Montessori math learning is a fun filled hands-on method of learning where concrete materials are used to introduce math concepts.

Once the child understands that a number symbol written on a piece of paper also has a quantitative value, the kid is ready for abstract mathematics. This easy to clean plastic place mat available at Walmart can be used to introduce numbers to your child.

montessori mathematics - introduction to addition - numbers placemat

Without a strong foundation in preschool, the child will find it difficult to visualize when complicated concepts like number bonds, fractions and multiplications are introduced in Primary school.

The following addition lesson can be introduced only after the kid is able to identify numbers from 1 to 10 and she understands that each number is associated with a quantitative value. So when she sees 1 and 10, she knows that 10 points to a larger volume / length / size.

For example,

  1. 2 rectangles kept side by side will be broader than 1
  2. 2 stacked cylinders will be taller than 1
  3. 5 units long strip of paper will be longer than papers that are 4 and 2 units long.

introduction to addition - building blocks

Montessori materials can be bought. In some places, they can get quite expensive. I am a DIY person and it is more fun if you involve your child in making these manipulatives. It will make them eager to learn because they made it themselves.

So lets get started

Introduction to Addition the Montessori way

How do we explain what addition means to a 3 year old?

What is Addition? What happens when two numbers are added? Here is a simple activity to demonstrate this.

Items Needed

  1. Paper / Plastic cups
  2. Scissors
  3. Paper towel roll
  4. Any small item like lego blocks / plastic chips.

introduction to addition - addition funnel

Make two funnels like this and tape them to a wall or door. Make sure you use painter’s tape that will not leave glue residue.

Let your kid add the “+ ” sign and  “= “sign using the sticky tape.

introduction to addition - addition funnel

Demonstrate how plastic chips from two different sources are combined together on the towel.  This is addition. The chips on the towel is the total / Sum.

(Leave it on the wall for a little longer because your little one will want to use this as a slide for her little dolls or blow it as a trumpet) 🙂

introduction to addition - addition funnel

Now we know what happens when two numbers are added. How do we add two numbers? How do we find the total of two numbers. Let us find out.

 Stationary Items Needed

  1. Chart Paper / craft paper preferably in more than one color
  2. Pencil
  3. Scissors
  4. Ruler
  5. Markers

montessori mathematics - introduction to addition -diy math manipulative

Time to draw squares. Our metal ruler is 1 inch wide so we drew 1 inch squares. Allow your kid to draw this. This is a good exercise for their mind. It is also an opportunity to introduce the words – Horizontal lines and Vertical lines if your kid is old enough. Or you can stick with Sleeping lines and Standing lines for now.

montessori mathematics - introduction to addition -diy math manipulative

Then we drew the vertical lines

montessori mathematics - introduction to addition -diy math manipulative

Make sure you choose a paper that is at least 10 squares long.

Now your kid can count the squares and write numbers like this.

montessori mathematics - introduction to addition -diy math manipulative

Then count the remaining squares in each row and add numbers like this.

montessori mathematics - introduction to addition -diy math manipulative

Common Addition terms

  • Total
  • Sum
  • Both
  • Plus
  • Add
  • Join
  • Combine

Demonstrate using this puzzle how to make ten.

9+1 = 8+2 = 7+3 = 6+4 = 10.

We will touch upon this again later. So it is okay of the child does not grasp the concept.

Many different combinations of numbers when added together can have the same Total or Sum.

At this point you may also introduce the various terms used when two numbers are added.

Since we are going to teach them to add two different numbers, I prefer to use two different colors of paper.

montessori mathematics - introduction to addition -diy math manipulative

Now we are ready for some cutting. Knowing how to use scissors is an important motor skill milestone. So if your kid knows how to use one, let her cut the strips of paper like this.

montessori mathematics - introduction to addition -diy math manipulative

Write down a few equations that you want your child to solve. Make sure you don’t push your kid to solve everything in one day. If you make this with thick craft paper, it can be used again and again. Any new concept requires repetition. So if all you can do on day one is till this step, it is still okay. You kid learned how to draw squares and cut strips of paper.

montessori mathematics - introduction to addition -diy math manipulative

Make a base board with 11 by 11 squares. Tape this white sheet to the floor using painters tape if possible.

Before we get started, arrange the strips in random order and ask for help to arrange the strips in proper sequence – Biggest number at the top.

montessori mathematics - introduction to addition -diy math manipulative

Now everything is in order and we are ready to add.

montessori mathematics - introduction to addition -diy math manipulative

Our first equation is 8 + 1 = ?  Let us find out the total now.

Ask your kid to get the strip that is 8 units long and keep it like so.

montessori mathematics - introduction to addition -diy math manipulative

Then identify and place the 1 unit long strip near the other strip.

Now using your finger, point to 9 and teach her how to find the total. Also make her write the answer in the equation. This way we are showing her the connection between the concrete method of adding and the abstract method of addition using equations.

montessori mathematics - introduction to addition -diy math manipulative

More examples – let her play around with more equations.

montessori mathematics - introduction to addition -diy math manipulative

Show how the total is going to be the same irrespective of the order in which the orange and green strips are placed. In the previous example, the orange strip was placed first and in this example, the green strip is placed first. Move them around to demonstrate this.

How to make 10 / Bridging

Bridging to ten or learning to make ten is a math milestone. Start with this random example first and then ask your kid if there is any other way to make 10.

montessori mathematics - introduction to addition -diy math manipulative

Now we are ready with everything in proper sequence.

montessori mathematics - introduction to addition - make 10 / bridging

I added more orange strips because we will need two 5s to make 10.

montessori mathematics - introduction to addition - make 10 / bridging

There are two methods to do this. Arrange all the orange numbers and then add the green numbers or go row by row.

On purpose keep it in the wrong place and make your kid to correct your mistake so she can learn that 7 + 2 != 10. Point to the blank square and ask what went wrong and show how even though there can be many combinations to make 10, 7 + 2 is NOT equal to 10.

You can either move the 2 units long strip and place it near 8 or bring the 1 down to show how 3 numbers can be added to make 10. Your creativity is the limit.

montessori mathematics - introduction to addition - make 10 / bridging

(Yes I finally stopped being lazy and got up and got the tape and taped the paper to the floor)

montessori mathematics - introduction to addition - make 10 / bridging

You can also mention about the concept of adding identical numbers. 5+5=10; 3+3 = 6;  4+4=8 etc

montessori mathematics - introduction to addition - make 10 / bridging

Slowly ease out and let the teacher take over. Give her full control over the items and let her teach Pooh and rainbow dash.  ;-).

Winnie the Pooh by the way is recuperating from a surgery (Thank you Dr. Mcstuffins) hence the band aid. Rainbow dash had to get her hair pleated so her hair does not interfere with learning. Hmmm where have I heard that before?

montessori mathematics - introduction to addition - fun and play

Math lessons progressed to shapes.

Oh BTW that is pretty much how my floor looks like sometimes all the time. There I said it. So fair warning …. in future if you tell me that you want to drop by and I give you that awkward pause, it does not mean that I don’t want to invite you home…..almost lost a friendship because of this. 😀

montessori mathematics - introduction to addition - fun and play

Other Methods to teach Addition

Bridging or Make 10 using rainbow

This is another method to make 10. I made this using MS Paint. You can print this or better yet you can make your kid draw a rainbow to find out all the combinations that make 10.

montessori mathematics - introduction to addition - make 10 / bridging with rainbow

Addition using a deck of cards

Readily available deck of cards can be a very useful time pass activity during travel. Here we explored many ways to make 9.

introduction to addition - deck of cards

Adding identical numbers

Dominoes and playing cards can be used for this.

introduction to addition - add identical numbers

Using dominoes

montessori mathematics - introduction to addition - using dominoes

Adding Zero or nothing = changes nothing

introduction to addition - add zero using dominoes

Add one and the total is the next number

montessori mathematics - introduction to addition - add 1 using dominoes

Using physical items like plastic chips, cookies, logo blocks

This is an opportunity to introduce odd numbers and even numbers. When a chip does not have a partner, it is an odd number.

montessori mathematics - introduction to addition - using plastic chips

Draw shapes and then count and add them

montessori mathematics - introduction to addition - draw and count

Use Tally marks to add

Tally marks are clusters of 5 lines used mostly for score keeping during games. I bet this will be interesting to your kid if she knows skip counting by 5.

montessori mathematics - introduction to addition - tally marks

Last but not the least,

Throwing the dice

Find out how many combinations can make 12

montessori mathematics - introduction to addition - using dice

montessori mathematics - introduction to addition - using dice

It took me many hours to put this article together. I have added tons of pictures and as many activities as possible in this article so you can teach addition easily to your kids. Enjoy. If you like it, please share it with your friends.