First, let me give some background and a warning. The warning is that my reason for posting is to get some guidance on the Common Core (CC) pedagogy from anyone and this may be the wrong place to ask for it.
The background is that I am a one-or-two-hour-a-week volunteer for a first grade class and have absolutely no formal education in education. The classroom teacher is in my judgment not trained deeply in CC, and I have no expert person to communicate with, although the web contains very detailed Statewide CC documents (an example doc link is below). Also, there are a handful of web videos showing teachers in their classroom or lecturing on CC Math [1,2]. In a nutshell, I believe that the CC prohibits teachers from teaching or even mentioning what we might call in these forums "+ table" and "- table" and instead wishes to promote what might be called "mental math" using Fact Families! My question is, how do I manage to convince myself that this CC focus on Fact families, not tables, is a natural and effective way to learn math? I intend to continue to enthusiastically volunteer as I am doing now, even if no one can totally convince me, but I will feel a lot better if I can be shown, "the way." A little more of my research on this subject follows. I apologize for the length of this message. Of one fact, I am quite sure. All fact families are denoted as triplets for which the first 2 positive integers sum to the value of the third integer. 2,5,7 and 1,5,6 and even 5,5,10 are examples (NB. the first two integers may not be different in the case of what I call an "even" fact family, and the total may be a 2-digit integer). I am less clear about whether the triplets must be expressed as non-decreasing sequences, but they seem to always be so. Another fact, of which I am less sure, is that a fact family can be referred to by its largest integer, although that integer does not uniquely define a family. So 1,5,6 and 2,4,6 are both fact families of 6. Less clear to me is whether some fact families are not considered useful, or if there is a hierarchy of usefulness. But it is quite clear to me that fact families of 10, and to a lesser extent of 5, are most important. Also, it seems to me that fact families which include the number 5 as the second integer are a little more often used in mental math. The following link seems to be pretty clear on some aspects of Fact families with some examples I will mention. Other links at the same domain have been helpful to me, also, although I mostly have relied on .pdf, not .doc, files. https://www.engageny.org/file/1341/download/first-grade-module.doc For example, that document seems to refer to 2,5,7 as "fact family of 7" . Ultimately it mentions "fact families of 10" as being the most important because of our dependence on the decimal digits system and decimal place values used for addition and subtraction. The following example, also taken from the link above, makes an example of "a fact family of 5". [You may notice that there may be an error in the first sentence, where instead of "the first five fact families," they may mean " the first five fact family," where I believe there are altogether 2 fact families of 5: (1 4 5) and (2 3 5).] *********example below************* "For today’s lesson the teacher will only use the first five fact families, for example: 1 + 4 = 5 4 + 1 = 5 5 – 4 = 1 5 – 1 = 4 The teacher will demonstrate this using a visual image. Example: 1 purple fish swims to meet up with 4 yellow fish. We represent this as: 1 + 4 = ? 4 purple fish swim to meet up with 1 yellow fish. We represent this as: 4 + 1 = ? Once the students get the hang of this, the teacher uses an example where the sum from the original fact family is diminished: 5 fish are together and 1 fish swims away. We represent this as: 5 – 1 = ? 5 fish are together and 4 fish swim away. We represent this as: 5 – 4 = ? The teacher guides students to use their counting up and counting down skills to determine the answers and leads a discussion about why these numbers form a family." *********example above************* The example has helped me a little to put the Fact families in a meaningful context but I remain skeptical of their use and how to teach them, frankly . Thank you very much, -- (B=) <-----my sig Brian Schott [1] https://www.youtube.com/watch?v=twGipANcIqg [long, but great] [2] https://www.teachingchannel.org/videos/grade-1-math [shorter, but more for inspiration] ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
