One of the concepts that is so foundational and part of the very core of Montessori is teaching abstract math concepts with concrete materials.  I’ll be introducing you to Almost Montessori Unifix Cubes.

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All of my boys are extremely advanced in math (seriously, my 10-year-old is doing Algebra) and I give 100% credit to the way Montessori teaches Math.  This approach to math is so very logical, clear and highly effective. The students internalize math skills with these concrete materials and the progress toward the more abstract concepts. This allows children to thoroughly understand and develop a solid foundation where they master the concept.  They then move to solving problems with paper and pencil while still working with the materials.  Finally, completely abstract, where they are solving problems with paper and pencil without the materials.  That is the goal.

Note, I offer a  word of caution here…  Remember the goal is to teach our children to think abstractly.  It is so easy to fall  in love with the materials and want our children to get the full benefit from using them that we forget to follow our children when they steer right away from the concrete materials to work abstractly.  I wrote a whole post on my love of Montessori materials and how dangerous it is to be in that place.  The goal is for our children is to work abstractly… not to work with the materials.  The materials are tools to get them to abstract thinking. Long as we remember the goal, we will keep the materials in their appropriate place.

Montessori really focused on introducing the patterns that exist in math.  InfoMontessori stated it well:

Arithmetic deals with shape, space, numbers, and their relationships and attributes by the use of numbers and symbols. It is a study of the science of pattern and includes patterns of all kinds, such as numerical patterns, abstract patterns, patterns of shape and motion…. Montessori took the idea that the human has a “mathematical mind” from the French philosopher Pascal. Maria Montessori said that a mathematical mind was “a sort of mind which is built up with exactity.” The mathematical mind tends to estimate, needs to quantify, to see identity, similarity, difference, and patterns, to make order and sequence and to control error.

Using the Unifix cubes is a fantastic way of demonstrating this concept of patterns in math. Multiplication tables, addition and skip counting all require an understanding of and proficiency in patterning.  Below are some wonderful ways to use the Unifix cubes to really demonstrate the patterns.

The first product is a labeled number line. You can certainly see how quickly you could see patterns on a number line 100 numbers long!

The next product is essentially the 100 board but with a grooved grid that will hold the unifix cube in place.   Same concept, showing patterns, would be so visual and easy to see when learning to skip count, or working with evens and odds.  I love how this concept is grasped so quickly with these products.

You could purchase just the package of 100 cubes, which would be less expensive, but you would be unable to make the patterns consistent up through 100… which I think is absolutely necessary to see the patterns. So, even though this is significantly less expensive, it is not really viable.

Finally, here is a box of 500 cubes that gives you more cubes!  You may still need to get more than one set to accomplish the patterns to 100 (depending on what the pattern is). For instance, if you are showing even and odd, that is 50 of each color to get to 100.  Figure out the number of sets you will need to accomplish what you are teaching.

I see these serving as an extension to the 100 board work.  Many of the things our children do with the 100 board, you can do with this set. You could even label the unifix cubes so that you don’t have to use a 100 board at all… the grid could become your 100 board.

Below are some resources, website and blogs, to help you with implementing both the 100 board work and the pattern extensions.

First, I created a 100 chart for you to print and highlight the control chart for whatever skill you are teaching. For instance, if you are teaching skip counting by 3’s, you would highlight the 3, 6, 9, 12, 15…. or if you are teaching even patterns 2, 4, 6, 8 etc.  And if you are like me, you laminate it after you highlight it so you can use it for years 🙂  100 chart

Here is a video of the 100 board extension where she is teaching odd and even patterns!

State of Virginia has a 100 board pattern lesson and even has task cards!  So Montessori!

Here is another traditional school doing a fantastic job of teaching exploration of the 100 board! And this one is introducing multiplication and division patterns…   I love this lesson!

Finally, This lesson is great as well and covers quite a bit of ground!  From addition and subtraction to prime numbers.

I love to provide Strike the Imagination books to encourage our children to want to learn the concept.  So here are a few math pattern books and games to start with.

I hope these Almost Montessori posts are a blessing to you and your homeschool!  If they are, please help us get the word out by sharing them with your friends via your social media sites.

Until next time…..