Unit 5: Mathematics

Unit 5 - Math - Image.jpg

From counting to operations, all math should be “hands on learning” for young children. In this unit, we’re covering the development of number sense and the specific manipulatives that you can use to teach addition, multiplication, subtraction, and division. 


Your Learning Journal / Workbook is both your guide to this week’s topic and a place for your reflections. Next, you’re going to want that checklist of materials and explanations of the activities on hand.



Lesson: Intro To Mathematics

Lesson: What to Invest in

Lesson: The Development of Number Sense

Lesson: PLAY!

Lesson: Establishing Quantity

Lesson: Organizing and Identifying

Lesson: A Brief Introduction to Base 10

Lesson: Reaching Further Toward Abstraction


1. The colored beads we use for counting and the golden beads we use for Base 10 operations in Montessori are an investment you won't regret. Do you currently own them? If not, will you be DIY-ing them or Buying them? Watch my colored bead tutorial here.

2. Don’t want to DIY and can’t afford real golden beads? Do a search online for “base 10 blocks” and you’ll find that you can do everything with those that you can with the golden beads.

3. What songs might we sing with our children to count from 1-10 and backwards again, exploring addition and subtraction orally? One of my favorites is Ten in the Bed. The lyrics are linked here, as well as the book that we read and role played with (stuffed animals or toys on our real bed).

4. How many beads do you need? The answer is “it depends”. It depends on how you will be using them. I like to tell people, “a good, strong handful of each”. For the golden beads, you want to make sure that you have more than 10 of each kind so that you can do some exchanging. More than that will give you more flexibility.

For example, if you plan to do the 45 layout with the golden beads, you will need 45 units, 45 tens, 45 hundreds, and 45 thousands. For homeschoolers, the wooden cubes can be hard to store, and I think the flat or paper versions are a great alternative.

If you’re looking at colored beads, 11-20 of each color will allow you to do quite a bit of Montessori math, but 55 of each color would give you a full deconomial set to take you into elementary math.

Read this article for a full explanation.

5. If you are an especially crafty person and you enjoy taking on projects like this, you might be inspired by this detailed DIY version of the Montessori math beads.

6. Here’s another fantastic example of a golden bead DIY (and she’s an HSR alumni as well!).

7. Read this post by a parent who created a one-to-one correspondence game based on one of her child’s favorite books. Now look in your own stash of books and peruse them with a mathematical mindset. Do you see any way to create a similar game from a book you already own?

8. Read about this extension with the golden beads. Traditional materials can always be combined with Montessori materials to teach. Think about other possibilities, like using a deck of cards.

9. While the pretty mat is 100% optional, watch this video for a very clear example of how to do dynamic addition with the golden beads.

10. If you have a toddler who is not quite three, the small bead frame may be quite far in your future, and it might look at first complicated. However, this Montessori material need not be intimidating to you! To know what to expect, watch this very basic lesson on static addition.

11. When you’re ready to tackle division, there is no better way than with the stamp game! By the time children get to this stage, they are well into abstract thinking, and the stamps give them a way to transition away from the concrete (but not too much!). Read this post and look at the photos for a nice example of how to do a basic division problem with the stamps.

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Aubrey Hargis