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The Elegant Eight

The Elegant Eight

Mathematics Manipulatives and Ancillaries

for a MathStrongLab

in a school, community center, or home-schooling home

(revised 07-07-2008)


Suggested by Fran Endicott Armstrong, Ph.D.


These materials are the basic sets of mathematics manipulatives and related ancillaries suggested by Fran Endicott Armstrong, Ph.D. that she would use to set up a MathStrongLab to deal with the following areas of mathematics:


Arithmetic operations (i.e., addition, subtraction, multiplication, and division  of)

Whole numbers (Cuisenaire Rods®, Pegboards, Base 10 Blocks, EquaBeam® Balance)

Fractions (Everything’s Coming Up Fractions with Cuisenaire® Rods

Fractions with Pattern Blocks)

          Decimals (Base 10 Blocks)

          Integers (i.e., the whole numbers and their opposites or negatives)

                 (Eli's regular and magic peanuts)


Basic Percent Concepts (Dr. Fran’s Pegboard Book:  Percent-Common Fraction-Decimal Relationships)


Perimeter, area, volume, and surface area (From Here to There with Cuisenaire Rods.  

This book also features as a bonus a delightful lead-in to the use of a variable in algebra.)


               Basic Algebra (Hands-On Equations® and Algebra Lab Gear®)


               Combinatorics (Cuisenaire Rods®, Pegboards, Pattern Blocks, 

                                           Dr. Fran’s Combinatorics Book)


After one becomes comfortable and competent with the following, one might want to expand further with additional ancillaries or acquire additional sets of manipulatives for further development of mathematics subjects such as geometry, probability, and statistics.


1.)     Cuisenaire® Rods



          #4212AQA         Six-Trays Pack of Cuisenaire Rods                            $ 49.95

       74 Plastic Rods                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    


          #4211QA            Cuisenaire Rods for the Overhead                             $   7.95

       60 Plastic Rods                                                             


          #020310QA        Cuisenaire Rods Template                                           $   4.50


  #40453                Idea Book for Cuisenaire® Rods--Primary Level             $ 12.95


  #40467                Idea Book for Cuisenaire® Rods--Intermediate Level       $ 12.95


  #030030              Cuisenaire Rods Alphabet Book                                        $  9.95

       by Maria Rizzo Marolda                                  


   #40715                Addition & Subtraction with Cuisenaire® Rods             $ 22.95

       by Patricia S. Davidson                                              


  #030040              Picture Puzzles with Cuisenaire® Rods                           $ 10.95

       by Patricia S. Davidson and Jeffrey Sellon      


  #4286                  Multiplication and Division with Rod Patterns and Graph Paper 

                              by Patricia S. Davidson and Robert E. Willcutt         $   9.95

  #4285                  From Here to There with Cuisenaire® Rods:  Area, Perimeter and Volume 

       by Patricia S. Davidson and Robert E. Willcutt        $ 10.95          

       (This book provides a bonus with a lovely lead-in to the use of a variable in                        

         algebra on pp. 32 - 39.)

  #4270                  Everything’s Coming Up Fractions with Cuisenaire® Rods

       by John Bradford                                                            $  10.95

I suggest using the same Corner Square with Cuisenaire® Rods, Base Ten Blocks, and Algebra Lab Gear®.


Trafford Publishing (www.trafford.com)

                        Dr. Fran’s Combinatorics Book

        by Fran Endicott Armstrong, Ph.D.        

        Available soon           


SRA/McGraw-Hill (Creative Publications)

#0322062802          Corner Pieces, Set of 10                                                $  6.30

        (use 1 corner piece with each set of Algebra Lab Gear 

        and each set of Cuisenaire Rods                                                            


For very young children, you may want a set of Jumbo Rods which match the colors of Cuisenaire® Rods but with a ratio in volume of 8 to 1.  The smallest rod is 2 cm cube.  The largest rod is 2 cm x 2 cm x 20 cm.  Keep in mind, however, that the ancillaries fit the regular rods.



#010110              Jumbo Cuisenaire Rods Intro Set, Set of 56                   $  24.95


#4213QA Jumbo Cuisenaire® Rods Class Demo Set. 

     Set of 154 Jumbo Rods.                                                     $  64.95


For enrichment, I suggest the following:

#40594                Cuisenaire® Roddles™ Kit                                              $  22.95

                             (includes a set of 74 Cuisenaire® Rods as well as 16 board games and puzzles                             

                             and a 28-page booklet with pre-game activities and post-game questions)    

                             Grades 3 and up 

#4280                  Spatial Problem Solving with Cuisenaire® Rods 

                             by Patricia S. Davidson and Robert E. Willcutt 

     (A book of blackline masters)  Grades 4-8                      $  11.95


         #40251                Rod-Clue Puzzles                                                                 $  13.95

                                     by Evelyn B. Christensen and Susan E. Christensen

     165 intriguing puzzles to stimulate critical-thinking skills

     Grades 5 and up                                               


2.)              Numerical Balance Scale

         This is very useful for student explorations concerning addition and multiplication up to                     sums and products of 12 (if using the EquaBeam® Balance whose arms go out to 12) after students have developed some conceptual understanding of these arithmetic operations with a manipulatives such as Cuisenaire Rods and Pegboards.

The number balance provides an opportunity for experimenting with the sums and products, drill and practice, and a powerful way of thinking about equations which also leads nicely to Hands-On Equations®.



        #9215                  EquaBeam® Balance                                                          $  29.95


        Trafford Publications (Can be ordered on www.trafford.com)

ISBN 1-4120-7549-1              

        Dr. Fran’s Balance Book, revised                   Available soon
        by Fran Endicott Armstrong, Ph.D.                 
        Dr. Fran’s Balance Book:  Multiplication     Available soon
        by Fran Endicott Armstrong, Ph.D.                                                                      

3.)              Pegboards                                                                                      

         One set for a student consists of two 10 hole by 10 hole plastic pegboards 

         and 200 beaded pegs (33 or 34 of each of six colors) in a plastic container.


                 School Specialty Publications

                 1-56451-832-9     Beaded Pegs, 300, 6 colors                                $   8.99


                 1-56451-825-6     Plastic 100-hole Pegboard 6”x6”                      $   2.99


         Five Pegboard Sets each consisting of 2 pegboards and 35 pegs of each of the six colors 

         can be made from 10 Pegboards plus 7 sets of 300 Beaded Pegs. 


         For young children (i.e., pre-Kindergarten and Kindergarten and maybe Grade 1) the             following is very useful.  The Jumbo Pegs Set is also useful for introducing multiplication since the pegs stack onto each other.


                     School Specialty Publications

          1-56451-853-1     Jumbo Easy Grip® Pegs and Playpad Set      $  12.99

              (30 jumbo pegs and one 25-hole Playpad™ Pegboard)


          Trafford Publishing (www.trafford.com) Available soon         

          Dr. Fran’s Pegboard Book: Designs, Counting, and Inequalities                          

  Dr. Fran’s Pegboard Book: Addition and Subtraction

  Dr. Fran’s Pegboard Book: Multiplication and Division                                                 

  Dr. Fran’s Pegboard Book: Exponents-Powers & Roots

  Dr. Fran’s Pegboard Book: Percent-Common Fraction-Decimal Relationships

  Dr. Fran’s Pegboard Book: Patterns, Formulas, and Series

        all by Fran Endicott Armstrong, Ph.D.        


4.)              Base Ten Blocks                  


    #40971                Interlox Base Ten Units, Set of 100                             $   2.95

                                (centimetre cubes)


    #40972                Interlox Base Ten Rods, Set of 50                      $   8.95

                                (decimetre long)


    #40973                Interlox Base Ten Flats, Set of 10                      $   9.95

                                (decimetre square or flat)


    #40974                Interlox Base Ten Cube, Each                           $   4.95

                                (decimetre cube)


To economize, you may want to purchase cardboard decimetre cubes.

#5561                  Cardboard Thousands Cubes, Set of 10          $   9.95


I suggest sets consisting of 30 centimetre cubes (in the ETA/Cuisenaire catalog these are called “Base Ten Units”), 20 decimetre longs (in catalog these are called “Base Ten Rods”), 10 flats, and 1 decimetre cube (in catalog this is called a “Base Ten Cube”), and one corner square.  I also include in the sets 20 centimetre squares (one millimetre thick which are listed in the Wright Group/McGraw Hill catalog as  “Thousandths Chips”).  Remember, you will need some spares of each block.


        SRA (Creative Publications)

        #0322055555      Thousandth Chips, Bag of 500                                  $  14.95


I suggest using the same Corner Square with Cuisenaire® Rods,

Base Ten Blocks, and Algebra Lab Gear®.


SRA (Creative Publications)

#0322062802      Corner Pieces, Set of 10                                               $    6.30


SRA (Creative Publications)

#0884887669      Understanding Place Value: Addition & Subtraction binder

     by Micaelia Randolph Brummett and Linda Holden Charles            

     [12-09-2003 “out of print”]                                         

#0884887677      Understanding Place Value: Multiplication & Division binder by Linda Holden Charles and Micaelia Randolph Brummett                  [12-09-2003 “out of print”]  

#0884889599      The Decimal Factory Activity Binder

by Linda Holden Charles and Micaelia Randolph Brummett                                                             $  36.75


To prepare middle school students or older who have not previously used base ten blocks to use them to develop decimal concepts, I suggest the following to help the students learn the relationships among the various base ten blocks.


Trafford Publishing

Dr. Fran’s Decimal StartUp    

by Fran Endicott Armstrong, Ph.D.        

Available soon           



5.)              Pattern Blocks 

A bucket of Pattern Blocks consists of 25 yellow hexagons, 25 orange squares, 50 red trapezoids, 50 green triangles, 50 blue rhombuses, and 50 tan rhombuses.



          #4414                  Pattern Blocks, Plastic (250 blocks)                            $  17.95


          #4446                  Overhead Pattern Blocks (set of 49)                 $   4.95


          Stokes Publishing Company                            

#200                    Geo-Graph Template                                         $   3.95

(30 or more @ $2.00 each)



IN034809             Investigating with Pattern Blocks

by Marcia Miller and Martin Lee                         $ 10.95


SRA (Creative Publications)

          #0884880508      Fractions with Pattern Blocks

by Mathew E. Zullie                                          $  22.26


A bucket of Pattern Blocks is adequate to share among four students.  However, it is unwieldy to have four students share and also to count the blocks before and after use.  Therefore, I suggest you split each bucket of Pattern Blocks into four individual student sets (6 Yellow Hexagons, 6 Orange Squares, 12 Red Trapezoids, 12 Green Triangles, 12 Blue Rhombuses, and 12 White Rhombuses) and put them into containers of the appropriate size preferably along with the templates.  I suggest one template per student or, if the budget is tight, sharing a template between two students.  Put the extra Pattern Blocks into the Spares Container.



6.)              Eli’s Magic and Regular Peanuts                                          


Trafford Publishing

Eli's Quandary--Teaching Arithmetic Operations on Integers (Whole Numbers and their Opposites)

(includes directions for making the peanuts manipulatives using plastic bingo chips)               

by Fran Endicott Armstrong, Ph.D.        

Available soon           


Bingo Chips (24 chips per individual student set)


Zip type plastic bags (one bag per individual student set)


7.)        Hands-On Equations® Learning System                                  


          Borenson and Associates

          C-1010                 Teacher’s demonstration balance and game pieces, ten

student kits, classroom worksheet reproduction rights

                                                                             $ 189.95 


C-1020                 Teacher’s demonstration balance and game pieces, twenty student kits, classroom worksheet reproduction rights                                                              $ 249.95


C-1030                 Teacher’s demonstration balance and game pieces, thirty student kits, classroom worksheet reproduction rights                                                                  $ 309.95


C-1040                 Teacher’s demonstration balance and game pieces, forty student kits, classroom worksheet reproduction rights.                                                                 $ 369.95


Notice that the price of each student kit when bought in these class sets is $6.00 each and the price of the teacher’s demonstration balance and game pieces and classroom worksheet reproduction rights in these class sets is $129.95.  If you buy a class set (of 10 or 20 or 30 or 40), you may at that time or later purchase additional students kits @ $6.50.


8.)              Algebra Lab Gear®


SRA (Creative Manipulatives)

#1561076872      Algebra Lab Gear® Complete Set (includes a Student Pair Set and 3-D Algebra Lab Gear)           $  63.72


#33341                Algebra Lab Gear® Small Group Set (consists of 3 Student Pair Sets)                                        $ 139.96


#1561072567      Algebra Lab Gear® for the Overhead Projector $  44.08


#0884889637      The Algebra Lab®--Middle School:  Exploring Algebra Concepts with Manipulatives                                   $  57.40


#31424                The Algebra Lab® Lab Gear Activities for Algebra I

                                                                                                         $  57.40


#0322062802      Corner Pieces, Set of 10                                               $   8.84



Additional Materials

1.)              Crayola Classic Colors Washable  (8 thick) markers                           $   3.49


2.)              Highlighters  (Note:  a green highlighter can be used to match the

green [G = 3W] Cuisenaire® rod and the green Crayola marker can be used to match the dark green [D=6W] Cuisenaire® rod.)              $    .99


Use one container for a set of 8 Crayola markers plus one green highlighter.  For easy access, when the students use the markers have them put 5 markers on the lid set next to the container and leave 4 markers in the container.


Highlighters of various colors


3.)              Guess My Rule Puzzles for which pp. 22-34 & 37-39 provide a good introduction to Functions when used appropriately.          



#4296                  Wollygoggles and Other Creatures

by Thomas C. O’Brien                                       $   8.95


4.)              For metric measurement and geometry activities, in addition to From    

         Here to There with Cuisenaire® Rods, I suggest the following:




#4710                  Patty Paper Geometry Set by Michael Serra   $  34.95

Guided and open-ended investigations encourage students to explore and discover geometry using the square pieces of waxed Patty Paper that butchers use to layer hamburgers in a stack.  Teacher Resource Book and 80-page Student Workbook, and 1000 sheets of Patty Paper are included.  Grades 6-10


          #9387                  Power Solids, Set of 12                                                $  14.95


          #029079              Investigating with Power Solids

by Erica Dakin Voolich                                               $  11.95


#522                    Multicolor 150 cm tape measure, Set of 10

(Each decimeter is banded in a different color for easier reading and the salience of a decimeter.)  

$  18.95


          #4603                  Liter Volume Cube                                            $    7.95     

          #596                    Indoor/Outdoor Classroom Thermometer

                                      (both Fahrenheit and Celsius scales)                $    6.95

Buy two—one for inside your classroom and

one for outdoors.


          #578                    Overhead Demonstration Thermometer                   $    5.50


          SAFE-T™ Classroom Products, Inc.


          #33060                Flat Flexible SAFE-T Ruler™                           $    .49

                                      30 or more @ $ .43 each


          #15743                SAFE-T™ CIRCLE PERFECT™ COMPASS   $   1.85

                             30 or more at $ 1.65 each


#25773                VIEW-THRU™ SAFE-T PLASTIC® small protractor

(4-inch diameter)                                                         $    .35

36 or more @ $ .31 each



1.)         Mancala


#4951                  Mancala set includes a folding, 18” x 6” wood board, stones, and instruction                                                 $  13.95


2.)     ETA/Cuisenaire 24® Games                                                 

#2080                  “24” Add/Subtract--Primer                                       $  19.95


#2081                  “24” Multiply/Divide--Primer                        $  19.95


#2083                  “24” Single Digits                                            $  19.95


#2082                  “24” Factors—Multiply/Divide                       $  19.95


#2084                  “24” Double Digits                                           $  19.95


#40478                “24” Integers                                                     $  19.95


#42164                “24” Fractions & Decimals                               $  19.95


#2087                  “24” Algebra Readiness                                   $  19.95


#2085                  “24” Variables—Single/Double Digits           $  19.95


3.)        #5615A                Mastermind®                                                     $  15.95


4.)         #1540                  Tangoes                                                               $  11.95


5.)                                     Battleship



1.)         ETA/Cuisenaire

#40277                2-Book Set Mathematicians Are People, Too              $  35.90                or


          #500217              Mathematicians Are People, Too Volume 1                $  15.50


          #500218              Mathematicians Are People, Too Volume 2                $  15.50


2.)     Stokes Publishing Company

          #101                    Notable Numbers

by Williams T. Stokes                                                $   9.95




Borenson and Associates                         ETA/Cuisenaire

P.O. Box 3328                                           500 Greenview Court

Allentown, PA  18106                              Vernon Hills, IL  60061-1862

Phone:        800.993.6284                          Phone:        800.445.5985

Fax:            610.398.7863                          Fax:            800.ETA.9326


School Specialty Publications                  Creative Publications

3195 Wilson Drive, NW                          Wright Group/McGraw-Hill

Grand Rapids, MI  49544                        12600 Deerfield Parkway, Suite 425

Phone:        800.253.5469                          Alpharetta, GA 30004

Fax:            800.543.2690                          Phone:        888-205-0444

                                                                   Fax:            888-205-0916


SAFE-T Classroom Products, Inc.        Stokes Publishing Company        

PO Box 26                                                 1292 Reamwood Avenue

Bloomingdale  IL  60108                         Sunnyvale  CA  94089

Phone:        630.627.4757                         Phone:        800.550.5254

                                                                   Fax:            408.541.9149


EAI                                                             Trafford Publishing

567 Commerce Street                               www.trafford.com

PO Box 644                                                Phone:        1-888-232-4444  

Franklin Lakes  NJ  07417-0644

Phone:        800.770.8010

Fax:            201-891.5689