Our number system is called base 10. Also known as “decimal” or “denary”, the base ten counting system is so universal we sometimes forget other base counting systems exist. The Mayans had a base 20, or vigesimal, counting system. Most digital languages are built on a binary system or base two.
What Does a Base System Mean?
Number bases are just different ways of writing down numbers - just as Roman Numerals or tally charts are - but other than that the numbers behave as normal. This doesn't mean that their arithmetic is fundamentally different - in fact, the way number bases behave is entirely consistent. In base ten, we use 10 numerals. They are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. To represent quantities higher than 9, we must use only these 10 symbols in different placements. In a binary system there are only two numerals, 0 and 1, in an octal or base 8 system there are eight numerals and in vigesimal a system there are twenty numerals.
Why is Learning Place Value So Hard?
Children must first understand the symbolistic idea that placement of the number dramatically changes the quantity represented. Spoken and written language also has some place value but we use inflection and punctuation to help give context. Compare “Bananas are yellow.” with “Are bananas yellow?” No such clues are given in math. And think of the cute way toddlers and preschoolers talk. It takes years to master the “place value” or grammatical structure of our language.
In our decimal system a “9” written in the “10s place” means a totally different quantity than a 9 in the “hundreds place” or 9 ≠ 90 ≠ 900. This may seem logical to an adult, but it is actually a pretty difficult concept for children. To make matters worse the numeral 0 plays some funny tricks with place value. 1.0 = 1 but 10 ≠ 1.
Like learning the patterns of language, children need ample opportunity and time to explore our number system in a variety of ways and modalities before they internalize it. If your child is getting confused with numbers over 9 and you’re wondering why, try using binary for a few days and see how you do! You can explore how to write different numbers here and different bases here.
Math Emergency!
Unfortunately, many first and second grade classes do not devote enough time for children to adequately explore and understand place value using the base 10 system. If children don’t fully internalize the system, they end up with critical learning gaps. All of arithmetic is based on the base 10 system! Do not wait to see if they catch on next year! These initial gaps in understanding with build upon themselves and soon your child will be falling further and further behind, even if you don't see this reflected in their grades. Bring them into Mathnasium today so they can get the time and experience they need to succeed in math. We Make Math Make Sense.
This article was written by and owned by Cuttlefish Copywriting, www.cuttlefishcopywriting.com . It is copyright protected. Mathnasium of Parker has permission to use it. Other Mathnasium locations should contact Heather at [email protected] before using it.
