Creating a numerical language – Part II

This module is a preparatory guide for understanding decimal structures, or the decimal system. About 25% of children encounter challenges when learning how to tackle vertical addition problems. I promise to write about these essential topic in greater depth. If your child is one of these individuals, this sequence of lessons could be especially beneficial.

This tutorial is a continuation of the topics discussed in the previous post, “Developing a Number System – Part I.”

Resist the urge to instruct the kids on how to tackle the problems. Encourage them to embrace the struggle. The resolution of these problems need not be formulaic. Errors could play a significant role in their learning journey. Be careful not to deprive them of the joy of unearthing solutions on their own.

Let’s dive in!

We start by borrowing the representation of 10 (X) and 1 (I) from the Roman numeral system for all our exercises.

Phase 1 begins with basic addition problems, such as XXXII + XXXXI (32 + 41).

In Phase 2, we transition to subtraction problems, for instance, XXXII – XXI (32 – 21).

Phase 3 includes addition problems where there are more than ten units of one, like XXIIIIIII + XXXIIIIII (13 units of one).

During Phase 4, we tackle subtraction problems that necessitate breaking down ten, such as XXXXII – XXIIIIII.

Step 5 gets us closer to the decimal system. For example, 32 would be represented as 3X 2I, which transforms XXXII + XXXXI into 3X 2I + 2X 4I.

Lastly, in Step 6, we make the triumphant return to the decimal system. The previous example, 3X 2I + 2X 4I, simplifies to 3 2 + 2 4 in our familiar decimal system. Kudos, we’ve done it!

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