As the parent of a first-grader, I can try to address some of this. I see it as a way to practice the skills that underlie algebra. Commutativity, identities, inverses, etc.
They don't talk about the "3,5,8" group. They practice moving around numbers: 3 + 5 = 8 5 + 3 = 8 8 - 3 = 5 8 - 5 = 3 Any adult can generalize to: A + B = C B + A = C C - A = B C - B = A but the concrete practice is a useful thing for people just developing their number sense. Instead of just practicing that "3 + 5 = 8", they practice the whole set of permutations algebraically implied by that fact. It seems pretty reasonable to me. Practice the facts before you jump to the abstract rules. -Johann On Wed, Jan 14, 2015 at 10:06 AM, Brian Schott <schott.br...@gmail.com> wrote: > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
