## Montessori Number Rods, Sandpaper Numbers, and Spindles are first concrete numeracy materials to introduce math to a toddler or preschooler starting at about two-years-old.

Traditional Montessori math materials are excellent to teach a young child about quantity versus numeral association. In the early Montessori math curriculum, Number Rods are among the very first math materials to introduce to a toddler at around two-and-a-half years of age, followed by Sandpaper Numbers and then by Spindles. With the help of these concrete materials, a child learns numeracy through hands-on lessons rather than abstractly.

After a child is familiar with SENSORIAL Red Rods, you would start with a MATH curriculum, by introducing the Number Rods (which have red and blue segments). During this lesson, we are combining Numbers Rods with number cards, spindles from the Spindle Box, and Sandpaper Numbers.

Adrian has been counting till ten in two languages since about at 27 months, however, I realized that he memorized the number sequence abstractly (like we recite a heart-learned poem). ROTE counting is very different from RATIONAL counting. Thus, we need to work on number recognition and quantity association, because when I would ask him to show me the numeral (“Where is number 2?”), he would get confused. So, it was time for Numbers Rods (also called Montessori Numerical Rods) ~ learning that one is small and ten is big!

## Montessori NUMBER RODS

### EARLY MATH PRESENTATION

Toddlers need gross-motor stimulation, so position the Rods stand in the other room to offer a child an opportunity for movement. Ask a toddler to start bringing rods one by one starting with the smallest unit “1” (limiting to 3 rods per presentation.) Start with a Montessori Three Period Lesson.

#### Montessori 3 Three Period Lesson:

1. (P1) “This is 1, this is 2, ….3” – introducing the quantity, actual rods (for example, for the “two rod” you can take a single unit rod and show 2 parts … we are just making 1 bigger)
2. (P2) “Will you show me 1? Will you show me 2? … 3? “
3. (P3) “What is this?

*If a child makes a mistake, rather than correcting, reiterate the lesson. For example, if, to your question: “Will you show me 2?” the child points to 1, you may proceed by saying: “This is 1, This is 2. Will you show me 2?”

For more, read here a post on Montessori 3🅿️🌠 Three Period Lesson in Action (using First Phonetical Set: s m a t).

## NUMBERS RODS Extensions

Once a child very concretely understands that rods have a different numerical value simply by feeling the difference in size and weight, you can add an extension to this lesson by using number cards. By integrating number cards, a child will be able to associate quantity (holding actual rods) to an abstract concept of numbers/numerals (symbols we chose to represent the actual quantity). Here, the 1st Period would have a slight variation:

1.  (P1) This is 1 (lay an actual rod), and This says 1 (show a numeral card)
2. (P2)Will you show me 1?”
3. (3) What is this?”

Adrian is exploring the quantity, as he applies abstract number memorization to practical implementation by counting three spindles.

He then places spindles next to the “3” numeral – a symbol representing a quantity of actual rods he just counted.

Adrian would then find the corresponding numeral amongst the Sandpaper Numbers trace it, and place next to its quantity.

For the 2nd Period,  Will you show me?” Adrian accurately points to all three numbers. However, with the 3rd Period:What is this?” he doesn’t always get it right.

Second Period: “Show me 1” – he finds one and traces it.

## THREE PERIOD LESSON

With a Three Period Lesson, you would generally introduce three numbers at a time, so you would stop at number three. To instill the love of learning, we should end before the child’s attention span starts to wane, or the child becomes tired, overwhelmed, or overstimulated. The next time, you would introduce the next three numbers and so on. When the child is familiar with all numbers rods, you may also show that a larger number rod is made up of smaller units.

By counting the “8-rod” using “1 unit-rod”, he realizes that number 8 is comprised of 8 units!

Having the muscular impression of length really solidifies the concept that 8 is big!

## Montessori RED RODS vs NUMBER RODS

The difference between the Numbers Rods and Red Rods is that the former is a math material (Numbers Rods), while the latter (Red Rods) is a sensorial material. Red rods is a material for teaching length: where the shortest piece is a unit of measurement for all the rest. As such, the second piece is double the first, the third is three times the first, etc., and, whilst the scale of length increases by ten centimeters for each piece, the other dimensions remain constant (i.e., the rods all have the same section). Presentation: show the child how to carry each rod to the mat by holding each rod at the top with one hand and at the bottom with the other in an upright position as to not bump into others (such gives the child a muscular impression of length). The rods should be randomly placed on the mat. Show the child how to build the rods starting with the shortest rod. Then, using your middle and index finger lightly trace along the entire length of the rod. Find the next longest rod. Bring it into position next to and above the previous rod and trace along its length again etc till the stair is entirely built. Pause and admire the stair and then mix up the rods and invite the child to try. Once the child has successfully built the stair, show him how to fit the shortest rod into each successive stair. Put them away starting with the longest first.

## COUNTING OBJECTS on NUMBER RODS

Here is a FUN extension for Number Rods! Find small objects that will fit on each segment and COUNT UP! This lesson is also great to reinforce RATIONAL counting, 1:1 correspondence, and the concept of cardinality. Cardinality is the total number/quantity of items in a set — your last counted manipulative. That is the cardinal number for each rod will be the number displayed on a wooden card.

Here, we are using animal figureens to practice important counting skills! Invite your child to place an animal on each rod’s segment.  One ~ giraffe. Two~ a lion and a lioness. Three ~ deer family. Four ~ gorilla family. Five ~bears: brown, black and a polar bear and their cubs. Six ~ family of cats: black panther, tiger, jaguar, cheetah, and a leopard.  Seven ~ horses.  Eight ~ farm family. Nine ~ birds. Ten ~ forest animals

Tell me and will I forget. Teach me and I will remember. INVOLVE me and I will learn!

Benjamin Franklin

Children learn BEST when they are engaged in what they are doing!  So, to teach them RATIONAL COUNTING, offer them to TOUCH each manipulative as they coun ALOUD, matching each number to the corresponding numeral! That’s 1:1 correspondence in a nutshell! We want a child to match a set of objects to its corresponding numeral and recognize that a number is a symbol we use to represent quantity! Young children often learn “rote counting” without having an understanding of  1:1 correspondence! Children might count till ten just like a heart-learned poem! (That is they memorize the numerical order without really understanding what each quantity means.) To lean RATIONAL counting, they need to learn to associate quantity to numeral! How? PRACTICE, PRACTICE, PRACTICE!

## Rote vs. Rational Counting

The difference between ROTE and RATIONAL counting is that the former is a process of sequentially memorizing number names while the latter is the process of understanding number value. Merely reciting numbers in order, just like a heart-learned-poem, does not indicate the actual mathematical understanding of numbers. Thus, once a child is able to count to 5 or 10, shift focus from making that number bigger to making sure that a child can reliably count a small number of manipulatives and assign that quantitative sum to a numeral. Trust me, 1:1 correspondence is a much better indication of your child’s mathematical mastery than a long list of memorized numbers. And the best part, you can introduce 1:1 correspondence starting at an early age by modeling through hands-on Montessori math materials, real-life manipulative (like counting objects), and hands-on DIYs. Invite your child to TOUCH each object and provide various hands-on invitations to count, by offering play dough, buttons, beans, blocks, Lego pieces, food items, etc. Make sure that experiences are fun and engaging in order to sustain curiosity and develop the love for numbers and math.

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