I have a 3 year old so I'll be learning this in a few years. Truthfully, I had to read the fact family example a few times to understand it. I skimmed it the first time.
I recall that I did not do so well with multiplication tables in elementary school. I don't remember addition or subtraction tables. I think we started by learning to just count adding and removing things, which isn't as practical once you get into multiplication or division. Fact families didn't make as much intuitive sense until I thought of it as human family. This use of the word family may be what they are going for instead of a more academic use of the word to define similar groups. I don't know. Using the human family metaphor, I guess you could say the family is made up of the total number of people in the extended family. "So 1,5,6 and 2,4,6 are both fact families of 6." -> 6 being the total number of people in the family. You could describe an extended family as being made up of an uncle, and a mom and dad with two kids (6). The uncle is a family of one and the other family has five people. Altogether that extended (fact) family is 6. I don't know if that really flies or not... It just crossed my mind as I was reading through it. My daughter is really into the idea of our extended family as it's something we make an effort to teach about. On Wed, Jan 14, 2015 at 10:28 AM, John Baker <[email protected]> wrote: > Oh boy, > > May the Flying Spaghetti Monster save us from the marginally educated with > a new theory of education. > > I admire your gumption for volunteering but the few years I spent in the > bowls of the formal educational beast simply reinforced Sturgeon's maxim. > "never let schooling interfere with education," in my mind. > > If it was me I would break the rules outside of class - it's a life long > habit. Good Luck > > > On Wed, Jan 14, 2015 at 9:06 AM, Brian Schott <[email protected]> > 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 > > > > > -- > John D. Baker > [email protected] > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
