Teaching First/Second Grade Math Using Montessori – Addition, Subtraction, and Place Value

Elementary Montessori Math graphic

Several of my readers, friends, and fellow homeschoolers have asked me to create a post detailing the Montessori materials that I used with my own children to teach them addition, subtraction, place value, and other early elementary math concepts. I am happy to do that. I love Montessori and it provides such a solid foundation for children to build upon. It works so well because it teaches elementary-age children in the way that their brains are wired to learn at this stage of cognitive development. Too often, in public and private schools, and even at home, we expect our 5-9 year-olds to learn via abstraction. Youngsters at this age are not ready for abstraction. Even when they grasp the concepts well enough to memorize facts and get through their worksheets, they aren’t internalizing those math concepts at a fundamental level. In order to do that, they need concrete, physical objects that relate what they are learning to the real world. This is what Montessori provides.

That having been said, it is easy to get lost in the huge amount of products and lessons that compose Montessori primary education. In this post, I am going to single out what I feel are the MOST helpful materials to teach elementary math to your student. These will work whether you are using the materials full time as your only homeschool “curriculum”, supplementing another curriculum with them, or trying to help your traditionally schooled child to better understand math. Along with each material, I will provide either a step-by-step on how to use it or a video showing someone giving the Montessori lesson that corresponds to the material.

Quantity and Place Value

I am beginning my recommendations with typical 1st grade concepts. I assume (for the sake of this post) that your child has mastered most Kindergarten math. In the case of quantities, I assume that they can count comfortably to 20.

Hundred Board – The hundred board is a great way to teach your kids about place value without having to “teach” them anything. As they complete the hundred board, they will develop an understanding of how our base-ten system works without any further explanation from you. My fourth grader STILL loves to put together the hundred board. However, if you want more activities, there are literally dozens of games you can play using the actual Montessori hundred board material and/or a laminated chart to go with it.

CLICK HERE to Add the Montessori Wooden Hundred Board to Your Amazon Wish List

You may notice that there are quite a few cheaper options for the hundred board floating around on Amazon (the ones with the natural finish on the tiles, rather than white.) I don’t recommend these because the boards are 30% smaller than the standard size and they are too small for little hands. I recommend checking to make sure you are purchasing a full-size board (the sides should be at least 13″.) The one I link to above is full size. (Speaking of links…if you add items to your cart using my handy-dandy links, I may earn a small referral fee that helps me to continue to purchase products for lessons and reviews. This fee comes from Amazon and you don’t pay a penny more for the item.)

CLICK HERE for an Easy Step-By-Step on How to Use the Hundred Board

You can find lots of ideas online for activities using the Hundred Board. Here are a few of my favorites:

  1. Skip Counting – Have your student complete the Hundred Board while skip counting by threes (or fives, or twos, or tens).  They do this by turning all the squares down that don’t appear in the desired sequence. So skip counting by threes, starting at zero, would look like: backside of square (which is blank), backside, 3, backside, backside, 6, etc. Then try skip counting by threes starting at two: backside, 2, backside, backside, 5, backside, etc.
  2. Play “Guess the Number” – You can easily come up with these little riddles yourself, but here’s a fun .pdf to get you started: CLICK HERE for “Guess the Number” for the Hundred Board
  3. Rounding to the Nearest Ten – It is so much easier to teach the concept of rounding numbers when children can actually SEE that 53 is closer to 50 than it is to 60.
  4. Addition and Subtraction of Larger Numbers – I DO NOT recommend using the Hundred Board as the initial means of introducing addition and subtraction to your child. However, once they have used the other materials (listed below) and have a firm handle on what adding and subtracting actually mean, then you can use the hundred board to help them begin adding and subtracting larger numbers without fear. (Hint: begin by asking your child to add or subtract 10 from a certain number…then move to 9 and 11, etc.)

Montessori Golden Bead Material – The absolute best tool I have ever seen for teaching children what place value actually represents is the Montessori Golden Bead material. Unfortunately, the actual Montessori Golden Bead material is ridiculously expensive. If you can find it at a discount, I highly recommend it. Otherwise, you can buy one of the less expensive, plastic base-10 modeling systems and then teach the Golden Bead Lessons using these materials instead.

CLICK HERE to Add the Base 10 System to Your Amazon Wish List

This is a good video showing how to introduce the idea of the Base 10 system to your child:

Once your child understands and can complete the “three periods” of the lesson as described in the video, you can then move on to introducing the numeric symbols that we associate with units, tens, hundreds, and thousands. To do this, we use the Number Place Value Cards.

CLICK HERE to Add the Montessori Wooden Number Cards to Your Amazon Wish List

I love the sturdy feel of the wooden material, and I love that they’ve lasted me 10 years. But if you are looking to save some money, you can also print out number cards and laminate them. Here’s a link to a Free printable version: CLICK HERE to Download Montessori Number Cards

After your child is very comfortable with labeling a unit using the “1” number card, a ten using the “10” number card, and so on, you can progress to having them “assemble” numbers using the Base 10 (or Golden Bead) material. For example, you put together the number 1352 using the Montessori number cards. You then ask your child to gather the Base 10 components that make that number: 1 thousand cube, 3 hundred squares, 5 ten bars, and 2 unit cubes. After this, switch the process. Have your child assemble a number using the material and then have him/her gather the appropriate number cards to make the number that represents the amount they gathered.

The final step is to teach the child to write the actual number themselves. Don’t rush this step. Only move to writing the number when the child is ready.

Addition & Subtraction Facts

You should introduce the concept of addition to your child by using concrete objects. You can literally use anything: beads, coins, apples, toys, etc. Start with two groups of objects and have the child count each group. Then combine the groups and have the child count the combined pile to determine the sum. Once you are sure that your child fully grasps the concept of what it means to add two groups of objects together, you can move to the Montessori Addition Strip Board.

I really can’t say enough good things about this material. Many parents worry because their children are struggling to memorize their addition facts. The addition strip board will teach your child addition facts in a way that doesn’t require drilling or flashcards and in a way that will be retained by your child. It accomplishes this by creating a mental picture for your child of how each fact “looks”…most especially in reference to the number 10. A common fear with parents new to the Montessori method is that their children will not learn their facts “by heart” as long as they continue to use materials to find the answer to math problems. Nothing could be further from the truth. As your child uses the material, they learn through repetition. Soon they discover that they don’t need to use the material for certain facts because they just know the answer. They will naturally “wean” themselves from using the board as they memorize more and more facts.  It is painless for the parent and confidence-building for the child because they are “discovering” addition themselves at their own pace.

Although this Amazon listing describes this product as a “Subtraction Strip Board”, it actually has all the materials that you need to use it for both addition and subtraction. Most of the other options on Amazon do not, so I recommend this particular listing:

CLICK HERE to Add the Montessori Addition and Subtraction Strips Board to Your Amazon Wish List

Here is a great video explaining how to introduce the Montessori addition strip board to your child:

As you are using these materials, it is important to remember that writing the facts down is not a necessary step…especially at first. Also, one thing I like about the Montessori method is that it introduces the proper math grammar (or vocabulary) right from the start. I encourage you to do this with your child as well. Use the word “addend” to denote the two numbers being added together and the word “sum” to describe the answer.

You will introduce subtraction to your child in the same way that you introduced addition: using concrete objects. This is the most “real” way for a child to understand what subtraction actually means. Once you are sure they have internalized this concept, you can move to the next stage of abstraction, which is the Montessori Subtraction Strip Board. If you purchased the strip board that I recommended above, you have all you need to teach subtraction as well using this material.

Here is a video explaining how to teach subtraction using the strip board:

Adding and Subtracting Larger Numbers (Static and Dynamic)

I have one Montessori material that I use for teaching both addition and subtraction of larger numbers…the Montessori Stamp Game. If I could only purchase one Montessori math material, it would be the Stamp Game. Not only does it work wonderfully for teaching both static and dynamic addition and subtraction, but you can also use it when you get to multi-digit multiplication and division in the later grades. It is incredibly versatile and money well spent!

All Montessori lessons use the concept of the “bank” to teach dynamic addition or subtraction. When adding two numbers that amount to more than 9, the child gives 10 of one denomination to the “bank” and gets from the “bank” one of the next higher place value. So, for example, if the child adds 9 + 4, they will exchange 10 green units for 1 blue ten. They then see that the answer is 1 ten and 3 units…or 13. The same procedure is repeated in reverse for subtraction. If the child needs to subtract 9 units from 4 units, they will not have enough. So the child will exchange 1 blue ten for 10 green units. They can then subtract the 9 that they need. The videos below show this technique in action.

I recommend the following stamp game.

CLICK HERE to Add the Montessori Stamp Game to Your Amazon Wish List

This video shows how to use the Stamp Game to teach multi-digit addition, both static and dynamic:

This video shows how to use the Stamp Game to teach multi-digit subtraction, both static and dynamic:

These are the materials that I used with my own children in the elementary grades, and in fact the same materials that I used when I attended Montessori school as a child. They provide students with a firm grasp of addition and subtraction and allow them to not only memorize their facts with true retention but to view math as something that makes sense. If you have any questions, please don’t hesitate to ask in the comments.

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