative learning.” MARS site description.

The assessment tasks are shorter, but still allow for some amazing mathematical discussions, especially when implemented using the format of #5pracs model.  Tasks are organized by levels with the expert involving a wider range of Mathematical Practices, less structured and requires more problem solving /centent knowledge.  Where as the novice seem to be more straight forward, provide a bit more structure.  Which task to choose? Well, it depends on your students and your purpose of assessment for a particular standard.

The classroom challenges (FALs) are much more lengthy.  Usually 2, even 3 day total for complete implementation of the lesson.  I am okay with ‘sacrificing’ this time when students are engaged, having mathematical conversations.  The productive struggle they may experience causes the ideas to stick with them.  For example, this year, some of my Algebra 2 students referred back to a lesson from their 9th grade year about “Tom” which was a lesson on time-distance graphs…one of the first FALs I ever attempted.  How many other lessons have I taught over the years that truly stuck with them?  Monster Trucks @mathprojects, definitely, but my lecture, notes, worksheet practice…never.

FALs are either problem-solving based, usually students attempt a problem individually, then in a pair or small group, then they analyze student samples of the same task.  The concept development often uses cards sort activities.  Using these have impacted how I present other lessons as well.  I see the value in student discussions and sharing, allowing them to create their own ideas rather than me telling them every single step.

Like any other resource, FALs can be modified to fit your learners. However, I have seen greater impact on learning when I follow the layout of the lesson closely.  Teachers have tested these lessons, anticipated student strategies/misconceptions and even outlined possible questions you may ask to move a learner forward.

Each FAL is outlined to show intended learning goal, along with mathematical practices that will be evident in the lesson. There is prep time involved. Don’t think you can download the night before, make copies  before class the nest day and begin. 

Ideally, the FALs would be placed about 2/3 through the corresponding unit of study.  I have found them to be very eye-opening to my students’ thinking.  Some FALs require some pre-requisite skills, so you must go through the lesson in order to see what the students will be doing.

Also, if you are an Algebra 1 teacher, dip back into 7th & 8th grade for some great lessons, especially if you are in the transitioning phase of CCSS.  I especially like Increasing Decreasing Quantities by a Percent, Interpreting Distance Time Graphs, Modeling Situations w Linear, Representing and Combining Transformations Equations from middle school lists.

If you have specific questions, please share in comments.  I am no expert, but I have implemented enough of the lessons in the past 3 years to know they have a place in my classroom.

Pam Wilson, NBCT
Currently Reading
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like  a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough

CCSS Appendix A Traditional Course Outlines #made4math

It seems many are just now beginning the transition to CCSS.  These files may be helpful as you begin outlining your curriculum.  All they contain are the standards as outlined in Appendix A of CCSS – recommendations for each traditional course.

Algebra I CCSS

Geometry CCSS

Algebra II CCSS

These files are only intended to help you ensure you have addressed each standard within your local curriculum.  How you organize your units can vary to district to district, but I am hoping these will help you as you organize with the CCSS.

If you have any issues with the files, please contact me, I can email them directly to you if needed.

#geomchat: Come Chat! | Algebrainiac

Please join!  #geomchat

http://algebrainiac.wordpress.com/2013/06/30/geomchat-come-chat/

Pam Wilson, NBCT
Currently Reading
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like  a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough