Wednesday, October 18, 2023

More Notes from Math Club (x, +, -)

The Montessori manipulatives are wonderful for introducing math concepts but they can also be used remedially with children. Children who need to see and hear the concepts explained in a different way, or who need more practice but with work that feels fresh and interesting, really respond well to the Montessori approach, especially if they learn best by being able to explore the math concepts physically through manipulating materials or benefit from the visual support of the color coding cues for place value.

Here are all of the notes in this series:


While it may seem strange that we went from Place Value and reading big numbers straight into Long Division, long division is actually not all that hard in Montessori!

The Long Division Material makes long division easy to understand, the material is extremely visually enticing to kids, and it is great reinforcement for reading numbers to the millions place. It was a logical next step for us.


Once we hit Session 4, the Math Club students were beginning to feel comfortable with the Montessori hands-on method and color coding, and the concept of working individually on the work that is right for you, checking your work independently, and progressing at your own pace.

They began to set individual goals for what they each wanted to focus on next, and we broke into small groups accordingly. One student wanted to practice long division with decimals, so he did. Two students wanted to explore long multiplication, so they did. One student wanted to work on understanding dynamic addition (with regrouping) and dynamic subtraction (with borrowing), so she did.

Multiplication, addition, and subtraction are good to work on together because they all involve solving the problem by beginning with the digit all the way to the right. This is not true in division, where you solve the problem by beginning with the digit all the way to the left! (Division is also different because you write the answer above the problem instead of below it.)

Here are some notes as to the specific materials they are using for their computation, as well as the order in which I have introduced them:


Long Multiplication


Dynamic Addition


Dynamic Subtraction


There are many other Montessori math materials, and my job is to choose the ones that I think will best serve each individual student.

For each of these operations, children are meant to move to abstraction whenever they are ready. With Montessori students this typically occurs around age 9, but that's not true for everyone, especially people who haven't had math presented to them in a hands-on way and they are learning it all over again.

Children will progress from the manipulatives to pencil & paper once they have fully internalized what is happening with the manipulatives. If they get lost they can imagine the manipluatives and what they would do with them, or go back to them and double check the steps in the problem.

These notes will be ongoing as I work with the Math Club students. After everyone is comfortable with the operations with whole numbers, we will work through the operations with decimals, fractions, and negative numbers. We will also play math games and I'll keep that list up to date as well!


Math Games


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