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MATH

COPYRIGHT NOTICE. Please note that the copyright symbol indicates typeface choices and or designs that are my original creations. You are permitted to use these designs and adapt them to your own personal, homeschooling co-op, or classroom use. Under no circumstances are you to use these files to resell these items to another person.

Counting

Decimal System

Memory Work

Abstraction

1). Counting

Teens and Tens   © 2003

Designed to fit in a tackle box - Laminate and cut individual pieces - put the boards together with clear packing tape (leave tiny gap between tens and teens to allow for folding) so that cards fold back and forth accordion style.

 

   

Hundred Board (above) made with ceramic tile and Sharpie marker

(right) storage for Hundred Board tiles - wooden basket from Target

 

Hundred Chart   © 2003

For learning the sequence of the numbers 1-100

 

               

Thousand Chain (above) close up  -  (center) laid out on 9ft. table  (right) Thousand Chain stored in Rubbermaid silverware organizer tray.

We made all our short (square) chains and long (cube chains) out of 48" neon shoestrings and pony beads... Square chains with green shoestrings and Cube chains with pink shoestrings (to match the control chart). 

 

Hundred chain is (9) green beads for the units and then (1) blue bead for the 10s, repeat 10 times except that the 100th bead is red. Rather than the traditional golden bead chain for hundreds and thousands, we have a chain that matches the color coding of the Numeral Cards.  Thousand Chain is 10 Hundred Chains tied together.

 

We made our Square and Cube Chains with the appropriate number of beads, for example the Square of Five Chain is made with 5 light blue pony beads, then a knot in the shoestring, continue with 5 beads then a knot, until you have 25 beads or the square of 5 which is (5x5) or 5². The Cube of Five Chain is made the same way (planning your knots to attach another shoestring when necessary). The Cube of Five Chain has a total of 125 beads -  (5x5x5) or 5^3.

(Above) Arrows for Long Cube Chains

When cutting out chain arrows, cut exactly between the colors horizontally to leave a white border. Cut the back end of the arrow straight and the front end of the arrow with a point, leaving a white border around all edges.

               

(Above) Tackle Box for Short Square Chains - (Center) Layout for Skip Counting on Short Chain of Four (i.e. four squared)

Thousand Chain Arrows   © 2003 C

Square Chain Arrows  (Short Chains)   © 2003  (includes 100 Chain arrows)

Cube Chain Arrows  (Long Chains)   © 2003

Alternative Cube Chain Arrows for Cuisenaire users  (Long Chains)   © 2003 

Squares and Cubes Control Chart   © 2003

 

2). Decimal System   

Golden Bead Thousand Cube Pattern   © 2003

 

(above) Golden Bead Place Value Layout - (right to left) unit bead on green mat, ten bar on blue mat, hundred square on red mat, thousand cube on green mat.

Note: the thousand cube is actually the Unit for the next number family - so in continuing this pattern the Thousand is the next Unit (on green mat) the Ten Thousand (a bar of ten Thousand cubes) would be on blue and the Hundred Thousand (a square of one hundred Thousand cubes) on red, and One Million - the Unit of the next number family - (a cube of one thousand Thousand cubes) on green. This extension is known as the Montessori Geometric Hierarchy of Number.

 

Making the Thousand Cube: Use downloadable Thousand Cube pattern and print out on goldenrod paper. Lightly glue to sides of a 1/2 gallon milk carton cube using (2) half gallon milk cartons. Use bottom of one milk carton to mark the other, then cut with utility knife and fit one inside the other to form a cube. Use clear packing tape to laminate all paper surfaces.

Golden Beads: All beads are 10mm faceted beads from Bolek's Crafts put together with 18 gauge wire.  This keeps the beads in proportion with the milk carton cubes and with the wooden Pink Tower (made from square doweling). Note:  The Thousand Cube is ten cubed (10cm x 10cm x 10cm) and so is the largest cube of the Pink Tower (which is made with lengths of square wooden dowels glued into cubes). The golden ten bars of beads, if made with ten 10mm beads keeps the pattern consistent.

(The golden bead color is Sun Gold #23).

 

Numeral Cards    © 2003

Large Set (0-1000s) for the larger number in the equation

Small Set* (0-millions) * need two sets for the two smaller numbers in an equation

Fraction Decimals - Large Set (tenths to thousandths)

Fraction Decimals - Small Set (tenths to thousandths)

                           

(above left) Numeral Layout                                

(next) subtraction with numeral cards

(next) number with numeral and fraction decimal cards

            (light blue tenths, pink hundredths, light green thousandths)

(far right) layout with Fraction Decimal Cards

 

Stamp Game   © 2003

The green, blue and red skittles and discs are from Learning Resources.

Tackle Box is Plano 3705 from Cabelas.

 

3). Memory Work

Snake Game Videos!!  © 2003

Videos for the Positive, Subtraction, and Negative Snake Games - Six videos in the Math section at the Montessori Materials website.

Blue Marker Paper - Blank for Math Table Practice   © 2003

1cm Graph Paper   © 2003

2cm Graph Paper   © 2003

1/4 inch Graph Paper   © 2003

1/2 inch Graph Paper   © 2003

1 inch Graph Paper   © 2003

ADDITION - Math Facts

                           

 (Left) Addition Charts, Math Tables, Equations and Bingo Tiles for the Blank Chart

(Right) Addition and Subtraction Strip Boards

Addition Equations   © 2003    

MULTIPLICATION- Math Facts

                     

(Left) Multiplication Charts, Tables, and Equations. (Center) Multiplication and Division Boards. My original design!! Using push pins on a laminated cork board instead of beads on a wooden board!! (Right) Close up of Equations Tackle Box with Addition, Multiplication, Subtraction and Division operations slips and answer cards

Multiplication Equations   © 2003

MULTIPLICATION - Decanomial

           

Geometric Decanomial (left)      Math Chart #3 - Pythagoras Chart (right)       

The Geometric Decanomial is a simplified 2-D sensorial representation of the chart of multiplication tables, also known as the Square of Pythagoras, and included as Math Facts Chart #3. The colors coordinate with the colored bead stair - red for ones, green for twos, pink for threes, yellow for fours, light blue for fives, purple for sixes, white for sevens, light brown for eights, dark blue for nines, gold for tens. The following link will show you how the equations work into the decanomial:

Geometric Decanomial  Control Sheet  

Geometric Decanomial with Equations

Later the children learn how to put together the  Bead bar Decanomial. 55 Bead bars of each number 1-10 are needed for this activity. With the bead bar layout the representation of the multiplication facts becomes a 3-D manipulative.

 

Bead Bar Decanomial Control Sheet

Decanomial Paper Blank   © 2003

Decanomial - technically the word "decanomial" refers to the alebraic decanomial square - a polynomial having ten terms - just as the trinomial cube refers to three terms and the binomial cube refers to two terms. In more practical language it refers to the multiplication of all ten math tables in a geometric formation.

The Geometric Decanomial is a 3-6 work - often listed with the Sensorial materials - and its layout consists of flat colored squares and rectangles matching the color coding of the bead bars. We made our Geometric Decanomial out of mat board with the unit of 1 cm x 1 cm for the 1x1 flat. Or you could make them out of colored graph paper and laminate. The Sensorial Bead Bar Decanomial is laid out with the colored beads bars. You can use the Paper Decanomial  as an extension to the Bead Bar layout, filling it in much like you use the Dot Game - *filling in the dots* with colored markers as you work through the multiplication tables.

You can work through the Decanomials in three different layouts - the following only refer to the manner in which the bead bars or flat rectangles and squares are laid down, the final layout remains the same:

Vertical layout proceeds with 1x1, 1x2, 1x3, all the way down to 1x10, then up and over to 2x1, and proceeding down through 2x2, 2x3, 2x4 and so on working through the math facts in columns..

Horizontal layout starts with 1x1, 2x1, 3x1, 4x1 and works over to the right 10x1, then down to 1x2, proceeding over to 2x2, 3x2, 4x2 and so on, working through the math facts in rows..

Angular works diagonally from the squares of each number and then back and forth through the Commutative multiplication equations, then on to the next square and the next sets of Commutative equations and so on - working from 1x1, then to 2x1, 1x2, 2x2, and then 3x1, 1x3, 3x2, 2x3, 3x3, and so on proceeding in an L-shaped fashion as in the Geometric Decanomial (below left)..

SUBTRACTION - Math Facts

Subtraction Charts, Tables, and Equations

Subtraction Equations   © 2003

DIVISION - Math Facts

Division Charts, Tables, and Equations

Division Equations   © 2003

4). Abstraction

Dot Game Paper  

Small Bead Frame Paper   

Large Bead Frame Paper  

 

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Last modified: 05/20/08