HOTM Blog Hop- Montessori: Mathematics

Welcome to 10 Days of Homeschooling Montessori, Day 5!
(And a giveaway!)

Today completes our first week of Montessori and we will explore the math materials and methods that have such a wonderful reputation for creating solid understanding of mathematical principles.
To find the previous posts:
*Be sure to scroll to the end of this post for a giveaway, and then come back next week for another giveaway on 
Friday, February 18th!*

“By age four, the child is ready for the language of mathematics. A series of preparations have been made. First the child has established internal order. Second, the child has developed precise movement. Third, the child has established the work habit. Fourth, the child is able to follow and complete a work cycle. Fifth, the child has the ability to concentrate. Sixth, the child has learned to follow a process. Seventh, the child has used symbols. All of this previous development has brought the child to a maturity of mind and a readiness of work.” 

This topic is so huge, one post cannot do it justice.  But I’ll try to outline the basics and give you a jumping off point for future exploration.  Here we go!
Montessori math is based upon a very clear progression of concrete understanding by the child.  Many of the materials in the Sensory area begin preparing the preschooler for mathematics by the presence of the number ten: ten cubes in the pink tower, ten cylinders in each set of knobless cylinders, ten red rods, etc.  Our whole number system is based on the number ten, so presenting it in the environment before a child even understands why allows the familiarity of the concept to sink in long before beginning any kind of formal math.
Bead stair
Ocean Animal Race 
The first thing for a child to learn is one-to-one correspondence, or the idea that, when counting, each item gets its own number.  There are many activities to create which will help to reinforce this concept:
  • Use index cards with the numbers 0-9 and pipe cleaners.  Have your child line up the cards in a row and put the number of pipe cleaners beneath each card.  Make sure you have 45 pipe cleaners exactly.  The child will be able to self-correct- if there are any pipe cleaners left, or he runs out, he will know there was an error. (The numbers 0-9 are all the numbers there are in our decimal system, if you think about it.  Above 9, you move into the “tens” column with a “1″ and a “0″.)
  • Use little terra cotta pots, labeled with a sharpie with the numbers 0-9, and 45 glass beads.
  • Print out a blank Hundred Chart, get a 10-sided die with the numbers 0-9 on it, and 100 buttons.  Have your child roll the die and place the buttons on the chart (in an orderly progression, left to right, top to bottom) and continue until she’s filled up the chart.  Make it a game and have two play at the same time; the one who fills the chart first wins.
  • I’ve always loved these Grid Games.  I laminate them and use a variety of counters.
  • Create a table with 10 squares and give your child a mini stamp and stamp pad.  Label each box of the table from 0-9 and have them stamp the amount in each box.
  • My kids love this Ocean Race game.  They roll a die and cross off one of the numbers that was rolled.  The first number to be rolled ten times, wins.
  • Here are some more counting ideas.
  • Use the Montessori bead stair.
Number rods

Once the child has learned to consistently count well, it’s time to introduce the teen numbers, and the decimal system.  The Montessori bead materials are wonderfully designed and beautiful to look at.  They provide everything needed to learn the decimal system, skip counting, squares, and multiplication tables in a concrete, hands-on way.  You can make the bead materials yourself with pony beads and pipe cleaners.  Make sure, however, that each number is a different color, 1-9.  You can see a post about making the materials with wire and beads, and also see which colors are for which bead number here at Homemade Montessori.

Lessons are designed to identify each step in learning about numbers in a very simple and non-frilly way.  You can see a video example of a teen bead lesson here.

Introducing the decimal system is just a small step further, and a Montessori child who has already been familiar with numbers 0-9 and one-to-one correspondence, is ready to learn that when you have ten of something, you trade the ones in for a ten.  Then when you have ten tens, you trade them in for one hundred, and trade ten hundreds in for one thousand.  The bead materials make this very clear in the way they are created since ten ones wired together is a ten, ten tens wired together is a hundred, etc.  Laid out in this fashion, and with the concrete, hands-on materials, the decimal system is easy for even a 4 or 5 year old to grasp.

Here is a video example of the Montessori Bank Game.   We have some of these materials (ones, tens, hundreds, thousands) but not the exact Montessori materials.  These are a very important addition to your homeschool, so I would suggest having these in your home.  There’s really nothing like being able to manipulate these tangible examples of an abstract concept such as our decimal system.

Once you have worked with your child and he understands the ones, tens, hundreds, and thousands and how they function together to create larger numbers, the next step is addition, and then subtraction.

Fraction insets (I traced them and had my son match them)

Hundred board (I put ten tiles in each little pot to make it easier to complete)

Hundred bead chain with labels

Here are some other math activities:

  • We have this hundred board which you can make yourself using any number of different materials.  It is wonderful for skip counting, ordering numbers, etc.
  • Pattern blocks: make hexagons using triangles, rhombuses, and trapezoids, use these templates, printed and laminated.
  • Fraction insets for exploring parts of a whole.  You can also find plastic ones cheaper here.
  • Number rods for number comparison and adding.
  • I love the book, “Games for Math” by Peggy Kaye.  I find that the games I play with my children go a long way in reinforcing what we are exploring in our Montessori time.  There are many great games for working with the decimal system, for example.
Whew!  I’m pooped!  I know that’s a lot to take in, but more research and reading will help you get more familiar with the wonderful math methods of Montessori education.  You can read a more detailed post about Montessori Math here.

Monday we’ll look at the Language materials and learn about how to use them.


And now for the giveaway!!!






If you’re not going to the HOTM Online Conference, you should be!

I’m giving away one ticket to the conference to a random reader and commenter today.  To enter, simply leave a comment on this post telling me what interests you most about the Montessori Method.  I will draw a name at random on Sunday, February 13th before I go nighty night.


Don’t forget to visit the rest of the blog hop ladies today!

10 days of socialization for mom | The Homeschool Chick
10 days of classical education | Milk and Cookies
10 days of large families | Chocolate on My Cranium
10 days of special needs | Special Needs Homeschooling
10 days of struggling learners | Homeschooling the Chaotic Family
10 days of homeschooling girls | Homegrown Mom
10 days of homeschool enrichment | Confessions of a Homeschooler
10 days of building a spiritual legacy | Mommy Missions
10 days of frugal homeschooling |The Happy Housewife
10 days of Charlotte Mason | Our Journey Westward
10 days of unschooling | Homeschooling Belle
10 days of organization | Confessions of an Organized Homeschool Mom
10 days of getting started | Blog, She Wrote
10 days of homeschooling boys | The Tie That Binds Us
10 days of homeschooling Montessori |  Fruit in Season
10 days of preschool |  Delightful Learning