Saturday, June 16, 2018

June and Graduation

Last Week and Graduation

There were no formal math classes the last week of school.
The 7/8s were prepping for graduation and the 4/6s were finishing up projects in homeroom.
My speech for the graduating class is below:

I’ve tried out 9 ways to speak about these nine graduates and continue to have trouble. They are nine individual who make a coherent whole, with interests both wide and overlapping.

What else comes in nines? Analogies are always a great way to write these speeches how about that:

Nine Justices of the Supreme Court, nah, who wouldn’t want to be RBG, but then what; nine planets of the solar system, orbiting the bright center that is SK--the astronomers tanked that one a few years ago; Muses? I simply can’t force Melpomene (tragedy) on any of these delightful children. Baseball players? Naw, all of these kids are way out in left field, but Then it came to me: 9 rings for the kings of men! No, while I had someone in mind for the Witch King, I’m not sure who else is ready for a life of service to Sauron.

When analogies fail it must be because there is something incomparable about the group. So, I decided to trust myself like I trust these children. I’ve been with some of these kids since my first days at SK, and I’ve watched them all grow from brash,  timid, and eager children into assertive, confident and excited adolescents.

This class means a lot to me: they are the second (and final) class of Samurai. They have been with me in faery camp, through magic shows and Magic cards, disconcerting bus rides, a trip to Mars, forced marches for cheesesteaks, short circuits (really don’t plug the thermistor in backwards), and all sorts of adventures with fruit. We’ve faced down zombified creepers and told more puns than I can remember (from me and them),

And so, I as I literally have my back turned to you all today; know that it is not because I’m ignoring or forgetting you--that will be impossible, but because I know you’ve got my back.

Thursday, May 31, 2018

Week of May 24

Week of May 24

4-6 Math Class

We used this week to finish up assignments and activities that were started during my leave. We spent Tuesday and Wednesday digging more deeply into the abstract algebra and group theory assignments the class worked on during my leave. Specifically, we looked at a more complex group with two cyclical elements with different periods. (The rules were: YYY can be deleted, ZZ can be deleted and Y ⇔ ZYZ; the operation was “multiplication”.) The operation table for that group is in the center of the photo below:
After discussing the idea that sometimes to simplify a statement you needed to make it more complex first (a key step in developing the table for the above problem), we moved on to the simplest finite group I am familiar with using numbers: (-1, 0, 1) on multiplication. The students were able to identify the identity element, the inverse (or lack thereof) for each element and conclude that the situation was a group; they were also able to explain why these numbers would not be a group under addition, division, or subtraction because of a lack of closure. We finished out our look at groups thinking about a few infinite groups: even and odd numbers under multiplication and/or addition. Including discussing why odd numbers was a group under multiplication but not addition.

(The 7/8s are on their Spring Trip this week.)

What Happened in April

April 6, 2018

Sam’s 4-6th Math Class

This week the students completed the class-made reviews from before break, presented and received feedback on their statistics research, and did an investigation relating area and volume, in addition to working on their usual curricula.

Algebra and Pre-Algebra

The ⅞ Solar Schools Projects were due this week and a large portion of our efforts were diverted toward that end; of course, that project includes applying the mathematical concepts (particularly related to the financing) that we’ve been studying. The class also had a couple of sessions to get back into their individual math progress after all working together on simple and compound interest. On Friday, Ed Feng came and talked to the whole group more about probability and how to use technology (Python) to calculate probabilities and expected values.  

April 13, 2018

Sam’s 4-6th Math Class

It’s tax season in Sam’s math group. This week in addition to Singapore, each pair of students received two W-2s, a 1040A--students who did this activity last year got a full 1040 and a schedule A--and an additional paper with further information about their tax filing status (student loan or mortgage interest, dependents, medical expenses, etc). We talked about the US income tax system, how to read the W-2, and find the relevant IRS instructions online. Then with their partner they set about filling out the 1040 return. For you parents doing your taxes this weekend, if you have the fortitude to inquire, see if your kids are interested in helping, or at least better prepared to empathize.

Algebra and Pre-Algebra

We’re into the time of year when the 8th graders are thinking about their math placements for next year and making plans to complete the material to be prepared for the chosen class next year. The Completing Algebra group have been focused on factoring quadratic equations, this week we primarily looked at factoring by group and the difference of squares pattern. The other algebra students are working on a variety of topics related to linear equations (mostly solving systems of linear equations), and some of them are moving on to studying exponential growth and decay.

April 20, 2018

Sam’s 4-6th Math Class

On Monday we finished up with taxes; in addition to signing their forms, the students learned how to find the proper mailing address in the 1040 instructions based on their pretend address and whether they owed or had a refund coming. (We also had a mini-lesson on how to address an envelope, which a fair number of them had never done. We didn’t actually mail the forms, of course.) Tuesday we had a game day with Wendy and Lisa’s classes; it’s always nice to have some time for community building with a math focus. The other enrichment for this week was a discussion of very large numbers, exponents, scientific notation, the metric system motivated by a reading about estimating the size of all human knowledge, and/or the Internet.  

Algebra and Pre-Algebra

Most of the students spent the week reviewing or working on a chapter assessment. Everyone has an approximate plan in place for the rest of the year and is working on that mostly independently with check-ins. (At this time of year the 8th graders tend to be very focused on HS readiness and having the math plan established has historically helped with any anxiety in that regard.)

What Happened in March

March 8, 2018

Sam’s 4-6th Math Class
This week we only met on two of the days, (the 5/6s were taking the iReady test the other two days) so the class worked in their math books. Most of the class is working on some form of geometry: triangles, quadrilaterals, parallel lines, tessellations.  

Algebra and Pre-Algebra

The 7/8s also took the iReady math test this week on Wednesday, so we only had formal math class three days. The kids are working on a variety of topics, including a few are doing work related to their Solar Schools project. Rushil and Will used data from the Google Solar Calculator to derive a more general formula for the cost savings of installing solar panels, since the Calculator didn’t allow for buildings with electric bills over $500/month.

March 15, 2018

Sam’s 4-6th Math Class

This week we’ve been digging into statistics more. After learning about five-number summaries and box-and-whiskers plots, the students each developed a research question and are collecting data that can be displayed in the box-and-whiskers format (the questions must have a single numerical answer for each response). Some of the students are working together to create and compare multiple related plots. We also spent a day learning how to use Google Sheets to do most of the calculations and create the box-and-whiskers plots for us.
Next week, we’ll be taking a look at the data collected and talking about what it might mean.

Algebra and Pre-Algebra
This week all of the 7/8s are working on math related to the Solar Schools project, specifically, financing. Everyone is working on something related to simple and compound interest or more advanced business math calculations--like time to pay off an investment, or expected value of a portfolio--depending on their previous exposure to the content.

March 22, 2018

Sam’s 4-6th Math Class

This week students completed their statistics research and analyses and also wrote their own review problems for upcoming Singapore assessments.

Algebra and Pre-Algebra

This week all of the students focus their mathematical efforts on researching financing options for the Solar Schools Project.

Monday, February 19, 2018

Winter 2017/8 -- A Very Overdue Update Posting (Dec 18 - Feb 9)

Note: You'll notice it hasn't been updated in a while. My bad; however, members of the SK community have access to all the information here through the Google Doc attached to the weekly newsletter.

December 15 and December 21, 2017
Sam’s 4-6th Math Class
This time focused on getting everyone to a good place to take a vacation. Many of the students worked on assessments. The students who did not have an assessment to work on (because they’ve already done at least one this year) took a look at a foundational problem that links geometry and number theory--specifically, the number of regions created by n lines inside a square. They focused on looking for patterns in the maximum possible number of regions for a given number of lines and developing first an iterative and then explicit formula for the number of regions based on the number of lines. One student commented on a connection between this problem and the famous (if apocryphal) story about Gauss and the sum of the first 100 whole numbers. The last days before break we also took a look at what happens when you try to build Pascal’s triangle in binary--surprise, the result is the Sierpinski Triangle with 1s and 0s.
Algebra and Pre-Algebra
These groups are also working toward completing a chapter or unit before break. The Pre-Algebra class is working with factors, multiples, and fractions concepts including variables.
The Beginning Algebra group continued work on writing linear equations based on points, a data set, or other relevant information. The Completing Algebra group was introduced to the Quadratic Formula and mostly worked on finding solutions (zeroes) of quadratic equations.  

Also, as part of their presentations on electronics components, the students looked at direct applications of Ohm’s Law, and more general proportional reasoning as with a variable resistor.

January 12, 2018
Sam’s 4-6th Math Class
This week we worked on a common math puzzle for the beginning of a new year. The goal is to write expressions that evaluate to all the numbers from 1 to 100 using just the digits of the current year. We played around with different sets of restrictions, beginning with very prescriptive rules: the digits 2, 0, 1 and 8 must appear in that order and the only other symbols (operations) allowed were: parentheses, +, -, X, /, !(factorial),(square root) , ^ (putting things in exponents). We were able to get about 25 with this set of restrictions. We then loosened the rules to allow for concatenation (so 2 and ) could be used to make 20, etc), this got us quite a few more of the numbers. On the last day, we dropped the order restriction which was sufficient to get us most, but not all of the 100 numbers.
As a teacher, I love puzzles like this because they allow for students with a wide variation in knowledge to still all access the same problem, all the while emphasizing analytic reasoning, order of operations and accuracy in calculation.
Algebra and Pre-Algebra
The pre-algebra class learned about rules for exponents this week, including the meaning and use of negative and zero exponents. The Beginning Algebra class looked at the relationship of the slopes of parallel and perpendicular lines. The Completing Algebra group is working on memorizing the Quadratic formula and did a lesson where they researched and analyzed the quality of youtube videos on that topic. My favorite video they found is here.
Following on our visit to AVL, we encountered concepts related to pressure, so we talked about the proportional relationships between pressure, volume and temperature (Charles’ and Boyle’s Laws).

January 19, 2018
Sam’s 4-6th Math Class
The week for this group was a little staccato. On Tuesday, I was home ill, and the class worked with Wendy’s group on problems about symmetry and geometry. We used Wednesday to catch up on Singapore work that was planned to get done last Friday. Thursday was move up day; the 6th graders were travelling with the 7/8s and, as the 4’s were visiting with the 5’s, they all met together for a math activity with Wendy and Lisa. On Friday we got going on Singapore assignments for next week. Most of the students are working on concepts with place value: unit conversions, percents, decimals.

Algebra and Pre-Algebra
The Pre-Algebra group are all working on the chapter 4 assessment, covering topics with exponents and powers. The Beginning Algebra group continued talking about equations of lines and writing equations of parallel and perpendicular lines. They also spent one class period goal setting; planning out their workflow with the optimistic goal of completing chapter 6 (on inequalities) before Mid-Winter break. We got out the planners and talked about how to decide what times would be useful to work during and how much you might expect to get done. In Completing Algebra we’re wrapping up a chapter on graphing quadratic equations, including an introduction to the quadratic formula. This week we especially looked at how to use the quadratic formula and real world meanings of “finding the zeros of a parabola.”

January 26, 2018
Sam’s 4-6th Math Class
This week had us going further with geometry and measurement in the form of letter dissection
puzzles. Building off the T and H puzzles we’d worked on before, students used grid paper
to make their own letter puzzle then tried them out with friends and made revisions.
The activity culminated with the students learning to use Tinkercad, 3D modeling software,
to create a makefile for their letter puzzles, which are then being printed on the Makerbots.
There wasn’t enough time to print all of the puzzles last week; everyone should have a
completed and printed puzzle to take home by the end of the day on Monday January 29.

Algebra and Pre-Algebra
The Pre-Algebra group all wrapped up their work in chapter 4 and have moved on to chapter 5, covering fractions and rational numbers more generally; for the next few couple of weeks, they’ll be solidifying their calculation skills with fractions and applying those concepts to solving single variable equations that include rational numbers. The Beginning Algebra group is starting a series of lessons on inequalities and absolute value; we had a lecture and discussion about the basic concepts on Thursday and will dig more into those concepts next week. The Completing Algebra group is working on finishing up their initial study of parabolas; some of the students are still working on applying the Quadratic Formula to get the zeros of parabola, others have moved on to thinking about factoring quadratics more generally.

February 2, 2018
Sam’s 4-6th Math Class
This week we began working with some concepts in pre-algebra, in particular, variables and solving equations in one-variable (with whole number coefficients). We are making connections between concrete models, using the Algebra Lab Gear; pictorials models, like the Singapore bad models, and fully symbolic algebraic notation.  

Algebra and Pre-Algebra
The Pre-algebra group is continuing their work on chapter 5, now looking at expressions with rational (fraction/decimal) coefficients, the Beginning Algebra group is beginning to discuss inequalities and absolute value while the Continuing Algebra group wrapped up the chapter on graphing parabolas and the Quadratic formula.  
February 9, 2018
Sam’s 4-6th Math Class
On this snow shortened week, we continued working with the lab gear, this week introducing rules for working with negative numbers, and the distributive property. The students noted that the lab gear blocks (and by extension discrete manipulatives in general) do not do as good a job of modeling fractions and decimals as integers (though we aren’t using all of that vocabulary, yet).

Algebra and Pre-Algebra
The Prealgebra group is motoring through chapter 5 (on fractions), some would have finished if not for the two snow days. The Beginning Algebra class had more time to develop concepts around absolute value, particularly thinking of absolute value equations and inequalities as something about distance from a designated central point. The Continuing Algebra class has mostly wrapped up graphing parabolas and is now studying arithmetic with polynomials, especially factoring quadratic equations. Two students also have completed Algebra and begun work in Geometry. This week we met to talk about the basic underlying “rules of the game” of Euclidean Geometry with points, lines and planes as the “playing pieces” and a few very basic rules to get us started (Euclid’s first four postulates).

Friday, December 8, 2017

Week of December 8

December 8, 2017

Sam’s 4-6th Math Class

Etienne and Ishan work on Sierpinski Carpet fractal.
Counting boxes to make the fractals.
This week we continued to look at fractals. The class spent a significant amount of time working on a fifth iteration Sierpinski Carpet, which is now on display in the MS across from the elevator. It was a technically challenging experience for many of the students that required following an iterative process with a high degree of attention to details. If even one square was miscounted the whole image looked wrong. (If you get a chance to see the finished product, you can see a few places where someone had to correct an error.
Algebra and Pre-Algebra

Nick and Niko explore the relation between batteries (voltage),
 resistance (lightbulbs) and current (brightness of bulbs)
Math this week largely was combined with science activities. As we are working with the Arduinos, we’ve begun to learn some of the basic concepts surrounding electricity and currents. Tuesday’s batteries and lightbulbs investigations emphasized proportional reasoning and we formalized that connection with the introduction of Ohm’s Law on Wednesday.

The d=rt and V=IR graphic organizer pyramids visualize
the proportional relationship of those quantities.
In more formal math classes, the Completing Algebra group has been working on graphing parabolas; especially investigating establishing a relationship between changes in the coefficients of the terms and the appearance of the graph. The Beginning Algebra group continued to work with linear equations and the Pre-Algebra group is going into more depth on single variable equations and inequalities.

Friday, December 1, 2017

Week of December 1

December 1, 2017

Sam’s 4-6th Math Class

This week we dug into concepts related to ratios and fractals. We watched the thought provoking Nova episode: Fractals the Hidden Dimension and then talked about what it means to be “self-similar” and how an object can have a finite area but an infinite perimeter.
It was also very interesting that in their Morning Meeting presentation about Wildlife in Michigan, they mentioned the length of the coastline, which led us to another discussion about fractals and measurement related to “How Long is the Coastline of Britain.”
Algebra and Pre-Algebra

The 7th and 8th graders have mostly been completing assessments this week. All of the groups also had some new material introduced. The pre-algebra group started a unit on factors, fractions and exponents; the beginning algebra group is learning how to write the equations of lines from points or graphs and the completing Algebra group has started working with square roots and quadratic equations.