Remedial Mathematics - Video Fun

Just another one for fun.

Remedial mathematics, variation on the 2nd period of the 3 period lesson. Having a little fun - and then it backfired on me!

;)

Geometry - Parts of a Circle - Old Work

Some of +Joshua+'s work.

Labeling parts of the circles - and some decimal math work.

I love how he decided to abbreviate "circle" as "circ." - saves SO much time! LOL!

Fractions Videos !!!

The fractions videos are finally being uploaded - I truly thought they were already up!

Here is a teaser!

This is from the fractions chapter in the elementary Montessori mathematics album - for Keys of the Universe that is "chapter 5".

All the others are available at Keys of the Universe!

And hopefully I will get caught up posting all my draft posts from... APRIL !? Ouch. We have had 2 boys come and go (to their permanent home), 2 older girls move in, then 2 little siblings move in. Addressing the needs of traumatized kids in the public school system. Family vacations.

And all the reality of how the Montessori approach is SO suited to the meet the needs of children with special needs and coming from traumatic situations.

I am in love with the Montessori approach more and more every single day. Even more so the days I don't approach things in this respectful, needs-based way - and go the way of the world - and everything literally falls apart.

More to come!

BLOOPERS! 

How many times was that!? 

I'm hungry! 

Cuz we can't be serious ;)

Longevity of Montessori: Mathematics

The Montessori approach meets the needs of children where they are at - both collectively and individually. Therefore, it is an approach that meets the needs of ALL children. The only limitation is the preparedness of the adult to meet those needs ;)

A recent post at MariaMontessori.com introduces this concept as it applies to primary (3-6) and elementary (6-12). Montessori is Developmental

Even in our material,


Let's look at math specifically - just some highlights: 

With infants and toddlers, we do a lot of natural one-to-one correspondence. Few toys, each that belongs in a particular place. Matching activities in sizes, shapes, colors. Helping to set the meal-table using a diagram of what goes where.

We can also give the language of numbers (counting), and children love language at this age, so most do pick up on counting numbers, although they typically skip a few numbers or repeat a few sequences ;)



Primary Mathematics:
While we don't typically start math in primary until around age 4, we begin with a few materials that extend into primary mathematics as well as into use at elementary and adolescence. Sensorial and Mathematics materials are both noted here:

• Red rods - extend into the number rods 
• All the groups of ten we have extend into the decimal system
• Pink Tower and Brown Stair can be used in geometry at elementary
• Binomial Cube and Trinomial Cube (elementary and adolescence)
• Geometry Cabinet and Solids (elementary)
• Golden beads (elementary and adolescence)
• Bead Cabinet and contents (elementary and portions in adolescence)
• Snake games (if you purchase the negative snake game, it includes all you need for primary as well as elementary and adolescence)
• Decanomial bead bar box (elementary and adolescence)
• Stamp game (elementary and adolescence)
• Short Division with Racks and Tubes becomes Long Division with Racks and Tubes (elementary)

Common Threads: 

• Place value color-coding remains consistent throughout all levels - into the checkerboards that are the visualization of the multiplication process, the bank game (just numbered cards, no beads), and more.
• The bead cabinet colors also remain consistent through all levels - even into the solid wood blocks of the cubing material that is used in elementary and adolescence. 

Additional posts of interest:

Toddler Exercises of Practical Life

All Montessori Trails posts on Mathematics

Mathematics Logic Game from Wff'n Proof

Review post on Adolescent Algebra Album

And that, dear friends, is today's show ;) 

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)