Sunday, March 1, 2015

History of Montessori Education


The Life and Legacy of Dr. Maria Montessori

Dr Montessori learned, as I learned, and as every teacher must learn, that only through freedom can individuals develop self control, self independence, will power and initiative. There is no education except self-education. There is no effective discipline except self-discipline. All that parents and teachers can do for the child is to surround him with right condition. He will do the rest; and the things her will do for himself are the only things that really count in his education."   
~ Anne Sullivan Macy, teacher to Helen Keller

Enjoy this interactive timeline courtesy of Giraffe Childcare  (wait for it to load below) :



The History of Montessori Education by Giraffe Childcare

Friday, February 6, 2015

How Many Beads Do I Need for Montessori Math?




For those who are using Montessori Math materials in the home 
I have condensed the Montessori bead materials into 
SIX basic sets of materials: 

Teaching from a Tackle Box - Bead Bundle - (Sets #2-5)
(top to bottom) Short Chains, Snake Game, Decanomial, Long Chains, Squares and Cubes


Boleks ordering information is HERE.
All sets are based on Boleks Bead Chart and here is the basic materials list:
  • Boleks - #101 faceted 8mm beads (do NOT use pony beads for Montessori math works)
  • Boleks - 18 gauge wire, silver and/or gold depending on the set
  • 10 mesh Darice plastic canvas
Tools needed:
  • wire cutter pliers - (with the cutter at the front tip not inside at the hinge)
  • Round nose jewelry pliers
  • Long needle nose pliers 15cm - (smooth on inside - not with ridges)
  • wooden dowel - for rolling jump rings

NOTE: I wanted to get this post out because there have been lots of questions on various groups about beads - but please note that I still need to get an accurate count on the number of wire spools you need for each project so I will be revising this post and adding those numbers shortly. I will also be doing a bead making tutorial next month - March 2015 -  at my new Facebook group: 
NEW Facebook Group!

1). The Colored Bead Stair and the Teens & Tens Bead Bars are in my Intro to Math collection.
If you have older kids and you do not need all of the numeration materials you should still introduce the Teens and Tens boards with the Decimal  System works, and you can use bead bars from the Decanomial set and  just add (45) golden unit beads.




SET #1
INTRO TO MATH SET

Note:  Listed here are the beaded materials ONLY for the Intro to Math set. 
The other materials will be covered in a separate tutorial.

COLORED BEAD STAIR, TEENS BOARD & TENS BOARD
Boleks #101 - faceted 8 mm beads
I use 18 gauge GOLD wire for this entire set because
* The Colored Bead Stair introduces numeration #1-9, while the * Hanging Bead Stair introduces numeration to #19. With * two Colored Bead Stair simple operations of addition and subtraction through #18 can be performed. The * Teens and * Tens boards lead into the *Intro to Decimal System works with the Golden Bead materials. See Montessori Album for basic presentations with the Montessori Math beads.

Colored Bead Stair
(1) each of colored bead bars - for positive numbers #1-9.
Second bead stair set is used for simple operations of addition and subtraction. 

Hanging Bead Stair #1-9
(1) each of colored bead bars - for positive numbers #1-9.
This material is a wooden frame with 10 hooks and 10 numeral tiles for colored beads #0-9.

Hanging Bead Stair #10-19
(1) each of colored bead bars - for positive numbers #1-9 (for hanging #10-19).
(10) golden ten bars
A wooden frame with 20 hooks and 10 numeral tiles for colored bead sets #10-19.

Teens Board
(1) each of colored bead bars - for positive numbers #1-9. 
(9) golden ten bars

Tens Board
(45) unit golden beads
(45) golden ten bars



COLORED BEAD STAIR,
TEENS & TENS BOARDS
Boleks #101  faceted 8mm beads
All bead bars with 18 gauge GOLD wire
For Colored Bead Stair, Addition & Subtraction with (2) Bead Stair, Teens Board and Tens Board

Boleks Color#
Boleks #101 8mm faceted bead color
Totals
Name of
bead bar

#17
Christmas Red 
 2
ONE
#07
Christmas Green
4
TWO
#08
Hot Pink
6
THREE  
#27
Yellow
8
FOUR
#19
 Light Blue
10
FIVE
#02
Dark Amethyst
12
SIX
#06
Crystal Clear
14
SEVEN
#24
Amber
16
EIGHT
#20
Dark Blue
18
NINE
#23
Sun Gold 
(45) units, (9) ten bars for TEENS board, (45) ten bars for TENS board
585 total
(45 +90 + 450)
GOLDEN TENS





SET #2
SNAKE GAME SET

I have an old set of videos online at MontessoriMaterials.org
Scroll down to Snake Game Demos.

The * Snake Game is all about adding 10's - using positive and negative numbers.

Boleks #101 - faceted 8 mm beads
I use 18 gauge GOLD wire for this entire set because the emphasis is on counting TENS.

Positive Snake Game
(5) each of colored bead bars - for positive numbers #1-9
(23) golden positive ten bars
1 set of (opaque) black & white positive remainder stair

Subtraction Snake Game
All of the materials above for Positive Snake Game
(5) each of (opaque) grey & white bead stair - for negative numbers #1-9

Negative Snake Game
All of the materials above for Positive and Subtraction Snake Games
(23) grey negative ten bars
1 set of (opaque) red & white negative remainder stair



SNAKE GAME
Boleks #101  faceted 8mm beads
All bead bars with 18 gauge GOLD wire
For Positive Snake Game, Subtraction Snake Game, and Negative Snake Game

Boleks Color#
Boleks #101 8mm faceted bead color
Totals
Name of
bead bar

#17
Christmas Red 
  5
ONE
#07
Christmas Green
10
TWO
#08
Hot Pink
15
THREE  
#27
Yellow
20
FOUR
#19
 Light Blue
25
FIVE
#02
Dark Amethyst
30
SIX
#06
Crystal Clear
35
SEVEN
#24
Amber
40
EIGHT
#20
Dark Blue
45
NINE
#23
Sun Gold
230
GOLDEN TENS
#62
Opaque Grey
grey tens, #1-5, and 5 grey on each bead bar #6-9
405 total
(230 + 175)
Negative #1-9
and GREY  TENS
#73
Opaque White
On each grey, red and black bead bar #6-9 accordingly with white beads 5 beads.
70 total (50+10+10)
Negative #1-9,
Positive Remainder,
Negative Reminder
#52
Opaque Black 
#1-5, and 5 black on each bead bar #6-9 
35
Positive Remainder
#67
Opaque Red
#1-5, and 5 red on each bead bar #6-9 
35
Negative Reminder





SET #3
DECANOMIAL SET
Can be used for:

Decanomial  - Vertical and Horizontal Layout
(55) each of colored bead bars #1-9 with SILVER wire
(55) each of golden ten bead bars with GOLD wire

Multiplication Layout (see presentation HERE)
(56) red ONE bars
(57) green TWO bead bars
(56) hot pink THREE bead bars
(57) yellow FOUR bead bars
(60) light blue FIVE bead bars
(57) amethyst SIX bead bars
(56) clear SEVEN bead bars
(57) brown EIGHT bead bars
(56) dark blue NINE bead bars
(45) golden TEN bead bars - gold wire

The * Vertical and * Horizontal Decanomial Layouts and the * Multiplication Layout are all about learning Math Tables from 1-10.

Decanomial - Angular Layout
This work transforms the bead bars into squares and cubes and then into the Jeweled Tower. The horizontal and vertical layout use 55 of each bead bar. However in order to do the angular layout add-on beads beyond 55 each are needed for the eight, nine and ten bead bars.

(1) red ONE bead
(4) green TWO bead bars
(9) hot pink THREE bead bars
(16) yellow FOUR bead bars
(25) light blue FIVE bead bars
(36) amethyst SIX bead bars
(49) clear SEVEN bead bars
(64) brown EIGHT bead bars  (55 plus add-on 9 EIGHT bead bars)
(81) dark blue NINE bead bars  (55 plus add-on 26 NINE bead bars)
(100) golden TEN bead bars - gold wire  (55 plus add-on 45 TEN bead bars)

The * Angular Layout of the Decanomial is all about solving for an equation with ten terms - working from the Sensorial-Geometric Decanomial, to the Beaded Decanomial, to the Numerical Decanomial, to the Algebraic Decanomial.

Multiplication Checkerboard - for Long Division
(20) each of colored bead bars #1-9 with SILVER wire
Note: no golden ten bars needed for this work

* The Multiplication Checkerboard is all about long multiplication.



DECANOMIAL & 
MULTIPLICATION WORKS
Boleks #101  faceted 8mm beads
#1-9 bead bars  with 18 gauge SILVER wire
#10 golden bead bars  with 18 gauge GOLD wire
(55) of each bead bar

With ad-on for Angular Decanomial Layout – adding (9) EIGHT bead bars, (26) NINE bead bars and (45) golden TEN bead bars.

For Vertical, Horizontal, and Angular Decanomial Layouts, Multiplication Layout, Multiplication Checkerboard

Boleks Color#
Boleks #101 8mm faceted bead color
Totals
Name of
bead bar

#17
Christmas Red 
 5 total
(55 + 1)
ONE
#07
Christmas Green
110
TWO
#08
Hot Pink
165
THREE  
#27
Yellow
220
FOUR
#19
 Light Blue
275
FIVE
#02
Dark Amethyst
330
SIX
#06
Crystal Clear
385
SEVEN
#24
Amber
55 bead bars + 9 more
512 total
(440 +72)
EIGHT
#20
Dark Blue
55 bead bars + 26 more
729 total
(495 + 234)
NINE
#23
Sun Gold
55 bead bars + 45 more
1000 total
(550 + 450)
GOLDEN TENS





  

SET #4
SHORT & LONG CHAINS SETS 

Short Chains
Chains are sets of bead bars according to the squares and cubes of numbers. For example a short three chain would have three sets of three bead bars.

The Short Chain of Three (3 x 3) has a set of three bead bars with three pink beads:  a jump ring, three bead bar, figure 8 connector, three bead bar, figure 8 connector, three bead bar, jump ring.

Long Chains
The Long Chain of Three (3 x 3 x 3) has three sets of three bead bars with three pink beads:
a jump ring, three bead bar, figure 8 connector, three bead bar, figure 8, three bead bar, jump ring,
three bead bar, figure 8, three bead bar, figure 8, three bead bar, jump ring, three bead bar, figure 8 connector, three bead bar, figure 8, three bead bar, jump ring.






SHORT & LONG CHAINS
Boleks #101  faceted 8mm beads
Short (square) chains for the numbers #1-10
(e.g 1x1, 2x2, 3x3, 4x4…)
Long (cube) chains for the numbers #1-10
(e.g. 1x1x1, 2x2x2, 3x3x3, 4x4x4…)
Chains #1-9 bead bars with 18 gauge SILVER wire
Chains #10 bead bars with 18 gauge GOLD wire
(aka Hundred Chain and Thousand Chain)    

Extra wire needed for the figure-8-links and jump rings.

For skip counting to the squares and cubes of numbers, and for the works in the squaring and cubing of numbers - to be used with the Beaded Squares and Cubes.

Boleks Color#
Boleks #101 8mm faceted bead color
Totals
Name of
bead bar

#17
Christmas Red 
 2 total
(1 +1)
ONE
#07
Christmas Green
12 total
(4 + 8)
TWO
#08
Hot Pink
36 total
(9 + 27)
THREE 
#27
Yellow
80 total
(16 + 64)
FOUR
#19
 Light Blue
150 total
(25 + 125)
FIVE
#02
Dark Amethyst
252 total
(36 +216)
SIX
#06
Crystal Clear
392 total
(49 +343)
SEVEN
#24
Amber
576 total
(64 +512)
EIGHT
#20
Dark Blue
810 total
(81 + 729)
NINE
#23
Sun Gold
1100 total
(100 + 1000)
GOLDEN TENS

The * Short and * Long Chains are a linear method of counting - but not in the traditional sense of Skip Counting to 10-times a number. Rather, these chains are specially designed to represent the linear form of the squares and cubes of numbers. See my post on Short and Long Chains HERE.


SET #5
BEADED SQUARES & CUBES








BEADED SQUARES & CUBES
Boleks #101  faceted 8mm beads
#1-9 squares and cubes with 18 gauge SILVER wire
#10 golden squares and cubes with 18 gauge GOLD wire

NOTE:  use 10 mesh plastic canvas with Squares and Cubes leaving 2 holes between each wire of beads.
For the works in the squaring and cubing of numbers - to be used with the Short and Long Chains.

Boleks Color#
Boleks #101 8mm faceted bead color
Totals
Name of
bead bar

#17
Christmas Red 
 2
ONE
#07
Christmas Green
16
TWO
#08
Hot Pink
54
THREE 
#27
Yellow
128
FOUR
#19
 Light Blue
250
FIVE
#02
Dark Amethyst
432
SIX
#06
Crystal Clear
686
SEVEN
#24
Amber
1024
EIGHT
#20
Dark Blue
1458
NINE
#23
Sun Gold
2000
GOLDEN TENS
 
To be entirely effective the Short and Long Chains must be used with * Squares and * Cubes. The works with these materials show how the Short Chain i.e. the "beaded linear form" of the number squared --- actually forms a "beaded geometric plane-form of a square, and how the Long Chain i.e. the "beaded linear form" of the number cubed --- actually forms a beaded geometric solid-form of a cube.






SET #6
GOLDEN BEAD DECIMAL MATERIALS

Intro to Decimal System
(1) golden unit bead, (1) ten bar, (1) hundred square, (1) thousand cube

Nine Tray
(9) golden unit beads, (9) ten bars, (9) hundred squares, (1) thousand cube

Ten Tray
(10) golden unit beads, (10) ten bars, (10) hundred squares, (1) thousand cube

Bank Game
(45) golden unit beads, (45) ten bars, (45) hundred squares - wooden, (9) thousand cube - wooden 

45 Layout (aka Bird's Eye View)
(45) golden unit beads, (45) ten bars, (45) hundred squares - wooden, (45) thousand cube - wooden


The BASIC beaded material for works with the Golden Bead Decimal Material consists of:
(45) golden units, (45) golden tens, (10) golden hundred squares and (1) golden thousand cube.




Golden Bead Decimal Material
Boleks #101  faceted 8mm beads

For Intro to Decimal, Nine Tray, Ten Tray,
Bank Game (with addition of wooden Hundred Squares and Cubes)

Boleks Color#
Boleks #101 8mm faceted bead color
Totals
Name of
bead bar

#23
Sun Gold
(45) golden units, 
(45) golden ten bars, 
(10) hundred squares, 
(1) thousand cube
1100 total
(45 + 450 + 1000 +1000)
GOLDEN UNITS, TENS, HUNDRED SQUARES, THOUSAND CUBE
 
The * Decimal Golden Bead materials introduce the progression of numbers from unit, to tens, to hundreds, to thousands, i.e. the family of numbers from a point, to a line, to a flat (plane), to a cube (solid) - which is actually a new point. They will learn later how that numeration progresses in consistent patterns with the * Hierachical materials which shows the geometric forms on number families to one million. The Golden Bead materials are also used for the formation of large numerals, and for operations in addition, multiplication, subtraction and division of large numerals 1-9999, feats which very young children can perform with ease!




Alternative colors for faceted beads if you use all opaque beads:
#67 Opaque Red
#57 Opaque Green
#64 Opaque Pink
#74 Opaque Yellow
#86 Opaque Aqua
#59 Opaque Lilac
#73 Opaque White
#56 Opaque Brown
#68 Opaque Royal
#23 Sun Gold





  • The black 15cm long flat nose is needed to straighten all the loops on the squares and cubes.
  • The purple round jewelry pliers is used to loop each end of the bead bar and to make the figure-8 connectors for the Short and Long Chains.
  • The pink jewelry cutters are used to cut wire rods for all bead bars and to cut the individual jump rings after the wire is wound around on a dowel.

I do offer my bead sets for sale at Etsy and I will consider custom orders. But take note of my caveat emptor (buyer beware) . . . bead making is one of the more labor intensive DIY works and it can take 2-3 months for me to complete a bead order depending on how many orders I have to work on. https://www.etsy.com/shop/LivableLearning




   
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