I have found Montessori materials the most fantastic way to present math concepts to kids. Once they have learned the hands-on techniques, I never hear children say math is tedious or difficult.
The progression works from sensorial -> concrete -> abstract
- Sensorial : The sensorial stage is designed to help children develop their senses and understand mathematical concepts through exploration and experimentation.
- Concrete: During the concrete stage, children use manipulatives to learn math concepts such as counting, addition, subtraction, multiplication, and division.
- Abstract: Finally, in the abstract stage, children use symbols and numbers to represent mathematical concepts.
Why it works
- Individual lessons
- concrete understanding first, then symbols are introduced
- children can work at their own pace
- we use these math concepts in all areas of education- e.g. fractions when cooking, multiplication when baking etc.
In this post, I am sharing the progression I took my kids through to keep their love for math learning alive.
Ages 0-2(Sensorial)
Spending lots of time in nature and talking to babies and toddlers is the best way to grow their brains in preparation for learning math. First, they notice wind, leaves, trees, ocean waves, and the laws of nature before learning the laws of numbers.
Ages 2-4(Concrete)
Using concrete materials to explain quantities
My kids have enjoyed using this beaded hanger to associate numbers 1-20 with actual quantities. Here’s a video explaining how to introduce the bead hanger to your kids.
Younger kids can even recognize written numbers with associated quantities like pebbles, sticks, spoons, etc.
Ages 4-6(Concrete + Abstract)
At this age, kids can perform Math operations. The best way to start is with golden beads and the bead cabinet.
I like introducing addition, subtraction, multiplication, and division using the golden beads. It is a bit cumbersome but good for their brains to remember the proportions of units, tens, hundreds, and thousands.
This video gives a good demonstration of how to introduce the decimal system to children.
Once they understand what each quantity is called- units, tens, hundreds, and thousands, we introduce them to operations with golden beads.
This lesson shows the association of quantity and symbols in more detail.
With these beads, kids can do all four arithmetic operations. One of my favorites is division, where we physically divide large quantities into smaller buckets. I created a playlist on YouTube that walks through all the operations.
Dynamic addition shows “carry overs”.
Kids can learn further operations using golden beads or the more compact stamp game as they get more advanced.
I printed the worksheets from Montessori Print Shop(https://www.montessoriprintshopusa.com/collections/math-bundles/products/math-operations-command-cards-color-bundle) so my kids could write the answers in the color-coded grids.
They love working with these as they can manually add the stamps and “carry over.” This method is perfect for concretely understanding quantities and then writing the abstract symbols down.
Here’s an example from our home. My daughter chose to work on the stamp game one morning. I quickly printed out the worksheets so she could use them to write down the answers.
The Bead Cabinet(Ages 4+)
It is a beautiful piece of Montessori material in our house. The kids use it for skip-counting and learning their multiplication tables. I do not emphasize memorizing multiplication numbers but understanding their relationship to come up with answers when needed.
For example, we needed to add 8 tbsp of cacao powder to a recipe while baking. Each tbsp is 6gm, and we were using a scale. To derive the total quantity, I encouraged my 7-year-old to calculate what 6×8 is.
With beads, she understands that 6×2 = 12
Then 12×2 = 24
Then 24×2 = 48
Getting the answer this way means she can use the knowledge to derive any multiplication numbers instead of memorizing them.
I purchased my bead cabinet and all the materials from Nienhuis Montessori. It was quite an investment, but I know that the kids will use it for years to come.
This blog post about The Bead Cabinet and How to Grow Your Child’s Number Sense At Home does a great job explaining the power of the bead cabinet.
Ages 6+
Montessori concepts can be taken further into advanced concepts like algebra.
Here is an example of a number line- sidewalk chalk integers. The teachers demonstrate walking on a number line with positive and negative integers. Creating this line in a physical space can give a clear understanding of how operations between signed integers work.
I love that this is a Math activity that can take the kiddos outside, and they can move their bodies to take a break, too.
This example shows using different colored wooden pegs and putting them on the number line to find the answers.
I found these exercises to be part of a course I took at Trillium Montessori. Here is the link for the course. It was affordable, and I immensely enjoyed it.
