Tuesday, November 6, 2018

Maths of Practical Life: Time

Here was our first "Maths of Practical Life" Measurement topic: Time. We spent Thursday and Friday on Clocks and Monday and Tuesday on Calendars.

Thursday, November 1

  • begin the story of measuring time by discussing Early Humans and Hunters & Gatherers and the simplest rhythms of the sunrise and sunset, the phases of the moon, and the cycle of the seasons
  • consider the impacts of the later evolution of Agriculture and the need to be able to track and predict; look at calendar stick illustrations in The Story of Clocks and Calendars by Betsy Maestro, pages 10-11

  • explain that the Ancient Babylonians had a special interest in the number 60 and that this still shows up in the story of our modern day Clocks; factor 60 on the board (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and show that this number is divisible by 1, 2, 3, 4, 5, and 6; explain that it was the Babylonians who divided our day into 24 hours, our hour into 60 minutes, and our minute into 60 seconds
  • explain that seconds are now divided even further in some special situations and look at the Olympic athlete illustration on page 7 of The Story of Clocks and Calendars; notice that since we were the ones who divided the second instead of the Babylonians, and we use base 10, we divided it into hundredths
  • look at the evolution of the sundial, the water clock, the candle clock, and the sand timer (The Story of Clocks and Calendars pages 34-35)
  • discuss examples of hourglasses in movies (such as the Harry Potter movies and The Wizard of Oz); watch the sand slowly slip through a two minute sand timer... is this how long you brush your teeth?
  • review that other clocks were invented because of the limitations of the sundial (it doesn't work when the sun isn't shining) and read The Story of Clocks and Calendars pages 36-37 and look at illustration of modern clocks with pendulums and gears
  • review that the numbers on a clock go up to 12 but that the minute hand has to be able to count up to 60 and look back at our factors of 60; present the Montessori Teaching Clock for follow up work; notice that it combines the color coding of other Montessori Math materials such as the red Fraction Circles for the whole, half, and quarter hours and the light blue bead bars signaling skip counting by 5's as used in the Short Bead Chains, the Checker Board, and the Decanomial
  • present calendar making project and make art for front cover

Friday, November 2

  • review by reading The Sun's Day by Mordecai Gerstein
  • discuss Daylight Savings Time (which ends Sunday, November 4) and look at the "Does turning back the clock really save anything?" article on the front page of today's newspaper
  • discuss Time Zones and the International Date Line and look at the illustration in The Story of Clocks and Calendars by Betsy Maestro, pages 40-41
  • continue calendar making project and make art and write in numbers for December 2018

  • add Clocks to MLB (this is our first ever MLB where we are writing in Script and using our fountain pens so it is very exciting!!!!!!)

Monday, November 5

  • review that the Ancient Babylonians lived on the flat grasslands with an excellent view of the nighttime sky and that they became famous astronomers
  • look at illustration on page 18 of The Story of Clocks and Calendars to see the list of "wandering stars" (ie. planets) which can be seen with the naked eye

  • read the paragraph at the bottom of page 17 about the evolution of the names for the days of the week from the initial names given by the Ancient Babylonians; diagram the list of conquering civilazations one after the other on the board and diagram the tree of languages which evolved (today was the first time I realized < Roman > is the base of the term < Romance > for languages descended from Latin)
  • read aloud the list of Roman names of the days of the week and compare them to modern Spanish; read aloud the list of Anglo-Saxon names of the days of the week and compare them to modern English
  • return to page 18 and talk about the rare celestial event which made the Ancient Chinese start their calendar at year 1; discuss what major events made other groups start their calendar at year 1 (the Islamic calendar and the Christian calendar)
  • explain the cycle of the moon (page 12 of The Story of Clocks and Calendars) and why it was so logical for early peoples to use it as the measurement of their month; explain that a lunar calendar causes problems because it gets out of step with the seasons; use the finger knitted string and white buttons to demonstrate this *
  • review that a lunar calendar will ALWAYS need correcting to bring the buttons back where they should be after they get out of whack; read about the struggles people had with their lunar calendar and its constant need for correction:

      page 15 about the Ancient Egyptian lunar calendar

      page 16 about their subsequent solar calendar

      page 17 about the Ancient Babylonian lunar calendar

      page 19 about the Ancient Greek lunar calendar

      page 24 about the Ancient Roman lunar calendar

      page 25 about their subsequent solar calendar changeover in year 46, Annus Confusionus

  • examine the changes in the names of the months of the year (including the +2 month fix to the lunar calendar that made Oct become the tenth month even though Oct means eight, and the emperor-ego-centered changes which gave us Julius and Augustus in place of Quintilis and Sextilis)
  • use the "knuckles" trick to help students remember which months have 31 days and which ones have fewer
  • continue calendar making project and make art and write in numbers for January 2019

Tuesday, November 6

  • review yesterday's lesson; add Calendars to MLB
  • do second step in penguin artwork
  • continue calendar making project and make art and write in numbers for February 2019

* Below is an excerpt from a blog post in 2018 where I wrote up a description of the calendar lesson I've developed over many years of teaching it in Montessori schools as part of the Fifth Great Lesson:

    Finger Knitted String

    The first material is something I invented after years of having students NOT understand why a lunar calendar isn't the same as a solar one, and why it gradually gets out of step. This is a finger knitted string consisting of 4 yards of yarn, in four different colors. Each color represents a season. A large green button is tied onto the string where the first day of Spring would be. Since the lunar calendar gradually gets out of step with the seasons, 11 days each year, I have a series of white buttons. These represent the lunar calendar and where it says the first day of Spring should be. We lay the buttons down, moving the lunar calendar's supposed "first day of Spring" further and further into Winter, showing how the calendars get out of whack a little bit at a time. This starts to make a big difference after a while! The cumulative effect of the 11 days adding up is clear to students because they can SEE it, and I leave this out in the middle of the floor and keep reading. Every time I get to a culture which had a lunar calendar and had to keep making adjustments to it (the Ancient Egyptians were the first to switch to a solar calendar), I point to the little white buttons. And it seems to work!

    Colored Index Cards

    In the middle of the yarn circle I placed my second demonstration. This is ten colored index cards with the original Roman months on them (Marius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November, and December). I have already prepared four more index cards of a different color which will show the changes to the calendar (these are Januarius, Februaries, Julius, and Augustus). When I explain that the Roman calendar, which was originally a lunar calendar borrowed from the ancient Greeks, got more and more out of whack, and that they had to add two months to the beginning to bring it back in step with the seasons, I lay down Januarius and Februarius, and when I explain the egos of Julius Caesar and Augustus Caesar, I replace Quintilis and Sextilis with Julius and Augustus. This is very satisfying for me because I remember as a child being puzzled that October has a prefix which means 8 but it is month #10 and December means 10 but it is month #12! Knowing that they had to do a +2 and chuck two months on the beginning of the calendar at some point makes it so much more clear.

Please let me know if you have any questions at all. It's NOT hard one bit to make a calendar string. All you need is four colors of the same weight yarn (I used Paton's Classic Wool Roving), a floral or green button to be the first day of Spring, a bunch of white buttons to be the start of the lunar calendar, a yardstick, and an eager first grader who wants to help out by doing all the finger knitting. If you make each season's piece one yard long, your solar calendar will be perfectly to scale with one centimeter equalling one day.

cloverleaf - spring

yellow - summer

plum - autumn

pacific teal - winter

This lesson works! The combination of visual and hands-on really helps make the abstract difference between the solar and the lunar calendar year become concrete and clear.

in the beginning the solar and lunar calendar both have the start of spring at the same time but the lunar calendar slowly gets farther and farther behind

the original ten months of the Roman lunar year

the extra 1/4 day each year adds up to one whole day after four years and thus we have a leap day

the yellow cards represent months added in or changed in the Roman calendar

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