The Montessori manipulatives are wonderful for introducing math concepts but they can also be used remedially with children. Children who need to see and hear the concepts explained in a different way, or who need more practice but with work that feels fresh and interesting, really respond well to the Montessori approach, especially if they learn best by being able to explore the math concepts physically through manipulating materials or benefit from the visual support of the color coding cues for place value.
Here is the plan for Session 1 (Sep 5) plus some additional resources:
- do the Infinity Street lesson
play the Dice Game
look at Montessori materials, recognize the place value color coding (Stamp Game, Small Bead Frame, Long Division Material)
Infinity Street
Here is a helpful blog post for the Infinity Street lesson.
We have houses and mailboxes up to septillion, and slips of paper with the names of all of the families up to novemdecillion:
-
Simple
Thousand
Million
Billion
Trillion
Quadrillion
Quintillion
Sextillion
Septillion
Octillion
Nonillion
Decillion
Undecillion
Duodecillion
Tredecillion
Quattuordecillion
Quindecillion
Sexdecillion
Septendecillion
Octodecillion
Novemdecillion
This list of family names is also a fantastic extension for children who are learning about prefixes! I like to give them the slips of paper after septillion and have them figure out how to put them in order.
Of course you can connect it to geometric shapes. I have also found Zin! Zin! Zin! A Violin by Lloyd Moss to be extremely useful in this lesson, especially for sliding under the radar the prefix < sex > as representing six (trio, quartet, quintet, sextet, septet, octet, nonet).
It's also a nice time to actually explain that September / October / November / December used to be months 7 / 8 / 9 / 10 (as would make sense with their prefixes) but are now months 9 / 10 / 11 / 12.
The Story of Clocks and Calendars
by Betsy Maestro
Other books that could work well to introduce the Infinity Street lesson are Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells and Infinity and Me by Kate Hosford.
Dice Game
Instructions for the Dice Game are in my How I Teach Place Value blog post from Sep 2020.
For this game, I like to use a ten-sided die.
I also like to have 8 1/2 x 14 inch paper for this game. Long paper is nice if you have a child who wants to play a round with a lot of digits!
For more practice in reading big numbers, I VERY highly recommend A Million Dots by Sven Völker.
I teach children to use a two-step process to read really big numbers! First, you orient yourself as to which family is which. To do this you begin at the right. The family all the way to the right will always be the simple family. The one to the left of it is the thousands, the one to the left of that is the millions, etc.
To actually read the number you will begin at the left. Read the number that is all the way at the left just like it's a "regular" number and then when you get to the comma say the last name of that family. Then read the next portion just like it's a "regular" number and when you get to the comma say the last name of that family.
Twenty-nine million three hundred sixty-five thousand one hundred ten.
Note: The simple family has no last name. You just say the number. That's what makes it simple!
Color Coding
More explanation of the color coding in Montessori, and pictures, are in my Place Value and Redwood Trees blog post from Nov 2022.
There are lots more notes on Place Value on my Place Value page. This is traditionally introduced in Waldorf in grade 2 in the Column Algorithms block (it is not common to incorporate the Montessori materials into the Waldorf environment, but I do).
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