Description D1 - Addition and Subtraction of Fractions with the Same Denominator (1) D2 - Addition and Subtraction of Fractions with the Same Denominator (2) D3 - Addition and Subtraction of Decimals D4 - Factors and Multiples D5 - Addition and Subtraction of Fractions with Different Denominators (1) D6 - Addition and Subtraction of Fractions with Different Denominators (2) A special math classroom that makes math enjoyable A new standard in arithmetic learning, developed by Soma Soma's magical principle-based calculation program, "Somasem." Unlike traditional arithmetic workbooks that rely on simple repetition, this book presents each calculation process through a variety of concrete objects and situations, helping children understand the underlying principles while thinking and learning in a fun way. Designed for just 15 minutes a day, 5 days a week, over 8 months, each stage consists of 8 books with short, manageable sessions to keep learning engaging and never tedious. Somasem's Approach to Arithmetic Learning ① Single-Digit Addition Over 10 The foundation of addition and subtraction lies in counting. It's important for children to understand that 8+4 means counting up from 8, four more times. While using the complement of 10 for carrying (thinking of 8+4 as (8+2)+2) is a useful technique, it's better to first build a solid understanding of the basic concept of addition when starting out. This book uses concrete examples so children can grasp the concept through tangible objects. ② Horizontal vs. Vertical Calculation Vertical calculation isn't inherently wrong, but practicing it repeatedly and mechanically—remembering only where to write the carried number like a formula, without thinking about the underlying principle—leads to calculation without real understanding. Working through horizontal calculations, on the other hand, encourages children to think about the principles involved and develop important numerical reasoning skills through processes like breaking apart and combining numbers. ③ Multiplication Tables Focusing solely on memorization when teaching multiplication tables can have significant drawbacks. Children should understand that multiplication is essentially compressed addition, and that memorizing the times tables allows them to calculate more quickly based on that understanding. While memorizing multiplication tables is important, understanding the true meaning of multiplication matters even more. A child who can solve 4×3 should never struggle with 45×3 simply because they haven't yet learned two-digit by one-digit multiplication. The Reality of Arithmetic Education The biggest problem in arithmetic education today is the distorted marketing of conventional workbooks claiming that "children will struggle in upper elementary grades if they aren't fast at calculation," along with an overemphasis on mechanical repetition. However, arithmetic learning based mainly on mechanical repetition not only causes children to dislike math but also limits the expansion of their thinking by neglecting concepts and principles. Elementary Math Curriculum and Arithmetic The elementary curriculum focuses on the concepts and principles of arithmetic, explaining them through words rather than symbols and notation—symbols are introduced later, starting in middle school. If you look at textbooks, you'll see that the principles behind every calculation are carefully explained. In practice, even descriptive questions that ask about the principles of calculation are appearing on tests, yet the prevailing belief remains that practice should come first. How Should Arithmetic Be Learned? Arithmetic should never be taught in isolation using only abstract numbers or symbols. Practice should come after children have thought about and understood concepts using concrete objects. Additionally, the focus should be on accuracy rather than speed, helping children build good habits that allow them to overcome mistakes.