Well, I was talked into it. I finally put together a price list using
.
Montessori Elementary Mathematics Materials List  click there to download the pdf file.
Here are the contents in even less pretty format ;)
Keys
of the Universe
Mathematics
 Materials Price List
Caveats: This is not entirely a complete comparison, because both
companies do not sell all the same materials. And you might purchase the least
expensive of any given option at each one of them. I also have not calculated
if you bought all available at one and filled in with the other. Consider this:
some of this you will find cheaper used; or you can indeed make it yourself.


Alison

IFIT

Keys/other

I. Introduction





Story of Numbers

8 Charts



Printable






II. Early Work  Numeration





Wooden
Hierarchical Material
Large
Bead Frame: Introduction
Exercises IIV
Commutative
& Distributive Laws
Multiples
Least
Common Multiples
Factors
Last
Steps of LCM to Abstraction
Divisibility:
by 2, 5, 25

wood materials
number cards
large bead frame
frame paper
decanomial bead bar box
number box**
bead cabinet
arrows in boxes
Tables A, B, C, E
pegboard & pegs
thin strips of cardstock
golden beads

350

20.00
85.00
153*
61.60
60.00

21.00
84.00
280
+240
38.00
88.00
$60**

patterns/ideas
printable
printable
printable
printable
hardware store
golf tees



749.60

811.00


Cabinet
currently not listed on Alisons.
III. Operations



30.00
18.00
63.00
deca
145
35.00



19.00
16.00
44.00
deca
88.00
24.00


printable
printable

Long
Multiplication
Large
Bead Frame
Bank
Game – buy/make as set – or make gray/colored to match golden bead cards size
Flat
Bead Frame – cut own strips of paper
Checker
Board: Exercises 1 & 2
Geometrical
Form of Multiplication
Category
Multiplication
Long
Division
Distributive
Division with Racks/Tubes
Group
Division
Group
Division & Word Problems w/ Fractions

large bead frame
Bank Game
flat bead frame
checkerboard
bead bars
Racks/Tubes
Stamp Game
circles fractions



291.00

191.00


IV. Squares and Cubes of Numbers





Prerequisites
to Squares and Cubes of Numbers
Notation
of Squares
Notation
of Cubes
Games
13
Game
4: Decanomial Square
Paper
Decanomial
Sums
Using Squares and Cubes

bead cabinet
prepared labels
bead bars
division skittles


(deca)



(deca)


printable






V. Fractions





Notes
on Fraction Charts
Introduction
to Fractions
Equivalence
of Fractions
Simple
Operations
Add
& Subtract Fraction w/Diff Denom
Exercises Leading
to Abstraction of Above
Multiplication
of a Fraction by a Fraction
Division
by a Fraction

21 charts
fraction circles
black strips
prepared labels
Add’l pieces 110
Practice Problems
green skittles
prepared problems
transparencies*
division fraction skittles

125
w/stds
50.00

60.00

85
w/stds
35.00

39.00

printable
printable
printable
printable
printable



235.00

159.00


VI. Decimal Fractions





Quantity
– pull beads from racks/tubes
Symbol
Linked to Quantity
Formation
and Reading of Quantities
Operations
Conversion
of Common Fractions to Decimal
Effects
of Mult/Div Numbers by Powers of 10
Multiply
Decimal Fraction by Dec Fraction
Introduction
to the Decimal Checkerboard
Decimal
Checkerboard
Relative
Size of Terms in Mult Problem
Relative
Size of Numbers When Dividing
Division
of a Dec Fraction by a Dec Fraction
Leading
to Abstraction of Mult of Dec Frac
Division
of a Decimal Fraction on Paper

decimal cubes
#s bank game
#s w/cubes
propeller
pushpin
decimal board
king symbol
black frame
felt squares
Decimal Checkerboard
Number Box
Bead Bars 19

55.00


*
24*

26.00


9.00
14.00
40.00

deca

Printable
printable



115.00

89.00


Black frame
= “Centesimal circle and Protractor”  Alison’s is green.
Alison’s
sells decimal board with pieces for 55; IFIT sells them separate for 26 and 9.
VII. Squaring and Cubing





Squaring
Transformation of
a Square, Ex 16
Passing From One
Square to Another
Squaring a Sum
Squaring with a
Hierarchical Value
Cubing
Passing From One
Cube to Another
Cubing a Binomial
Cubing a Trinomial
Cubing a
Quadrinomial
Cubing a
Trinomial w/ Numerical Value
The Story of the
Three Kings
Cubing a Number
with Decimal Value
Square Roots – could use portion of pegboard
Introduction to
the Concept
Exercises 14
Backtracking
Passages to
Abstraction
Special Cases
Recap of Square
Roots
Rule for the
Extraction of Square Roots
Cube Roots
Concept
Larger Numbers
Exercise 1: Next
Digit and Backtracking
Exercise 2:
3Digit Roots
Exercise 3:
Passage to Abstraction
Recap of Cube
Roots
Rule for the
Extraction of Cube Roots

bead squares
rubber bands
paper square of 10
bead squares
bead bars
golden beads
gold bead cards
pegboard/pegs
wood cube material
+ binomial cube
prepared labels
trinomial cube
prepared labels
“hierarchical trinomial
(aka algebraic/arithmetic)”
3 Kings prep tickets
Square roots board
units from div tubes
golden bead material
hierarchical guides
N Charts (2)
box of 1cm cubes
wood cube material

cabinet
cabinet
deca



450
40.50
59.50
54.00
22.50


30.00


cabinet
cabinet
deca



290.00
23.00
34.00
34.00
19.00
9.00


printable
printable
printable
printable
printable
printable



656.90

409.00


VIII. Other Topics





Signed
Numbers
Negative Snake Game
Operations
Powers
of Numbers
Powers of 2
Powers of 3
Combination Of Powers of Two/Three
Powers of 10
Operations – Exponential Notation
Expanded Power Notation
Operations Using Expanded Power
Other
Number Bases
Numeration (Introduction)
Operations
Conversion
Ratio
and Proportion
Introduction to Ratio
Problem Solving Using Ratio
Ratios and Fractions
More ProblemSolving with Ratios
Proportion
Word
Problems
Introduction to Word Problems
Introductory Word Problems
Distance/Velocity/Time: Sensorial
Distance/Velocity/Time: Arith Level
Distance/Velocity/Time: Algebraic
Principal/Interest/Rate/Time:
Sensorial
Princ/Interest/Rate/Time: Arith/Alg
Introduction
to Algebra
Introductory Algebra
Balancing an Equation
Solving for an Unknown in an
Equation
Algebra Word Problems
Solving for Two Unknowns

negative snake game
power of 2 cube
box 1cm cubes
number box
wood cube material
Nondecimal base board
gold beads
bead cabinet
receipt tape
operation finger charts
decanomial bead bars
number box
cups
Prepared envelopes w/ tickets
prepared cards

*
40.50



*





$59.00
23.00
*


*





Printable
printable
printable



40.50

82.00


I did not
see the Negative Snake Game at Alison’s.
I did not
see the 1cm cubes at IFIT.
Draw the
nondecimal bases on your posterboard or cardboard – this is NOT the one
available for sale!
Remedial Mathematics





Introduction
to Remediation
Numbers
110
Decimal
System – Quantity
Decimal
System  Symbol
Formation
of Numbers with Beads and Cards
Collective
Exercises: Operations
Memorization
of Tables
Teen
Beads and Boards: 1119
Ten
Beads and Boards: 1199
Final
Notes on Remediation

·
Bead bars – if the child is not yet counting to 10 OR
cannot yet write the numerals. Pull the bead bars from the Decanomial Bead
Bar Box. (need for elementary)
·
Golden beads (45 units and tens, 45 wooden hundreds and 9
wooden thousands) – need for elementary anyway
·
Teens and Tens boards (can be made on paper for the
purposes of remediation), with beads from the Decanomial Bead Bar Box and
golden units – but if you have them for another primary child, then use the
regular ones.
·
Stamp Game (need for elementary
·
Geometry materials: cabinet, solids, geometric solids –
need for elementary geometry

Teens/Tens Boards: 64.80

Teens/Tens Boards:
50.00

printables available soon



64.80

50.00


Contents of Operations Box (also called Number Box or Box
of Numbers):
·
Gray number cards 19, 0 (at least 5 sets)
·
White number cards 19, 0 (at least 5 sets)
·
Operation symbols
·
Decimal points
·
Parenthesis – 8 sets
·
Blank tickets
Printable = available in the album or at Garden of Francis
or at Keys online support
““ = listed above – use the same material
Assume: graphite pencil, colored pencils, paper, graph
paper in a variety of sizes, ruler
Transparencies: could be laminating pouch sealed together;
overhead transparency, page protector, etc.
IFIT Notes:
Golden
beads:
If
you don’t need the trays and cups, purchase the following:
·
9 Wooden Cubes: $24
·
45 Wood Hundreds: $26
·
45 Ten Bars: $11
·
45 Units: $1.50
·
(if you buy the bead cabinet material from
here, pull a beaded cube and beaded hundred from the bead cabinet for needed
presentations; otherwise, add 1 beaded cube and 1 beaded square  beaded cube
is $25; set of 9 beaded hundreds is $26).
·
You’ll need to add your choice of number cards
as well; or cut your own cardstock and make your own. (printable on Keys of the
Universe)
Alison Notes:
·
With the golden beads, verify which decimal
cards and sizes you are getting; consider printing your own.
IFIT
= $1791
Missing:
Hierarchical material, 1cm cubes, decimal cards
Alison
= $2152.80
Missing:
Negative Snake Game, golden beads, decimal cards, bead cabinet itself
PRIMARY OVERLAP

Alisons

IFIT

Keys

Large Bead Frame
Decanomial bead bar box
Bead cabinet, beads, arrows
Division racks/tubes
Stamp Game
Circle Fractions
Binomial Cube
Trinomial Cube
Negative Snake Game (use portions for Addition and Subtraction in
primary)

20.00
85.00
153.00 (beads)
61.60 (arrows)
145.00
35.00
125.00 (w/stds)
40.50
54.00
(don’t see it)

21.00
84.00
280 (beads)
240 (display)
38.00 (arrows)
88.00
24.00
85.00 (w/stds)
23.00
34.00
59.00

(paper)

TOTAL TO <MAYBE> SUBTRACT

$719.10

$976.00


Mathematics Materials List
Main
Materials – it is best to read the album page while preparing or purchasing the
materials, so that details do not have to be repeated here and you can
immediately see what each piece will be used for when considering alternates:
·
Golden bead materials – 45 units, 45 tens, 45
hundreds, 9 thousands (no more)
·
Decanomial bead bar box (bars 110, 55 of each
bar) –
o
Athome: some presentations need just a few
more bead bars – you could make the 47 extra with pony beads or connected
Legos
o
ideal for classes: add bead bar box of 110
with a smaller quantity
·
Box of bead bars 19 (schools may want 25 of
these; homes do not need it at all)
·
Box of number cards: white set with 19, 0,
gray set with same (3 copies of each #)
o
Could be same box with operation signs and
dots for decimal points
o
Another section for blank tickets and pencil
o
Classrooms need 3+ boxes
o
Could store some parentheses in here
o
A tacklebox is ideal
·
Prepared tickets for various operations
·
8 sets of parenthesis (cut from cardstock)
·
3 sets of small decimal system cards, 1 –
3000, stored on a tray/basket
·
Pegboard (30 by 30 ideal; 25 x 30 if that is
all that is available)
·
Box of hierarchical pegs (green, red, blue –
could be cut down golf pegs)
·
Tables A, B, C, E (on paper for children to
use)
·
Wooden hierarchical material and corresponding
number cards (used in early work and in Powers of 10 later) – this is the
material that goes to millions
·
Large bead frame
o
Large/long notation paper for the large bead
frame
·
Complete bead material (bead cabinet:
long/short chains, squares, cubes, labels)
·
Bank Game card material (colored background;
black font – NO beads)
·
Checkerboard for Multiplication
·
Flat bead frame
·
Rulers in various styles
·
Fraction circle insets (110)
·
Stamp game
·
Racks and Tubes (division)
·
box
labeled “squares of numbers” (usually homemade)
·
Packet
of 10 envelopes with the decanomials representing the decanomial square
(homemade)
·
box of extra fraction pieces
(wholes through tenths – equivalent of 10 wholes in each fraction – on red
material is best)
·
4 Cards with prepared fraction
operations  simple (can repeat from primary)
·
Fraction division skittles (whole,
half, third, fourth)
·
2 transparencies: rectangular –
one with 4 rectangles (lines drawn long side to long side), one with 3 (lines
drawn from short side to short side)  homemade
·
Packets
of prepared fraction labels
·
4 cards with more complex
fractions operations (one for each operation)
·
Black
frame with 0100 marked around the inner circle (similar to Montessori
protractor (geometry use) which is 0360)
·
felt 3” squares: green, red, blue, light
green, pink, light blue
·
Decimal Checkerboard
·
Additional green unit skittles (if a
classroom)
·
Decimal
Board (yellow board)
·
Decimal
Fraction material (cubes, number cards, black decimal points)
·
Wooden cubing material – wood cube of each
number, with 27+ wood squares for each number
110 – the beaded cubes cannot replace this material
·
Binomial
Cube
·
Trinomial
Cube
·
set of prepared tickets in a box labeled
“(a+b)^{3} (a+b+c)^{3}”
·
2 sets of prepared tickets in box labeled
“Three Kings”
·
Printed paper square of 10
·
Square Root Pegboard (15 holes by 15 holes)
·
N/N3 Chart
·
Box of plain wood 1 cm cubes (could use set
from geometry)
·
Hierarchical
Trinomial Cube
·
Elementary
Negative Snake Game (should include box of grey 10bars)
·
Power
of Two Cube
·
An envelope marked
"velocity" containing printed tickets
·
An envelope marked
"interest" containing printed tickets
·
NonDecimal
Base Board  homemade
·
4
Arithmetic table finger charts (nondecimal bases) – these are the working
charts from the primary level
·
a piece of card
divided into twelve equal strips, with small cards: pick & shovel
Other Materials:
·
Large
red felt mat (additional 10+ felt mats any color for classroom use)
·
Large
blank paper or posterboard for childmade charts
·
Envelopes
in varying sizes
·
Sets
of blank tickets in a container – may need 23 for a classroom
·
Paper/pencil,
colored pencils
·
Graph
paper – various sized squares from ¼” to 1”
·
Long
thin strips of cardboard (1/4 – 1/3 inch wide by about 11 inches long)
·
Thin,
narrow strips (2 inches by 11 inches long)
·
Strips
of paper (10.25 x 1.25 inches or so)
·
Marker (such as a clear glass pebble or
pretty stone or piece of glass)
·
Index
cards
·
Additional
transparencies for children to make their own fraction division pieces
·
Small
thin black strips (fraction lines)
·
Symbol
for a king (crown is ideal – fits on the decimal board unit space)
·
Container
with colored rubber bands
·
Colored
discs (one each: green, blue, red) – could pull from stamp game
·
two plastic cups with a line of black tape or
marker across each one
·
Roll
of adding machine tape
Charts:
·
History
of mathematics charts
·
Fraction
charts (homemade)
Other Resources to
Have on Hand:
§ http://livingmath.net for additional resources – perfect for cosmic
education
§ Life of Fred books can be interesting to this age and into middle/high school
·
Math Dictionary for Kids: The
Essential Guide to Math Terms, Strategies, and Tables (straightforward, nononsense,
illustrated)