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My DS is in first grade at public school. He came home with a worksheet regarding "fact families" which I had never heard of, but by looking at the worksheet seemed to be fairly simple, but I'm a little confused by the grading.

For example:

Fact Family 1, 1, 2

His answers 1+1=2, 2-1=1, 1+1=2, 1-2=-1

He was marked wrong for his last answer and I don't understand why, although I'm guessing he was supposed to repeat 2-1=1, as on subsequent problems that is how he answered and was marked correct.

Anyone familiar with fact families, is there a rule that excludes negative numbers?

Thanks!

#### purslaine

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His last answer was not computationally incorrect. 1-2 does equal -1.

It is not, however, what the teacher asked for.

She asked for the math families. It involves re-arranging the sequence of numbers, not using new ones (as "-1") is.

2+3=5
3+2=5
5-2=3
5-3=2

I think the teacher should have marked the paper as thus

"wow! You are correct 1-2 is -1! That is not part of the fact family,however, so I cannot give you credit for it"

It is confusing for children when they know an aswer is right, but it is marked wrong or with an "X". The teacher should have explained.

Edited to add: it is great Ds showed you the worksheet. You can explain it to him. If you are ever in doubt as to the teachers reasoning, you can use it as an opportunity to model asking for clarification by writing a note on the worksheet or agenda. Asking for clarification is a bit of a school/life skill. As he gets older (even now?) you could ask him to ask the teacher why it was marked wrong.

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Thank you kathymuggle! You are right, I didn't even think about -1 being an entirely different number as thus not to be included.

I will encourage him to ask his teacher for clarification in the future. He did think that he must have been wrong about the equation. It happened on another problem to, fact family 4, 4, 8 and he had answered 4+8=12, which was crossed out so he thought 4+8 did not equal 12.

This is the first time he has really received any wrong answers in math, so it was really confusing to him. (and to me as I didn't understand enough about fact families to help him).

Again thank you very, very much!

#### MJB

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My son is in 1st grade and boy do we hate these fact families! They are way, way too easy, repetitive, and a weird way of teaching math IMO. It seems like that math curriculum in public schools has been dumbed down a lot since I was a kid. I loved math, and my son loved math when he was homeschooled for K (doing 1st/2nd grade math workbooks) but he hates it in school because it is "so easy and boring." The kids already know 1+1=2 for heavens' sakes!

#### ollyoxenfree

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Quote:
 Originally Posted by kathymuggle His last answer was not computationally incorrect. 1-2 does equal -1. It is not, however, what the teacher asked for. She asked for the math families. It involves re-arranging the sequence of numbers, not using new ones (as "-1") is. 2+3=5 3+2=5 5-2=3 5-3=2 I think the teacher should have marked the paper as thus "wow! You are correct 1-2 is -1! That is not part of the fact family,however, so I cannot give you credit for it" It is confusing for children when they know an aswer is right, but it is marked wrong or with an "X". The teacher should have explained. Edited to add: it is great Ds showed you the worksheet. You can explain it to him. If you are ever in doubt as to the teachers reasoning, you can use it as an opportunity to model asking for clarification by writing a note on the worksheet or agenda. Asking for clarification is a bit of a school/life skill. As he gets older (even now?) you could ask him to ask the teacher why it was marked wrong.
Great advice. Yes, the teacher should have explained. I'd definitely point out to the teacher the confusion for the student, and that clarifying why it was marked wrong would have been helpful.

#### Ellien C

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We have these math families, too. My daughter really likes math. Are you using the Everyday Math Curriculum? We are and I've looked into it a LOT. I'm trying to be open-minded about it, but I have concerns especially after elem. I think we only use it for elem school and we do add drills and memorizations to it.

#### Linda on the move

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Quote:
 Originally Posted by MJB It seems like that math curriculum in public schools has been dumbed down a lot since I was a kid.
We did them in first grade back in 71 -- they aren't new.

I think that the problem for the OPer's son is that *most* fact families have 4 facts, but when the two addends are the same, there are only 3 facts because you can only make one subtraction problem. He tried to make a second subtraction fact, and he couldn't make one and stay in "the fact family." You should ask if the teacher wants him to stop at 3 facts or write the subtraction fact twice.

The point of fact families is to help kids understand that addition and subtraction are inverse operations.

Good for you little guy on understanding negative numbers!

Following directions in an important skill. I went back to college this semester and I'm watching a young adult crash and burn because he thinks he is above following directions. While I believe that all children should be challanged at some point during their school day, learning to just get stuff done and following directions is important, too.

#### shibababy

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I do not like fact families, for the record, but they are a part of the curriculum so I teach the skill.

I tell the students to take the first two numbers and then flip them for the second addition problem. Then take the answers (sums) and use those to start the subtraction problem, take one of the addends and then the other addend becomes the answer (difference). for example 2+4 then flip to 4+2, those equal 6 so they would take the 6 and write: 6-2=4 and 6-4=2.

HOWEVER, when the two addends are doubles (the same number) you only need one additon fact and one subtraction fact , not a total of four number sentences.

1+1=2 and 2-1=1

The teacher may have explained to your son why his answer was incorrect, but he may not have understood the concept still.

It is also best that he understand now that you cannot subtract a greater number from a lesser number. It will save both of you hours of agony when he has to do subtraction with regrouping.

I would always write or call the teacher to ask her to explain. I always circle wrong answers and have students correct them, immediately. The only time this doesn't happen is on tests. I have never understood the point of marking something wrong and not explaining why. It just teaches a child if they are wrong there is no way to correct their error or "better luck next time".

Hope this helps

#### Geofizz

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Quote:
 Originally Posted by shibababy It is also best that he understand now that you cannot subtract a greater number from a lesser number. It will save both of you hours of agony when he has to do subtraction with regrouping.
But that's not true. What he wrote was exactly right. It wasn't part of the fact family, but it was factually correct. Now, it makes subtraction with regrouping inconvenient at times, but there are ways to multi-digit subtraction by doing exactly as he did. It's how I subtract in my head, in fact.

In my head, if I am working:

93 - 64 =

I think 30 + (-1) = 29

My second grade DD evidently does it like this as well when she's working in her head. She regroups when working on paper, though. It does not seem to have confused her or slowed her down.

#### Ellien C

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Quote:
 Originally Posted by shibababy It is also best that he understand now that you cannot subtract a greater number from a lesser number. It will save both of you hours of agony when he has to do subtraction with regrouping.
I'm going to disagree with this part. Certainly when I grew up negative numbers weren't introduced until much later. However, my first grader's "number line" absolutely goes into the negative numbers. I think it goes from negative 5 to 10 or 12. They do the hops and stuff and we do number families. So it may be that the concept of negative numbers are there. I think for my DD these are "stretch" problems. I haven't seen any homework going into negatives, but she has created those kinds of problems and seems to get them.

#### Geofizz

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Not to derail the thread, but Ellien, are "stretch" problems part of the teacher's Everyday Math tools in the first grade?
(Looking for differentiation for math for my DD... Not getting much, teacher says she doesn't have tools to differentiate in EM)

#### Ellien C

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hmmm - OK, so I'm not as totally involved in her education as some.

She seems to bring home these half sheets of paper with 3 problems on them
left - right.

The one on the left is supposed to be easy, the one in the middle is what they are learning and the one on the right is the hard one. So the kids get a feel for where they are. There's none in her folder right now or I would post an example. She is currently working on 2-digit addition and subtraction. I'm not sure if they've gotten to "carry the tens place" in the classroom, but the older girls in aftercare taught her and then she told me all about it. I think her teacher let her do it as well.

My daughter talks about liking the "challenge problems," but can't really tell me what they are. "I don't know, I just like them." Actually I think that was on her quarterly report card.

So - yes, I think it's part of the curriculum. We've had it for a few years and we have a GREAT 1st grade teacher.

#### Linda on the move

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Quote:
 Originally Posted by Geofizz (Looking for differentiation for math for my DD... Not getting much, teacher says she doesn't have tools to differentiate in EM)
not an expert on Everyday Math BUT most math curriculums have a bunch of different parts and schools decide which parts to order. So it may exist for the program, but the school may not have it.

If the school started using the program before the teacher started, she may or may not know what all the parts are or how they are supposed to work together. When a school starts a new curriculum, the teachers get training on that specific curriculum from the vendor. When new teachers start, they don't get that training.

#### marasmom

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I am a second grade teacher, who uses EM, and there is absolutely a differentiation option to the program. There is a readiness and an enrichment activity with just about every lesson. Even without a differentiation option to the program, the teacher should still be able to differentiate.

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Thanks everyone! I went over what I learned here with DS and he understands now that the equations were correct, but that they were not in the fact family, so were not correct for THIS problem.

I know nothing about the math curriculum at his school, other than the worksheets I see that he brings home, and he hasn't struggled with anything before now. We did talk about how you have to understand what the teacher is looking for with the question and to ask for clarification if it doesn't make sense to him.

I guess we are just starting a long journey of figuring out how to work thru things with school and helping him navigate it as well.

Thanks again to everyone who took the time to chime in on this!

#### VisionaryMom

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Quote:
 Originally Posted by Geofizz In my head, if I am working: 93 - 64 = I think 30 + (-1) = 29
This is how I do math in my head as well!

We are homeschooling, but I've seen fact families in some form in most of the math curricula I've considered. I'll explain it, but I think that for children who have an intuitive understanding of math, it's unnecessary. DS knows that addition and subtraction are inverse just from general observation, but I do want him to understand what's expected wrt "fact families" in case he has to do standardized testing or return to conventional schooling at some point.

I have not introduced negative numbers, but DS seems to feel there is something "smaller than zero," so we'll probably get to them soon.

#### Geofizz

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Quote:
 Originally Posted by marasmom I am a second grade teacher, who uses EM, and there is absolutely a differentiation option to the program. There is a readiness and an enrichment activity with just about every lesson. Even without a differentiation option to the program, the teacher should still be able to differentiate.
Wow, this is great info. Thanks. What does it take to implement the enrichment activities? If DD and 3 other kids in the room of 20 need this, and the other 16 are either just doing ok or hanging by a thread, how much of an imposition is it to implement? DD's teacher is saying she has to change the numbers in the math journal for every unit, and because the activities on one day are dependent on the previous days, then the whole unit needs to be changed at once and coherently. The teacher is going through the workbook with white out and a pen.....

reader18, I like the way you discussed it with your child. A lot of getting through life isn't just doing the right thing, but figuring out how it needs to be in a particular situation.

VisionaryMom, negative numbers are pretty easy to demonstrate with a number line or grid, plus a few basic examples of situations where he might be familiar with borrowing or otherwise being in the hole.

#### Peony

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Not meaning to highjack the thread but since so many posters seem to be in "the know".
I am guessing that DD1's school does not do math families because I have yet to hear of them this year, 1st grade in a small private school. She is doing fractions through, and doing quite well at them. I seem to remember when I was a kid, fractions were introduced in 3rd grade or so. Is doing fractions in 1st grade normal now?

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Quote:
 Originally Posted by Peony Not meaning to highjack the thread but since so many posters seem to be in "the know". I am guessing that DD1's school does not do math families because I have yet to hear of them this year, 1st grade in a small private school. She is doing fractions through, and doing quite well at them. I seem to remember when I was a kid, fractions were introduced in 3rd grade or so. Is doing fractions in 1st grade normal now?
That's quite alright! i've enjoyed what everyone has had to offer to this thread. I have not seen fractions with my DS. In addition to these fact families, which was just new this week, he has been doing a lot of basic addition/subtraction worksheets, some story problems, and counting money. I can't think of anything else.

#### Ellien C

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Quote:
 Originally Posted by Geofizz DD's teacher is saying she has to change the numbers in the math journal for every unit, and because the activities on one day are dependent on the previous days, then the whole unit needs to be changed at once and coherently. The teacher is going through the workbook with white out and a pen.....
no, no, no, no no.....We still do the regular math journal. My kid just brought a completed one home. There's this graph of their heights - I hadn't realized she was THAT short (although we both are....).

Anyway, our "challenge" or enrichment problems are on top of that math journal. I think it's like morning work on transitional activities. We've also got these "5-a-day" worksheets with math problems on them. I'd think the teacher could do something along those lines.

Classroom abilities vary WIDELY in my school. But we do have a good teacher (not so much with the kindergarten teacher) and also a 1-day a week GATE program where they get other enrichment and the regular teacher can work on reinforcement with the rest of the class. We also have a math specialist and a reading specialist that the teacher can pull in - either to present something to the whole class in a different way OR work with any group of kids separately.

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