 # How to Teach Numbers and Counting in Montessori

The Montessori method is becoming an increasingly popular teaching approach for children. While there are schools that educate their students by using this method, homeschooling parents can use the same strategies and materials to implement the Montessori method at home, too.

Students are taught numbers and counting in the Montessori method by using these strategies: Numerical rods, sandpaper numbers, numerical rods with number tiles, spindle boxes, cards and counters, colored bead stairs, teens and tens boards, and golden bead materials.

These strategies are extremely effective when used in the proper order and with the correct implementation. Here is how you can use these strategies and materials to teach numbers and counting in the true Montessori way.

## Numerical Rods

The title of “Numerical Rods” might sound a bit deceiving because these rods have no numbers on them. They are first introduced to students to teach them the quantities and names of numbers.

There are ten Numerical Rods. The shortest rod is a pure red rod. The second is a red rod with an equally sized blue rod connected to it. The rods then increase by one-rod length, alternating blue and red to differentiate the sections of that Numerical Rod. The rods will always start with the red section.

Step One:

• With the rods in front of the student, allow the student to order them by their length.
• Emphasize that we always start counting with the red section.
• Point to the first, singular red rod and say “this is one.”
• Point to the second rod and say “this is two.”
• Count the sections of the second rod with the student, the red half being “one” and the blue half being “two.”
• Repeat the introduction of the rod’s name and counting the sections for each rod.

Step Two:

• The Numerical Rods are placed randomly before the student.
• Ask the student to give you a specific rod.
• When the student picks up the rod to give it to you, ask the student to count the sections of it before setting it down before you.
• As the student is setting the rods down in front of you, direct the student to place them in order of 1-10.

Step Three:

• The Numerical Rods are placed randomly before the student.
• You will pick up a rod and ask the student “What is this?”
• The student will count the sections of it and then tell you the rod’s name.
• Repeat this for each rod.

Step Four:

• The Numerical Rods are placed randomly before the student.
• The student will pick a rod and tell you the name.
• Then the student will count the sections to verify they got it right.
• Repeat this for each rod.

Step Five:

• The Numerical Rods are placed in order before the student.
• You will point to a rod and ask the student for its name, then the student will count to verify it.
• Repeat this for each rod.

## Sandpaper Numbers

The Montessori Sandpaper Numbers are palm-sized tablets with numbers written on them in sandpaper. They are used to connect the names of numbers to their written symbol.

Step One:

• Place tablets “1” and “2” in front of the student.
• Point to the “1” tablet and say, “this is how we write one.”
• Trace with two of your fingers the written “1” while saying “this is one.”
• Have the student repeat your actions by tracing the number and saying “this is one.”
• Repeat this process for each tablet, displaying only two at a time.

Step Two:

• The Sandpaper Numbers are placed randomly before the student.
• Ask the student to give you a specific number.
• As the student sets the numbers down in front of you, direct the student to place them in order of 1-9.

Step Three:

• The Sandpaper Numbers are placed randomly before the student.
• You will pick up a tablet and ask the student “What is this?”
• The student will say the name of the number.
• Repeat this for each tablet.

Step Four:

• The Sandpaper Numbers are placed randomly before the student.
• The student will point at a tablet and tell you the name.
• Repeat this for each tablet.
• Then, have the students put the tablets in order of 1-9.

Step Five:

• The Sandpaper Numbers are placed in order before the student.
• You will point to a tablet and ask the student for its name.
• Repeat this for each tablet.

## Numerical Rods with Number Tiles

Now that the student knows the written symbol for each number, the student will match a Number Tile with a written number to the corresponding Numerical Rod.

Have the students practice matching the Number Tile to the Numerical Rod with the rods in order and randomly placed to ensure the student’s understanding of numbers.

## Spindle Boxes

The Montessori Spindle Boxes are used to clarify that each written symbol represents a specific quantity of separate objects. This prepares the student for the ideas of addition and subtraction. They will also learn about zero and its written symbol.

Spindle Boxes are two boxes, identical in having five compartments. Each compartment has a symbol written at the back of it. The first box’s compartments are 0-4 and the second box’s are 5-9 (all in order). There are also 45 spindles and 8 ribbons/bands.

Activity:

• Have the student place the two boxes next to each other with 0-5 on the left side.
• Point out the compartments and the written numbers 1-9.
• As you point to each written number, have the student say the number’s name.
• Tell the student “This will tell us how many spindles to put in the box.”
• Point to the compartment with “1” and say “this box needs one spindle.” Have the student place one spindle in that compartment.
• Do that again for the second compartment and have the student count the spindles as they place them in the box.
• Repeat this for the first box (0-4).
• Then have the student place the remaining spindles in the second box (5-9) on their own.
• Once all of the spindles are placed, point to the compartment with a “0.”
• Tell the student “This is zero. Zero means nothing. That is why there are no spindles in this spot.”
• Ask the student to take out the spindles from the second compartment.
• As the student takes out the spindles, have them count each one before tying the ribbon or band around the two spindles.
• Then have the student place the bundled spindles back in their compartment.
• Repeat this for each compartment.

Clean Up:

• Ask the student to place the spindle for the first compartment back into its original container.
• Then ask the student to take out each compartment’s bundled spindles (one compartment at a time) and untie the spindles.
• Have the student place each spindle back into the original container, counting the spindles as each is put away.
• When all the spindles are put away, ask the student why there were no spindles in the “0” compartment.
• Put the boxes away.

## Cards and Counters

Montessori Cards and Counters further instill the student’s understanding of connecting a quantity to a number and what that number’s symbol is. This strategy also introduces which numbers are even and odd.

The cards are cut out numbers and the counters are small chips to represent the quantity of each number.

Step One:

• Ask the students to help you arrange the Cards in order and identify each number’s name.
• Then tell the student that we are going to put the quantities under each number using the Counters.
• Point at each number and ask “how many Counters are needed here?” The student will answer the number needed and then have the student place that many Counters under the number, counting as they put each one down.
• Have the student arrange the Counters in columns of two under each number.

Step Two:

Once all the Counters are placed, ask the student which numbers have Counters in pairs and which have a Counter in its own row. Then teach the student that numbers with pairs are even numbers and the ones that don’t have partners are odds. Ask the student to point out the even numbers, then the odd numbers. Then have the student separate the even numbers from the odds.

The Colored Bead Stairs are yet another strategy to visually show the relationship between written numbers, their names, and their quantities. Additionally, they can be used to introduce your student to the concept of “teen” numbers (11-19).

Colored Bead Stairs are beads that are linked together to represent numbers 1-10. When they are stacked vertically, they look like stairs or a pyramid. To teach teens, you need to have multiple of the “10” strands.

Step One:

• Place Number Cards in order on one side and the Colored Bead Stair in order on the other side.
• Have the student separate each layer of the bead stair to match the correct number of beads to the right Number Card.
• Ask the student to count each bead as they do so.
• When the student gets to ten, make a note that this is the special “10” bar.

Step Two:

This is for introducing the student to teens.

• Place the Colored Bead Stair, a pile of “10” strands, and Number Cards in front of the student.
• Have the student place one of the “10” strands next to the “10” Number Card.
• Then, ask the student to take the first strand from the Colored Bead Stair (“1” strand) and place it next to the “10” strand.
• Count each of the beads up to 10 and then say “and one more is eleven.”
• Place the “1” card on top of the “10” card to cover up the “0” and make “11.”
• Then do this process with each of the Colored Bead Stair strands to teach the student 11-19.
• Have the student practice arranging 11-19 in order and counting the beads for each number.

## Teens and Tens Boards

The Montessori Teens and Tens Boards are two boards divided into five compartments each (like the Spindle Boxes). Nine of the compartments have “10” written on them. In addition, there are sets of cards representing 1-9.

Step One:

• Place the two boards in a vertical line in front of the student.
• Randomly place the Number Cards next to the boards.
• Point to the first “10” and ask the student “what is this?”
• After stating they state ten, place the “1” card on top of the “0” to make “11.”
• Tell the student “this is eleven.”
• Repeat this with the following slots to make 11-19.
• When all of the numbers are placed, point at each number in random order and ask the student to state the name.

Step Two:

• Ask the student to use the board and cards to make 11-19 on their own.
• Then remove the cards and randomly ask the student to make a specific number (still 11-19).
• Have the student put 11-19 back in order and then count all of the numbers in order and backward.

The Golden Bead Materials are sets of individual golden beads, bars of ten beads, squares of 100, and cubes of 1000. This strategy is to help the student learn higher numbers and understand places.

• Place down a mat split into four sections.
• In the right-most section, have the student place individual beads representing 1-9 vertically (with one being at the top).
• Then when you reach 9, ask the student what comes next.
• Tell the student that we need to get a “10” bar instead of ten individual beads and that we need to move to a new place.
• Have the student place the “10” bar at the top of the inner-right section.
• Then, horizontally in line with the individual units the student made, have the student place the same amount of “10” bars going vertically down their new section. This represents 10-90.
• When you reach 90, ask the student what comes next.
• Tell the student that we need to get a hundred square instead of ten “10” bars and that we need to move to a new place.
• Have the student repeat the same process with the hundred squares in the inner-left section.
• When the student reaches 900, ask the student what comes next.
• Tell the student that we need to get a thousand cube instead of ten hundred squares and that we need to move to a new place.
• Repeat the same process with the thousand cubes.