Making Montessori Materials: Bead Chain Arrows

I got tired of the paper/cardstock arrows. So thin, they slip around, hard to pick up when the focus should be on counting. They get *lost*.

The file I original used has two of the colors switched; I was able to change them (after I'd already printed the wrong arrows), then ran out of ink so had to wait. One thing leads to another, years have passed and the children are just making their own arrows out of paper for those two colors. I tried to print them again, but lost the modified file and don't have Adobe that lets me modify things anymore (and don't want to pay for it). Yeah. Craziness.

I kept saying I was going to switch to popsicle sticks.

Well, I started making the Keys of the Universe elementary Montessori mathematics videos - and my mission is to work on the corresponding materials as I get to the videos that need them. So there you go - or there I go. A simple project that became a big deal when it sat in my living room for months ;)

This material is indeed very easy.

What do you need?

• A package of normal size popsicle sticks 
• A package of tongue depressors
• White very-fine-tip paint marker (for writing on darker colors)
• Black very-fine-tip paint marker (for writing on most of the colors)
• Paint in each of the bead cabinet colors (for "gold", I kept the sticks natural)
• I also used a gold paint marker to outline the wide stick that represents the cube of the number. 
• Note: I did not do the initial counting up at the beginning - these ones I will do in cardstock to keep them narrow. Easy enough to replace those for primary use (elementary students don't use them)

TIME: These took less time to make than printing, laminating and cutting the cardstock arrows.... Just saying.

I chose to paint just one end - just on one side at first; but I found it was easier to sort them and use them with the bead chains when the color was on both sides. So the *number* is currently only on one side (could be on both). 

The numbers are written so the arrows are placed below the bead chain; I really could have, should have written them so the numbers are placed on the far side of the bead chain from the child, yet readable. Wasn't thinking much at the time. ;) 

They still work for elementary. Will have to test for primary.

A video from elementary:

Tacklebox Montessori

Just a sampling of the tackleboxes used in our Montessori homeschooling...

Inspiration by Ms. Suzanne over at Livable Learning and Teaching from a Tacklebox.


As I go through each chapter of each elementary album, I am updating, refreshing, cleaning out and re-posting all of our materials - providing downloads of all that is possible, posting images of organizations, etc. I am really striving to streamline the process for Montessori elementary homeschoolers.

For the fun of it, here is some for everyone!


Retiring the old fractions box... It has served us well, but after 3 children sitting on it.... well, it was time for something that has a lid ;)

Plano 3750

The new one - with space for sample fraction problems.
If you make these pieces, please use red (the unit broken into pieces). NOT yellow ;) 

The box needed for the numeration chapter (early math). We call it a numbers/operations box. I would like to call it the Numeration Box because we have a separate box for the actual Operations chapter, but this one has the operation signs, fractions, decimals, etc.

Plano 3700

Operations Box

Holds the bank game, guides to create a child's own problems, stone for group division and more.
This is also a Plano 3700 

Not a tacklebox - but how we store our decimal system cards from primary - materials that are used into elementary and a bit into adolescence.

We also have a Plano 3500 for the Notation of Squares and Notation of Cubes.

And a Plano 3700 for our geography stamps.

Montessori - When to Present

There are many questions about "mastery" of late - how to know when to move on to the next material or presentation. I would like to submit/repeat an idea to consider, to ponder.

At the primary age ("Casa dei Bambini" or Children's House) - If you are using an album set that has 4 subject areas (exercises of practical life, language, sensorial, math), and you present ONE thing from one album and wait a few days to observe your child's response, they will have ONE choice that whole time. Put yourself in their shoes/socks/bare-feet and consider what that is like. One activity to choose from? Seriously? As a child I'd be finding something else to do and the adult would be very disappointed.

So maybe you present one thing each day, 4 days a week. By the end of the week, the child has 4 options. Would you be bored? (those of you using albums that have more than 4 subjects will find that with this method you only touch on a subject once every 2-3 weeks - or longer).

Getting Started with Presentations and Work Choices: 

This work is not successful
until EPL and language are successful. 

So start out with a series of presentations - the EPL album has all the preliminary work, some of it is just practice carrying objects, practicing walking quietly (then in the kitchen and the bathroom be showing various skills as appropriate); the language album has all the spoken language games - go with it - "Let's practice carrying objects!" and do a series of objects - slowly, focusing on each one, but you might do this for an hour or two hours. Stop when your child needs a break. The first days of homeschooling will be full of EPL and language - and consciously involving your child in all aspects of household/family life. He should have some free time with his favorite toys as well.

Walking on the line; playing outside; singing songs; reading books; being involved in everything that happens in the home; keeping things neat and orderly.

Thus the first days will be ***busy***. They will be ***full***. It should be natural and fun. And there will be almost NO MATERIALS beyond what you have at home already.

This lays the foundation for when you do get into the "official" Montessori materials (or modified from at-home materials).

They can't do this until they have the focus,
the process,
the trust in the adult to show them something valuable.
All lessons learned from exciting Exercises of Practical Life
- many of them -
throughout the day
and over the course of weeks.

Continuing on with this theme of when to present and how much:

MASTERY - does a child need to master one material in a subject area before moving on to the next?

Short answer: NO! Let's apply the same logic as above. If you have 4 subject areas as AMI does, at 3.5, the child is likely to only have EPL, language and sensorial (math typically comes closer to the 4th birthday). That is THREE work options if you are waiting for mastery in one concept before moving to the next, within each subject. Within each album can be found a few threads that come together at various points (such as language as separate preparations for the physical side of writing and the mental side of writing), so in reality, within each subject are parallel "threads."

Do we want to be presenting all day long? NO! But think about the classroom experience of a child - he may not get a new individual presentation each and every day, but he does get lessons in grace and courtesy during group time, he spends time observing his companions (a presentation in itself), and he works with some of these companions at various tasks.

In the home life, this equates to being involved in as many aspects of home life as possible, observing the doings of the various people in the home and the neighborhood, having real conversations using real language, and being shown new skills or materials that are appropriate for his age and development. This last part is where we look to the scope and sequence for what is typically appropriate, then modify according to the individual child in front of us.

How Often to Present Once Things Get Going: 

If you look at this post at Montessori Nuggets: Montessori Nuggets - Organizing Primary Presentations and you've actually then opened yourself to the true depth of the Montessori materials, you'll find that you're presenting something every weekday of a year-round school. Something. Sometimes more than one something. Some things are left for child-discovery (a good deal is), but there are enough direct presentations for a homeschool environment to do something with your child (who, after all, wants to be with you) every day. Explore with your child.

Every day.

That's not a new material every day - that's "let's look at something else we can do with the spindles!" (just one example - I have noticed many people forget the bundling stage, but this is actually crucial to gaining from the true depths of this rather simplistic-looking material). And it might even be a suggestion thrown out while you are washing the dishes ;) That happens a lot in our home - I say "I wonder if you could (fill in the blank) with (list a particular material)? And show me when I am done washing the dishes (or whatever I am doing at the moment)." And THAT might be my presentation for the day!

Given we typically have a daily social graces lesson or chat (grace and courtesy), lots of involvement in real life activities of the home, go off and play by yourself time, outside time, etc.

Three-Hour Work Cycle in the Home: 

I have recently heard from several individuals that they expected their child would work independently (which equates to being "alone" for some of these children) for a solid 3-hour work cycle.

• Humans are social creatures. Young children learn their social skills from the adults around them. 
• Our work cycles at home are 24 hours every day, not 3. If you want a set-aside school time where the materials are only available during that time, that is awesome, but your child will be learning throughout all of every day - and many of the Montessori "works" do not require specific "Montessori" materials (Exercises of Practical Life, art & sewing & painting, much of the language work, applying math concepts to real life, real life science exploration (cause and effect, asking questions and testing out answers, etc.) - so much more). *Most* of Montessori is about living real life, not about materials. 
• During a school-based work cycle, the child is chatting with friends, having a snack, in the ideal Montessori environment the child is free to go outside and play/garden/watch butterflies, observing classmates, using the bathroom, etc. The child is alive and learning, but not always engaged with the specific material. And he has role models around him to guide him in his choices and possibilities. This needn't be any different at home! The child should be engaged in the environment and that includes the adult. If you have a block of "school time" use that time to prepare your materials, to practice with the materials, to explore for yourself - and be present when authentically needed ;) 
• Will the adult get some "hey! my child doesn't need me at this moment!" times - yep! It will happen. But if you really want your child to work independently of you, you should be engaged in the materials (making them, practicing with them, organizing them, cleaning them) - or doing something else (household or family related) that the child can't "help" with right now, but that he can observe you doing during his own work time. 
• Read more about the 3 Hour Work Cycle at Home at this Montessori Trails Work Cycle page. 

Making Materials Takes So Long: 

Mom and son
together at Montessori school
He had been sitting and staring at the math materials for 30 minutes.
Doing some mental math he was trying to explain to me 

Most of you - I'll be honest, I love you all, so please know that going in to what I am about to say - MOST of you are making way too many materials. STOP!

• Your children should be involved in SOME of the material making. Extensions or ideas that they have? Let them help create materials! Primary aged children? Yep. Seriously, 3 year olds? Yep. And the 4s and 5s too. And if you have elementary children and teenagers - get them involved too. This is a lesson in creativity, using art skills in real life situations which is far superior than doing a craft just to do a craft. 
• If the children come up with an idea - they should be making it - or involved with the making of it. Wait, I repeated that. ;) I wanted to make sure you read that ;) 
• The children can SEE you making materials too. Let that be *your* work that they 1) observe and 2) makes you too busy to always be hovering like a helicopter. Your children might find they can problem-solve on their own sometimes, make their own decisions or get their own drink of water. YOU can do it! ;) 

Also see our Montessori Trails page on When Montessori Fails for futher insights into how the environment works.


Ask me other questions! I'll reply in comments and/or add to this post.

The Cost of Montessori Elementary Language - WORST CASE SCENARIO

My main caveat for the elementary Montessori language materials is that most of it has to either be made or purchased in packets that may or may not correspond with your albums/manuals.

For those using Keys of the Universe, many printables are available or will be available in the near future.

Language Elementary Montessori Materials - Click here for the full materials list and price comparison for IFIT, Alisons, what Keys provides

Alison’s: roughly $1200 if buy ALL (don’t buy all!) and some add-ons

IFIT: roughly $500 if buy all they have

NOTES:

Nobody has everything; much is printable from KotU or available at Garden of Francis – or purchase additional packets from Alison’s and change the presentations (less key-based though).

Literature books are not included (see enclosed lists)

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.

Caveats:

• 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.

		Alison	IFIT	Keys/other
I. Introduction
Story of Numbers	8 Charts			Printable
II. Early Work - Numeration
Wooden Hierarchical Material Large Bead Frame: Introduction           Exercises I-IV 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 1-3 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 1-10 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 push-pin decimal board king symbol black frame felt squares Decimal Checkerboard Number Box Bead Bars 1-9	55.00 --- --- ---* 24* 36.00 --- deca	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 1-6           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 1-4           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: 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 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 Problem-Solving 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 Non-decimal 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 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
		64.80	50.00

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

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 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

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 (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)