# What are the Foundations of Basic Numeracy and Number Sense?

We all understand the importance of math education especially early math education. Math education is built on the foundations of basic numeracy and number sense. Students learning math must understand how to represent, recognize, and count using our base10 numbering system. The abacus is one the most efficient ways to represent any number by assigning the digits 0-9 of a number to the 5 beads on each vertical rod. Unlike other number representations, the abacus beads are not only a simple number representation but also an highly efficient number representation that can be manipulated in calculation. We could have incorporated 9 or 10 beads per rod but this would be a much less efficient number representation. The additional beads would also slow a student computation speed and accuracy. So the use of 5 beads to represent all 10 different digits has proven to be an optimal and efficient number representation. Any student, not just those math inclined, can quickly learn to represent and recognize any number on an abacus.

The RightLobeMath.com online program starts by teaching students to represent, recognize, and count the first 5 digits, 0-4. The 4 lower beads below the reckoning bar, the bar that separates the top bead from the 4 lower beads, each have a value of 1. Using the 4 lower, or earthly, beads students not only quickly learn to count the first 5 digits but also learn their foundational relationships through adding and subtracting all the possible combinations of 0-4. Next students are introduced to the heavenly bead, above the reckoning bar, which has a value of 5. Combining the top bead with any combination of the 4 lower beads students can form the remaining digits 5 – 9. Since each digit of a number is represented by a rod on the abacus, students understand place value in the form of rod position.

Now that students can represent, recognize and count all the base 10 digits, the program begins teaching students all of the relationships between single digit numbers that either produce a carry or require a borrow from the next left digit. For abacus students however, we do not teach these relationships in the same way taught in most schools. Our abacus math program teaches students another foundation of our base 10 system – the complement. The RightLobeMath.com program first introduces the 10’s complements which are the 5 pairs of single digits that add to 10 such as 9 and 1, 8 and 2, 7 and 3, 6 and 4, and 5 and 5. These are the only 5, 10 pair, complements. Students are taught the skill of using these complements to add and subtract numbers that require either a carry or borrow from the next left digit. This is the same calculation method used by your computer (but your computer does it in base 2!). Using the 10 pair complements is the most efficient method for addition and subtraction.

After mastering the use of the 10 pair complements for both addition and subtraction, the RightLobeMath.com online program introduces another basic numeracy concept the 5 complement. The 5 complement is a pair of numbers that adds to 5. There are only two: 4 and 1, and 2 and 3. Whereas the 10s complements were introduced to show students the numeracy relationships between consecutive digits of a number, the 5 pair is introduced because we added the 5 bead above the bar for calculation efficiency. The 5 pairs are used to teach students addition and subtraction combinations such as 3 + 4 or 7 – 3 that take place within a single rod. Again the use of complements provides students not only with an increased understanding of our number system but also the simplest and fastest calculation method.

Lastly as part of the RightLobeMath.com Skill Training program, students are taught how to combine the use of both 10 and 5 pair complements within the same bead movement even across multiple digits of a number. This enables students to master combinations such as 14-7, 8 + 6, or 98 + 5. At this point in the RightLobeMath.com program the student has proficient knowledge of the foundations of our numbering system to represent, recognize, and count numbers. Students have the skill and mathematical understanding to solve all possible addition and subtraction problems of any size. With a little time and practice they will master very large number addition and subtraction with both speed and accuracy! Next the RightLobeMath.com program moves on to multiplication, division, and mental calculation. Come join the math journey!