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The Montessori Dot Game: Purpose and Presentation

Montessori math is presented to children in the order of concrete to abstract. The math materials start with manipulatives and move gradually toward having children work with written numbers only.

The Montessori Dot Game is typically the first math material a child works with that works toward abstraction without the use of manipulatives (beads, stamps, skittles, ect.).

In this article, you will learn what the Dot Game is, its purpose, and how to introduce it to a child.

image of child playing the Montessori dot game.

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What is the Montessori Dot Game?

The Montessori Dot Game is a math material that consists of a white dry-erase table with columns divided using the Montessori color-coding system for units, 10s, 100s, 1,000s, and 10,000s.

Each column has a grid that contains several rows of 10 squares. There are also 2 rows at the bottom of each category for recording and carrying, as well as a blank column on the right side of the board for housing the equation and sum.

The Dot Game can be used for subtraction and multiplication, however, its primary use is for addition.

During the Dot Game addition activity, the child will be marking dots in the grid, adding the dots in each category, and carrying the remainder to the next category.

The purpose of this material is to introduce children to solving math equations without the use of some of the materials they've been using up to this point, such as the Golden Bead Material.

The Dot Game is introduced to children in their final year of the Montessori primary program, around the age of 5-5.5 years old.

By this time, children have worked extensively with Golden Beads, as well as more abstract materials, like the Stamp Game, and are ready for even further abstraction.

You can purchase the Montessori Dot Game board here, or make your own by downloading this free printable from The Montessori Album and laminating it or placing it in a sheet protector.

If you know you will be getting a lot of use out of this material, purchasing a dry erase board and making the grid yourself is a great option.

For this activity, you will also need fine-tipped dry-erase markers in multiple colors and equation slips with the answer written on the back.

You can use index cards or any other thick cardstock for this, writing out the equations ahead of time.

Below my presentation instructions, I have included a Dot Game demonstration video that I think is a really helpful tool for those new to this material.

Purpose of the Montessori Dot Game

  • introduce dynamic addition without the use of manipulatives

Indirect aims

  • practice with addition

Control of error

  • the answer on the back of the equation slip
  • the adult

Points of interest

  • using different color markers to carry numbers
  • using multiple addends
  • marking the dots

How to present the Montessori Dot Game Addition Lesson

Note: There is no reason to introduce only two addends when first presenting this activity. However, you may find it easier for yourself if you are relatively unfamiliar with the material.

  • Invite the child to help you carry the materials for the Dot Game to the table.
  • Show the child the equation slip(s) and explain to them they will be solving the equation with the Dot Game.
  • Show the child how the board is divided into columns by units, 10's, ect. and introduce the 10,000 column.
  • Explain to the child that the board also has rows: 10 rows for each column and tall rows at the bottom of the board for tallying each column. Explain also that the black area on the right side of the board is for writing the equation.
  • Demonstrate to the child how to write the equation from the chosen slip onto the right side of the board with a black marker.
  • Ask the child to call out the number in the units place of the first addend, then fill in that quantity of dots, from left to right, in the first row of the units column using a black marker.
  • Draw a diagonal line through that number in the right hand column.
  • Continue these steps for each category of the first addend.
  • Tell the child that you will be continuing adding dots to each category and row using the numbers from the second addend.
  • Have the child call out the number in the units place of the second addend, then fill in that quantity of dots, starting after the last dot from the first addend, in the units column.
  • Continue these steps for each category of the second addend.
  • Explain to the child that it's now time to count the dots in each column to find the answer to the equation.
  • Count the dots in the first column. When you get to 10, cross out the 10 dots you just counted and mark a line through those dots. Draw a dot in the next to last row of the units column and explain to the child that this dot represents 10 units.
  • Continue counting the dots in the units column, crossing them out, and replacing each 10 dots with a single dot.
  • When there are less that 10 dots left in the units column, count them and record that number in the last row of the column.
  • Explain to the child that the dots in the next to last row represent 10 units each and they must be carried to the tens column.
  • Ask the child to use the blue marker to write that number in the second to last row of the tens column. (For Example: if there is one dot in the box, the child will write the number 1 in the tens box.) Then have them fill in one blue dot next to the last black dot in the tens column.
  • Continue on with this process for each category, using the appropriate color marker for carrying.
  • The numbers in the bottom row will be the sum of the addends.
  • Write the sum below the addends in the right hand column.

Dot Game extension activities

  • Use the Dot Game board for with multiplication equations by having the child mark the number of dots in the multiplicand the number of times indicated by the multiplier.

The Montessori Dot Game is an engaging material that really gives children a “leg up” when it comes to understanding math equations.

It's not difficult to introduce to children and it gives them an opportunity to finally get to “play” with written numbers just as they've been playing with quantities.

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