3.OA 6: What Is the Essence of Division? First Things First (#191)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 191

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Operations and Algebraic Thinking 3.OA
Understand properties of multiplication and the relationship between multiplication and division.
6. Understand division as an unknown factor problem.  For example, find 32 / 8 by finding the number that makes 32 when multiplied by 8.

As stated in earlier posts, this concept is solidified very early on since division is worked with in Grade 1, alongside the other 3 processes.  The white “unknown number” square is placed anywhere on the color practice strips to simulate the unknown factor in today’s standard.  When solid foundations like this are built early, familiarity wins the day as the same concept spirals back later on with greater and greater complexity.  So, the Math By Hand or Waldorf student will fully comprehend this concept in this standard, from Grade 1 on through the grades.

A really essential piece for teaching the 4 processes is conveying them with personality.  And this is beautifully accomplished in Grade 1 by applying one of the four temperaments to each of the 4 processes.  Division, as you may have guessed, is choleric, colored red!  The nature of each of the processes becomes second nature to the child, and more importantly, math becomes humanized and friendly, approachable.  All fears and phobias fall away in the face of such “personalizing.”

The 4 processes stories told in Grade 1 are simple, and aligned with that year’s story theme, the fairy tales.  The King might organize a counting house where the farmers bring their wares to distribute to the townsfolk in exchange for gems.  The glass gems shown above can be used as the first calculating tools, and many imaginative scenarios are created in which the 4 characters engage in calculations.

Here is Divida’s story, taken from the Math By Hand Grade 1 Daily Lesson Plans book.

Once there was a kingdom where 4 special children lived. Each one was different from the others, but in spite of their differences they got along well. All good friends. they always helped each other. More importantly, the kingdom itself could not get along without them. The King gave them honorary names and decreed that each wear an especially bright color so everyone would know who each one was at first sight.

DIVIDA was dressed all in red because she was so decisive! Whenever the King needed a strong, fair person to take charge and keep things in order, he called on DIVIDA. When a disagreement broke out among her friends or others in the kingdom, she was a wonderfully impartial judge, helping to settle matters fair and square.  

DIVIDA was respected because she could be counted on to step in and make all the tough decisions, but all that decision making sometimes made her feel that she alone was right. Sometimes the King had to step in and help her to see others’ points of view. At times like these, DIVIDE readily listened because she was so very fair after all. DIVIDA, all in red, was a treasure. Without her, the kingdom would often be stuck in confusion and indecision.

And here is Divida herself!  You can see that attaching personalities to each of the 4 processes helps to make them more friendly and less daunting, lifelong!  Do invest the time and energy it would take to personalize division as well as the other 3 processes, at any age or stage!  The Grade 3 personalities could coordinate to the stories that are told in that grade.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.


Item added to cart.
0 items - $0.00