Intro to Math App Guide

October 07, 2015

Greetings from Montessorium!

We like to think that the joy of learning doesn’t have to be invented, but rather, that it’s just waiting to be discovered. And in this sense, it’s a lifelong journey, not something that begins and ends in our years at school.

What could it be? This spark that inspires us to be curious about our world? It’s different for all of us, and we believe that having the tools to begin the adventure gets us that much closer.

With this in mind, Montessorium presents Intro to Math. The perfect introduction to numbers and the basic principles of mathematics. Feel and trace numbers 0 through 9. Visualize what each number represents with the Red Rods. Feel the satisfaction of counting the perfect amount of counters in Cards and Counters.

We’d love to walk through Intro to Math with you in this brief summary and guide. If you’re interested in learning more about Montessori classroom materials, or join in conversation, send us a note anytime. We’ll always be in touch, and can’t wait to hear from you!

All the best,


Bobby and June George

Intro to Math, by Montessorium

Every activity in Intro to Math is designed to allow your child the choice and freedom to follow their interests. All six activities are available from the very first time you open the app. That means there are no barriers, such as in-app purchases or ‘earning’ a new activity, between your child and the engaging and beautifully designed math materials of the Montessori classroom.

We’d love to explore the materials further, comparing their physical properties in the classroom alongside the activity in the app. Let’s get started!

Sandpaper Numerals

In the Montessori primary classroom, the first activity that typically engages children is the Sandpaper Numerals. So too, in Intro to Math on the iPad or iPhone. Starting as early as age 3, these sandpaper figures set on a green background allow children to trace, feel, and pronounce numbers 0 through 9.

A child first begins by tracing the figure and saying the number. As they become comfortable with the shape and characteristics of each number, they might progress to writing on a chalkboard, which then leads to writing numbers on paper. Addition is soon to follow, but it all starts with the basics.

In the app
Let’s take a look at the tracing activity on the screen:

The best part about the touch screen is that it so closely mimics the Sandpaper Letters in the classroom. Including a sandpaper sound effect, the arrow guides the child in the right direction, much like a teacher would.

Red Rods

The Red Rods are a great way for children to learn the tangible units that correspond to counting. Maria Montessori is all about moving from concrete to abstract, so accordingly, the Red Rods are the physical representation of numbers.

In the classroom, the material is displayed on a shelf, in order, from shortest to longest, or 10 centimeters to 100 centimeters. A child carefully takes all the pieces, one by one, and places them randomly on a floor mat. The child can then place them back in order, appreciating the different lengths. To know whether or not they’ve got them in the right order, the child can take the smallest 10cm piece and move it to the right of the next longest piece. If that piece is then aligned with the piece above it, you know it’s in the right spot!

This visual affirmation means the child doesn’t need confirmation from a parent or teacher, but rather is in charge of their own learning.

Let’s explore the Red Rods further in the app.

Number Rods

The Number Rods differ from the Red Rods only in their color. Instead of a solid red, the Number Rods feature a pattern of red and blue units alternating every 10 cm. The smallest rod is red, the second is red then blue, and so on, all the way to 10! When arranging the pieces on a floor mat, the teacher points out that the red end is always aligned to the left.

The presentation continues with naming the numbers, much like the voiceover in the app. “This is three. Let’s count, 1, 2, 3.”

In the app:

The voiceover demonstrates how to tap and count the units, then gently guides, “Now it’s your turn.” After naming and counting all the rods, it’s time to place them in order. Shake the device to mix up the pieces, and enjoy the playful marimba tones as the pieces pop into place.

Card and Counters

The Cards and Counters material is housed in a rectangular box, including cards with numbers 1-10, and 55 red circular ‘counters’. In the classroom, a child takes this material to a floor mat, arranges the numbers in order, and begins counting by placing the appropriate numbers of red counters beneath the number cards.

A secondary goal of this activity is to provide visual feedback of the difference between even and odd numbers. For this reason, there is a very specific way the counters should be placed, which we can touch on further in the app.

In the app:

Let’s get counting! The first activity is to put the number ‘cards’ in order.

Next, the red counters are displayed in a tray, ready to be called upon. If needed, the gray circle is a reminder of where the counter goes. As we mentioned in the classroom example, odd numbers are identified by the structure of the counters. For three, the odd counter comes beneath the two in a row. In the case of five, counters are arranged with two rows of two, plus a fifth centered below them.

Beyond the App

What are some of the practical things that you can do to help continue the numeracy that was started in the app? While we don’t recommend worksheets, as they primarily focus on rote memorization, we do recommend real world math type activities.

Here’s what we mean:

Let’s say that you’re headed on a road trip. Try some interactive and engaging games that focus on counting. For example, “Let’s identify the numbers on license plates.” Or, perhaps you have a certain exit you need to reach. Turning to your daughter, you ask, “Can you help me find exit number 77? It’ll be coming up soon.” You can also prompt your children with questions, “How many yellow vehicles are there? Let’s count.” This is the type of language we use, helping our students discover the answer for themselves.

“Son, can you help me count the red cards on the trip today?” Or, perhaps when you stop at the rest stop, you can assign your child a task, giving them responsibility and confidence, “Can you count to make sure all of the suitcases are here?” There are so many marvelous chances to engage math on a daily basis.

Let’s switch gears, just a bit, to provide you with some more concrete examples. Picture another often beloved activity: the farmer’s market. Environments like this are the perfect opportunity to put numeracy to work.

Exploring the vendors, you can challenge your child to help. As a matter of fact, you can empower them with a bit of support: “We’re looking for Summer squash. Can you help me find three of them? I hear the radishes are delicious. Should we take five of them home?”

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