Montessori Elementary Homeschool Blog - with documentation of our infant Montessori, toddler Montessori, and primary Montessori experiences; as well as preparation for the upcoming adolescent Montessori homeschool years.

Monday, March 9, 2015

The Cost of Montessori Elementary Mathematics - WORST CASE SCENARIO

Well, I was talked into it. I finally put together a price list using IFIT and Alison's Montessori.


  • These prices are based on full price, not sale price and assume you are making the list amount possible, buying everything new that you possibly can, and have no access to discounted used materials (and you don't want to call any nearby Montessori schools and ask about picking up any of their old materials). 
  • In other words, this is the MOST you could possibly pay. 
  • Prices do not include shipping (which could be free)
  • Neither IFIT nor Alison's carries everything listed in the Keys of the Universe albums, but between the two of them, everything is offered. 
  • Exception: I could not find the fractions charts or the Story of Numbers charts - however both of these are available at Keys of the Universe online support (discussion community) or Garden of Francis
  • The prices are awful on some items, which is your encouragement to make a bit more yourself! (wooden hierarchical material comes to mind!)
  • There are some things that still need to be hand-made --- either they are offered with the KotU online support (discussion community), will be soon, are offered at Garden of Francis, or are very easy to make from the album write-ups. 
  • Some things transition UP from Primary (ages 3-6) - there is a chart in the file regarding which items you may have already purchased/created that can be deducted from the main chart. 
  • Most items can be re-sold when you are done (after going through ALL your children!) for at least half their original cost, sometimes closer to 80%. 
  • All materials are for multiple children - these are not one-time uses. 

Montessori Elementary Mathematics Materials List - click there to download the pdf file showing the entire materials list as well as comparison chart.

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.

I. Introduction

          Story of Numbers
8 Charts


II. Early Work - Numeration

Wooden Hierarchical Material

Large Bead Frame: Introduction
          Exercises I-IV
Commutative & Distributive Laws

Least Common Multiples
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












hardware store
golf tees


Cabinet currently not listed on Alisons.

III. Operations



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
bead bars
Stamp Game
circles fractions


IV. Squares and Cubes of Numbers

Prerequisites to Squares and Cubes of Numbers
Notation of Squares
Notation of Cubes
Games 1-3
Game 4: Decanomial Square
Paper Decanomial
Sums Using Squares and Cubes
bead cabinet
prepared labels
bead bars
division skittles




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 1-10
Practice Problems
 green skittles
prepared problems
division fraction skittles












VI. Decimal Fractions

Quantity – pull beads from racks/tubes
Symbol Linked to Quantity
Formation and Reading of Quantities
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
decimal board
king symbol
black frame
felt squares
Decimal Checkerboard
Number Box
Bead Bars 1-9










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

          Transformation of a Square, Ex 1-6
          Passing From One Square to Another
          Squaring a Sum
          Squaring with a Hierarchical Value
          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 1-4
          Passages to Abstraction
          Special Cases
          Recap of Square Roots
          Rule for the Extraction of Square Roots
Cube Roots
          Larger Numbers
          Exercise 1: Next Digit and Backtracking
          Exercise 2: 3-Digit 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
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




















VIII. Other Topics

Signed Numbers
          Negative Snake Game
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)
Ratio and Proportion
          Introduction to Ratio
          Problem Solving Using Ratio
          Ratios and Fractions
          More Problem-Solving with Ratios
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

Non-decimal base board
gold beads
bead cabinet
receipt tape
operation finger charts
decanomial bead bars
number box

Prepared envelopes w/ tickets

prepared cards











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

Remedial Mathematics

Introduction to Remediation
Numbers 1-10
Decimal System – Quantity
Decimal System - Symbol
Formation of Numbers with Beads and Cards
Collective Exercises: Operations
Memorization of Tables
Teen Beads and Boards: 11-19
Ten Beads and Boards: 11-99
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


Contents of Operations Box (also called Number Box or Box of Numbers):
·        Gray number cards 1-9, 0 (at least 5 sets)
·        White number cards 1-9, 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

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)

153.00 (beads)
61.60 (arrows)

125.00 (w/stds)
(don’t see it)
280 (beads)
240 (display)
38.00 (arrows)
85.00 (w/stds)



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 1-10, 55 of each bar) –
o   At-home: some presentations need just a few more bead bars – you could make the 4-7 extra with pony beads or connected Legos
o   ideal for classes: add bead bar box of 1-10 with a smaller quantity
·        Box of bead bars 1-9 (schools may want 2-5 of these; homes do not need it at all)
·        Box of number cards: white set with 1-9, 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[1]
·        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 (1-10)
·        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 0-100 marked around the inner circle (similar to Montessori protractor (geometry use) which is 0-360)
·        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  1-10 – 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 10-bars)
·        Power of Two Cube
·        An envelope marked "velocity" containing printed tickets
·        An envelope marked "interest" containing printed tickets
·        Non-Decimal Base Board - homemade
·        4 Arithmetic table finger charts (non-decimal 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 child-made charts
·        Envelopes in varying sizes
·        Sets of blank tickets in a container – may need 2-3 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

·        History of mathematics charts
·        Fraction charts (homemade)

Other Resources to Have on Hand:
§ 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 (straight-forward, no-nonsense, illustrated)

[1] Small decimal cards could be the same ones that the children used in primary; each number is stored together (all three ones together, all three twos together)


  1. Wow.

    That was a lot of work! At my stage in the game it is a RELIEF to look through all that and realize I already own it all, LOL. In my head I always think of geometry as part of math so I DO have some geometry materials outstanding. I'll probably be ordering them soon and I keep thinking, "wow, I'll be done ordering materials." Of course, there will always be things I want from ETC and such, but still. I don't know if I'll EVER make those geometry charts. Yuck. Kids can make them.

    I have been meaning to ask you a question from the OTHER point of view. I am going to be selling a bunch of things soon. I am giving my shelves the old stink eye and thinking about what can get out of the way. Most things are an obvious yes or no. However, I've been eyeing up my 1000 cubes and 100 squares. I have 45 of each. AFTER we've done group division in elementary do I still need those. I am happy to keep them if you think I'll use them. I just keep looking at them and wonder if I'll be glad to have them in a year or two to revisit something. Wanted your opinion. Same with the 100 board. Will I find a use for it if I have it or should it go. (I keep thinking "multiples" but I think the paper boards are more useful for that.)

    1. I was so nervous doing this because I thought the numbers would scare people away! Maybe it still will, but the response so far has been one of relief. Yay!

      Exponential notation still uses the golden beads (not all 45 cubes though ;) ); after that you should be good. I should check the adolescent album though... if you decide to go down that route you might come hunt me down and say "you told me!" ;)

      100 board should be good to go.

    2. Quick glance at the adolescent - I don't see the golden beads listed.

      You've given me an idea though!
      I need to get on with some sewing and stamp-making, so by mid-afternoon, I hope to have posted scans of the materials list pages (3) from the adolescent album --- and will post in the discussion community. I can't provide the whole album, but I think I am ok with sharing the materials list so everyone knows what to keep if they continue with Montessori!

    3. Oh that would be great! I do plan on getting that adolescent algebra/math album in the future. I would love to know what I need to hang on to so that I don't sell off things I need. I'll look over that exponential notation album page(s) and see how far away we are and how much I might want to keep. I'd love to get some of these wooden number cards off my shelf too.

  2. Thank you Jessica for this...and WOW, that was a TON of work. A TON. Goodness. I am feeling like MBT here knowing that this year we have basically collected all the Montessori materials that we'll be needing through the end of KotU. (now it is on to all the other things we need.) I actually felt like I spent WAY more on materials than this, but I guess it could have been the primary stuff that makes me feel like this. There is a TON TON of that.

    This list also goes to show how much is made by the guide. It is amazing to me how any of us find the time. True dedication perhaps.

    Thank you again for putting this together! MBT I want to see your new elementary-only shelves when you are done with your re-org!

  3. Wow, that must have been a ton of work. So kind of you to share this!

  4. whoa, as I take a big gulp! Will I ever be able to come up for air from material making?? lol

    1. It truly does come to an end - or at least becomes a TINY trickle. ;) I am also a FIRM believer in the child creating materials as well - either by own design or as an assistant.


  5. Wow. So much material! Just for math! I absolutely understand sequential learning and really love that but, man! As an absolute beginner, it's highly intimidating.

    1. And for that - I wish I could make it look as good as it actually is!

      This is 6 years of materials (some of which can be used in primary; and some of which is also used into adolescence) - many of the materials are used again and again and again (you'll note where the symbol "----" is) --- only where a price is listed is there an actual material to purchase or make. The only new things for the last chapter ("Other Topics") for example is the negative snake game and the powers of 2 cube ;)

      So - it IS better than it looks ;)