Brandon's Notepad

April 9, 2020

April 9, 2020: Clipper Guards, Wheel Alignment, Capillary Action

Clipper Guards

With all of the hair salons temporarily closed due to the COVID-19 pandemic, many people are resorting to having their hair cut at home. This is something that many of us haven’t experienced or even attempted for decades. Clippers make the job much easier, especially for the boys, who often opt for a short buzz in the back if not all the way around. Of course, this coupled with the current health situation has led to a sudden shortage of clippers on the retail market. Ours will arrive eventually. In researching the options, I paid special attention to the accessories, and the guards most of all. These are the plastic combs that attach to the head of the clippers that keep the blades a constant distance from the scalp, resulting in a uniform cut (i.e. no uneven patches were the clippers got too close!). For a long time, my default request was a #3 cut, scissors on top. But what exactly does “#3” mean and is it the same for all clippers? As it turns out, the guard sizes are more-or-less standardized. The most common interval is 1/8-inch increments, so a #1 guard is 1/8-inch, #2 is 1/4-inch, and so on. Most clipper sets will include guards up to and including the 1-inch #8. There is some variation between manufacturers. Out of curiosity, I did a search for European clipper guards, and it appears that the same English/Imperial increments are used, but an approximate length in millimeters is presented to differentiate them. An eighth of an inch is approximately (but not exactly) 3mm, so the first eight guards are listed as 3, 6, 10, 13, 16, 19, 22, and 25mm.

Wheel Alignment

True story. I recently put my car in for an oil change and a few other minor services, including an alignment. When the report came back at the end of the visit, it said that one of the angles (caster/camber/toe; I don’t recall which it was now) was off by 0.25°. I decided to test the service rep a bit and asked him if that was a lot. I could tell immediately that I caught him off guard, because he asked to see the report, uttered a long “ummmmm”, and looked around the room (I assume) for a nearby mechanic. After a short pause, he pointed to the 0.25° pre-alignment metric and with confidence said, “You know what a 45° angle looks like, right? This is about half that, so yeah, that was pretty big.” I just nodded, thanked him, and drove away amazed that I had managed to get around town for so long without doing donuts up and down the road.

Capillary Action

Here is a neat experiment for the kids. Place six juice glasses on the counter or table arranged in a circle (or hexagon?) as close together as possible. Fill every other glass with water (i.e. empty, full, empty, full…etc.) all to the same level, about three-quarters full. In the three glasses containing water, add a few drops of food coloring (different colors; red, yellow, and blue are good choices) and stir well. Now take six napkins or paper towel squares, roll or fold each, and bend in the middle. Drape the napkins over the rims of the glasses such that one end of each napkin is in a glass with colored water and the other end is in one of the empty glasses adjacent to it. When finished, the six glasses should be “chained” together with the napkins. Now wait. Eventually you will see water gathering in the bottom of the empty glasses. The colors will mix, proving that some of the water is coming from the glass on the left and some from the glass on the right. If you took my advice on using the three primary colors (red, yellow and blue), then the glasses that started off empty will contain the secondary colors (orange, green and purple). This transfer of water will continue until equilibrium is reached and all of the glasses contain the same amount. This effect, called capillary action (and a few other names) is caused by a combination of surface tension and adhesive forces. [Note: the adult version of this experiment works as follows. Brew a cup of coffee. Place a napkin – or better yet, a super-absorbent paper towel – on top of the cup because a fly is loose in the house. Get distracted with some other vital task, like checking your blog stats or killing the fly. When the center of the napkin or towel eventually absorbs enough steam from the coffee, it will sink into the cup and a few minutes later, coffee will have transferred from the cup to the place mat and/or the super-absorbent and now super-stained table cloth.]

 

April 7, 2020

April 7, 2020: COVID-19 Dashboards, SafeYouTube

COVID-19 Dashboards

I doubt that anyone reading this is unaware of the current COVID-19 pandemic and the effect it has had on the world over the past few months. I really didn’t want to blog about it at all, but it’s really hard to ignore, so here we are. The following are a couple of dashboards I’ve been using to monitor the spread of the disease.

nCoV2019.live – This has been my go-to dashboard from the beginning of the pandemic. It was created by a very enterprising high school student in Washington State by the name of Avi Schiffmann. I like it because it looks nice on mobile and breaks down the statistics not only by country/region, but also by State (so I can keep an eye on Texas, of course). There is also a recovery and fatality rate shown for each section, which I think were added recently.

covid19dashboards.com – This site has a lot of graphs to play with. You can look at growth by state, projected mortality rates, all sorts of stuff. And on many charts, you can highlight specific states and see how they are faring against the national average. The “Deaths per Capita” is the chart I’ve been watching the closest.

SafeYouTube

Distance education is a new and interesting challenge, as many parents around the world are now discovering, especially when there is a variety of solutions and technologies being utilized with little or no consistency. Instructional videos have been my biggest peeve so far. Some teachers upload MOV files directly from their phones to Google Classroom, but most upload them to YouTube…which, unfortunately, we block as part of our parental-control regimen. He had to loosen controls for a while and hope for the best.

Thankfully, one of the teachers started publishing links to her videos using SafeYouTube.net. The great news is that anyone can generate links, even parents. Just visit the site and paste the URL to any YouTube video and a new link will be generated for you. Not only does the new page exclude all of the excess page elements, like search capabilities, related/suggested videos and comments, but the viewer doesn’t get blocked (at least not with our setup, but I cannot guarantee it will work perfectly for everyone without some additional configuration).

I had been toying with the idea of writing some sort of proxy server that would cache requested videos and present them in a similar fashion, but now there’s no need. The site has an API too, so I may end up creating a self-service function that will save me from having to generate links by hand. They will only be able to generate links using YouTube URLs they already have.

Sharing & Feedback

I have found the resources covered in this post to be incredibly helpful, so please, share this post with your friends. If you have questions or comments about the items above, please leave them in the comment section below or feel free to send them to me via Twitter (@brandonsnotepad). Thanks!

February 24, 2014

Mental Math Tricks

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Home > My Research > Math/Science > Mental Math Tricks


New Math was a teaching method introduced in the 1960s to give the United States a competitive edge in innovation in response to contemporary advances in technology by the U.S.S.R. The term has become far more generic that what it once was. Fifty years after its failed implementation in American schools, people who never even learnt the New Math jest about it when they encounter methods for teaching basic math skills that don’t quite coincide with their own experience in grade school. So too was my reaction when I was presented with a list of mental math tricks presently being taught to first graders.


Mental Math Hits Home

The following is a summary of mental math tricks that I recently obtained from a first-grade teacher in the form of a classroom handout. I know that the curriculum in question includes Saxon math, but web searches have failed to confirm that these tricks are a part of that specific program, at least by the names of the tricks I was given. The tricks rely heavily on the ability to recognize patterns.

Doubles. The method for memorizing doubles (5+5=10, 8+8=16, etc.) is the first trick on the page and is the basis for several other tricks. Unfortunately, it employs the use of a mnemonic device, a song to which the lyrics were not included on the page. I did hear the song recited once and I have to question the efficacy of this particular device solely because the connection between the numbers and the rhyming words was non-existent. I don’t recall them now, but they were something akin to Four and four is eight. Isn’t that great. What’s so great about it? Wouldn’t it be more practical to learn lyrics with meaning? Four and four is eight, like when I roller skate, referring to the number of wheels on a pair of skates, contains a visual cue to which kids can relate. In either case, there’s only so many words that rhyme with -teen. I suppose it works in the short term, and hopefully the children outgrow the need for this trick quickly.

Counting Numbers. The “Plus 1” and “Minus 1” tricks require that a student know their counting numbers backward and forward. Anytime a simple addition or subtraction problem is encountered that involved a “1”, the student just remembers to count in one direction or the other. Not a lot of magic here.

Counting By Twos. The “Plus 2” and “Minus 2” tricks require knowing how to count by twos, which also introduces the concept of even and odd numbers.

Counting By N. Actually, there are no tricks that involve counting by threes, fours, or even fives and tens! I only mention it because it seems like an odd omission to me.

Partner Numbers. Partner numbers are any two consecutive counting numbers. To add two partner numbers the “Doubles Plus 1” trick is used. As implied in the name, this is a combination of tricks listed above: the double of the lower number is found first and then the next number counting by one is identified. A subtraction problem containing partner numbers will always result in “1”. Similarly, subtracting “Odd or Even Partners” — that is to say, consecutive counting numbers on number lines containing only odd or even numbers — will always result in an answer of “2”.

Tens. The “Making 10” trick is just memorization of number combinations whose sums equal ten (1+9, 2+8, 3+7, etc.). The “Minus 10” is the corollary that informally crosses over into algebra (7+x=10 solve for x). The “Add/Subtract 10” trick is an abbreviated form of “long” addition: the student knows that to add ten to a number one need only increment the tens-digit column.

Nines. The “Plus 9” trick could just as easily been called the “Adding 10 Minus 1” trick, for it is a combination of the two tricks above.

More Doubles. Two more tricks extend the concept of doubles. Similar to the rules for finding the difference between partner numbers (where the answer is always “1”), the “Doubles Minus” trick states that the subtraction of any number from itself will always be “0”. Also, the “Half of Double” trick is similar to the “Minus 10” trick in that it approaches algebra (14-x=7, 16-x=8, etc.). Students are encouraged to recognize combinations of numbers memorized in the Doubles song.

Zero. Any number plus or minus zero is the same number.

Everything Else. The catch-all is to memorize a small subset of one-digit addition problems. Specifically, these are the number combinations that do not trigger one of the rules above (3+5, 3+6, 5+7, etc.).

I have mixed emotions about these rules. On one hand, I learned “long” math (carry the one, and no jokes about walking to school uphill both directions through three feet of snow in August) and after enough rote practice patterns would start to emerge. Eventually, the math happens happens almost automatically. With that experience as a baseline for comparison, the tricks described above seem to be a real grab bag and the inconsistency in naming doesn’t help make any of them particularly memorable in my opinion. On the other hand, I recognize that the essence of a few of them has been programmed into my own head over time. For example, I use an expanded variant of the “Making 10” trick all the time (e.g. to add 87 to another number in my head I would usually add 90 and subtract 3). I’ve taken many tests at the university level for which using a calculator (much less long math) meant not having time to finish the exam. Mental calculation proved to be an essential skill.

Mental Math Hits Facebook

UPDATE! 3/26/2014. A post on the Federalist Papers blog is making the rounds on Facebook, highlighting a Common Core math problem that completely baffled a frustrated parent (who happened to be a degreed engineer). The parent’s reaction is typical. Why must one draw a number line to subtract 316 from 427? I think the parent’s response would be completely apropos if the worksheet simply required finding the numeric difference. But this is not the question at hand. The instructions are to identify the flaw in Jack’s approach to solving the problem. One of the comments to this post provides a lot of insight: this is the type of question used to train math teachers on how to teach math. Substitute “your student” for “Jack” and “write on his paper” instead of “write a letter” and you will see what I mean.

The worksheet illustrates how to approach the problem mentally, in bite-sized chunks. If I needed to do this calculation on the spot and without any tools (pencil, calculator), I’d probably start by taking away the biggest chunks first, that is to say the hundreds digit, and work my way down from there. Patheos blogger Hemant Metha addresses a similar Facebook favorite that shows how the student counts up in stepwise fashion, basically working a subtraction in reverse. If you expect the student to solve this problem mathematically, then yes, this is so very backward; however, it makes perfect sense from a mental math perspective. Consider his example of how you would figure out (on the spot) how much change you should receive when paying for $4.70 worth of merchandise with a $20 bill (let’s see…30¢ brings us up to $5, then another $15 to make $20 — there we go! $15.30).

Unfortunately, what Metha brings out in his post, and what is mentioned in the comments of the FP post, is the political agenda behind these viral Facebook posts. Conservatives apparently view new methods for teaching math as a threat to traditional values and an effort to degenerate the ability of our citizens to think for themselves so that they can more easily be swayed by the government. As compelling as this argument may sound (in all of its various manifestations), it is irrational. After all, conservatives exercise mental math skills for more often than liberals do. Being successful business people, they are more likely to have $20 bills in their pockets, and thus they find themselves calculating the change they should receive from liberal neo-hippie baristas on the spot more often. Also, liberals don’t have to get any number right as long as they sound convincing when they deliver it in a campaign speech. See how ugly this can get? Of course, I’m being extremely cheeky to prove a point. Math is a highly objective discipline and different people learn it in different ways. For either side to use this as a mark of political partisanship makes them look petty and ignorant.

By the way, Jack, you forgot to subtract 10.


February 9, 2011

“Catholic” Universities


Catholic institutions of higher education are torn between the liberal secularism of modern academia and their Catholic identity. The result is often scandalous. The following is a list of events, derived primarily from headlines from online newsletters and news sites, which have crossed my desktop over time. Each can certainly be researched in more depth elsewhere.


2011

Madonna University cancelled a speaking engagement with a Planned Parenthood employee, Christine Gannon. The engagement was sponsored by the school’s Sign Language Studies department. Ms. Gannon provides services to the deaf through Planned Parenthood. More

The HERO student organization implemented the Atticus Circle’s t-shirt campaign at Gonzaga University. More

Fr. Ryan Maher S.J., Associate Dean of Georgetown College (within Georgetown University) posted a news article with an embedded video promoting the school’s religious diversity. He states “Our job as educators and as priests is not to bring God to people, or even to bring people to God.”

The National Labor Relations Board decided that the faculty of Manhattan College could indeed unionize, because “the purpose of the College is secular and not the ‘propagation of a religious faith’.” More

Former Indiana Governor and Senator Even Bayh addressed Notre Dame students on February 24th (photos)on “the role that government and politics play in the advancement of the common good in a global economy.” Bayh is very pro-abortion, having low NRLC and high NARAL scores. More

Boston College planned to celebrate the life of pro-abortion Congressman and priest, Fr. Robert Drinan, S.J. on the evening of March 7, 2011.


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