Tag: Math tutoring

The Taptana / Instructions Part 1

I was so fortunate to study with Rebeca and Mauricio Wild, two of the world’s foremost educators for child-based learning residing in Ecuador. During each of their seminars we worked with math hands-on learning materials, and one of the many materials they showed us was the Taptana, a calculator that is thousands of years old and was developed by the Inca people.
It consists of a wooden board with holes (there must be at least 10 holes) and beads in the Montessori colors. Here it is on the photo:

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As you see on the photo below, each hole and each bead have a specific value:
Each green bead is worth  1
Each blue bead is worth 10
Each red bead is worth 100
Each yellow bead is worth 1,000
Each light blue bead is worth 10,000
Each orange bead is worth 100,000

taptana-w-numbers

Depending on where we place a bead its value changes.
For instance a green bead (worth 1) is worth 1 in the hole labelled 1,
it’s worth 2 in the hole labelled 2,
it’s worth 3 in the hole labelled 3,
it’s worth 4 in the hole labelled 4, and so on.

A blue bead (worth 10) is worth 10 in the hole labelled 10,
it’s worth 20 in the hole labelled 2,
it’s worth 30 in the hole labelled 3,
it’s worth 40 in the hole labelled 4, and so on.

A red bead (worth 100) is worth 100 in the hole labelled 1,
it’s worth 200 in the hole labelled 2,
it’s worth 300 in the hole labelled 3
it’s worth 400 in the hole labelled 4, and so on.

This way it works for each bead…for instance, an orange bead (worth 100,000) is worth 900,000 in the whole labelled 9. I guess you can see where this is going. Can you imagine the possibilities ?

Practice recognizing the value of beads simply by laying various beads on the board. On the photo below which value do you see?

Here’s the value for the left side: 526, 840

What’s the value on the right side? (solution below)
taptana-w-beads-web

Solution: 9741

Math can be fun!…with hands-on learning materials!

Get inspired!! Math teacher, tutors and parents can make lessons way more interesting and accessible with hands-on learning materials. Children love to play and learn with the materials also after the lesson, in self-directed ways.


To see, touch and play with the ‘Times Tables’: The Decanom, developed by Dr.Maria Montessori


Learning decimals with REAL money!!


Deepening understanding for addition with Dr.Montessori’s beautiful Snake Game.


How much is 1000? How long is the pool? Experiencing length and width, and measuring real objects is exiting!

It is my joy to offer math tutoring for 6 to 14 year- old students with hands-on learning materials in Marin/San Francisco. Please write to Carmen@NewLearningCulture.com. References available upon request.

I utilize hands-on materials for addition, subtraction, division, multiplication for whole numbers, decimals and fractions, measuring materials, logic, strategy, pattern-recognition and fine motor development materials in order to give the abstract worlds of math a foundation in the concrete world around us.

Dear Math Tutors and Teachers: I offer consulting to introduce you to materials to help make your lessons experiential, efficient and fun. Contact me for a free introduction at Carmen@NewLearningCulture.com

Best wishes,
Carmen Gamper