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At what age should math facts be mastered?

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I think most neurotypical kids can have most or even all math facts memorized by 3rd or 4th grade.  Some kids can master them sooner or even much sooner, some are going to need more time and a lot of review.  And some may never be able to just rote memorize.  Some are going to need something to tie that information to, or will need other ways to get to the information quickly (such as rapid skip counting).  Different brains, different strengths and weaknesses. 

 

Understanding the concepts behind math while learning math facts separately can help.  For instance, in CLE math the math facts are worked on daily in targeted, very specific patterns, but the main lessons allow for a math reference chart so the student can continue to focus on math concepts/algorithms instead of getting bogged down and using mental resources to recall math facts that may not be automatic yet.  The program continues this practice through 5th grade.  Frequently, once a child gets into higher math, they can tie math facts to math that is more meaningful and often can then remember the facts better.

 

(FWIW, I had to accept that for my own kids all math facts may never truly be mastered (dyslexic plus other issues).  We still work on math facts and have for years (and many are sticking) but we also work on other ways to get to the information since rote memorization does not work with my kiddos and tying the information to other things is only hit or miss.  Thankfully there are ways to get to those math facts quickly, without rote memorization.  For instance, DS is excellent at rapidly multiplying a number by 10 then subtracting in his head until he gets to the answer he needs.  DH does not have all of his math facts memorized but is a very successful engineer.  I do not have all of my math facts memorized (not from lack of trying) but I run the finances for the family company without issue.  Therefore, my view is that while math fact memorization is very helpful and definitely something to work on, it is not the be all and end all of math, IMHO. )

 

Best wishes.   :)

 

ETA:  My estimate of when a neurotypical child should have math facts memorized is based on what local parents and schools seem to be pressing for.  Certainly 3rd or 4th grade has not been the case in my own family.

Edited by OneStepAtATime
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My daughter didn't get them down until we worked with xtramath.org at the beginning of 6th grade (she's on the youngest end of her grade, so she had just turned 11). Could she have done it sooner? Yes, I'm sure she could have if we had put enough focus on it. We had been working with Singapore (which didn't focus on fact memorization as I remember it) until 5th grade then switched to Saxon, which helped, but didn't do it fully. We had been working on the assumption that because she is gifted, she would get it with practice in working with problems rather than what folks call "drill and kill" (the same reason we stayed with Singapore long after we should have switched for this child). Well, she's gifted in verbal, not in math, so in our house, "drill and kill" in math is called "necessary focused practice to get it" ;). 

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I think most neurotypical kids can have most or even all math facts memorized by 3rd or 4th grade. 

 

I think that's probably true but it depends how much you and your math program care. Personally, I don't care if my kids have them memorized that early as long as they can work them out quickly, DS9 is starting fourth grade and has huge gaps in his memorized times tables but does know all the perfect squares up to 256. If he is going to solve 7x6 he either takes 7x3 and doubles it or takes 7^2-7. This is how he does lots of the higher numbers. It is fast enough for now and as he does more problems he will slowly internalize all the facts without explicit memorization.

 

So my goals are +/- facts by 3rd or 4th. Multiplication/division by  when you start or during pre-algebra.

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My kids are 9 (closer to 10) and one of them only knows maybe 2/3 of both addition and subtraction facts.  I think that kid is a little behind in that respect though.  Oddly she finds addition facts harder to remember than multiplication facts.

 

My other kid may or may not have all her facts memorized.  She's cognitively advanced, so if she's doing the computation vs. remembering the fact, it isn't obvious one way or the other.

 

In my childhood, facts were not emphasized in school.  I was in high school or maybe college before I knew all those facts by heart.  I was supposedly "gifted" and a very good math student.  So, if your kids don't have their facts down, don't fret.  :)

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It may help to not think of the facts as being for "4 different operations."  For many it may be easier to take a more big-picture, three-dimesional  perspective of number composition, with subtraction just being addition backward and division being multiplication backward.

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Massachusetts suggests the following fluencies that students must master by grade.

 

K

Add/subtract within 5

 

1st

Add/subtract within 10

 

2nd

Add/subtract within 20

Add/subtract within 100 (paper and pencil)

 

3rd

Multiple/divide within 100

Add/subtract within 1000

 

4th

Add/subtract within 1,000,000

 

5th

Multi-digit multiplication

 

Like reading if you don't provide time for them to practice at fluency they never really master it.

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..., DS9 is starting fourth grade and has huge gaps in his memorized times tables but does know all the perfect squares up to 256. If he is going to solve 7x6 he either takes 7x3 and doubles it or takes 7^2-7. This is how he does lots of the higher numbers....

 

I'm 42 and have a BS in math and am a high school math teacher by trade... To this day I *still* cannot seem to memorize the answers to 6x7, 6x8, and 7x8. I always have to go back to answers I know (6x6 or 7x7) and then add up. It baffles me that this still happens, but I do the calculations so fast that no one ever has noticed. 

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We do a LOT of informal mental math and play a lot of math games. But the only things we work at memorizing are the multiplication facts, and we don't start trying to memorize until about 4th grade. By then, all but the hardest facts have been absorbed through regular use, and memorizing the last few doesn't take too much effort.

 

We don't stress over it, but the kids need to be fast enough (by memory or by using strategies like Noreen described) by 5th grade that it doesn't hinder their other work. If they are still lagging, we'll take time out then and focus on multiplication, using the strategies I describe in this blog post series.

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My kids go to school Tues/Thur, and are home Mon/Wed/Fri.  Last year, I assisted in the fourth grade math class.  They used Singapore Standards 4A and 4B.  In this class, there was a very close correlation between the kids who knew their facts cold, and success in the class.  I thought it was just kids who knew their facts were also the ones who were just better at math, but I found out close to the end of the year that several kids who had done great in prior years had not had a great year, and vice versa.  The teacher was excellent - it wasn't that.  

I truly think the topics that were added in fourth grade (factoring, multiples, fractions, etc.) are just significantly more challenging if you are trying to hold your place in a problem in your head while working out a math fact.  

I have one kiddo who has never been very good at fact retention, despite years of daily review.  We hit it hard this summer, upping the practice to twice daily.  We started retaining, but gains were still slow.  We finally went to 15 minutes three times every single day, 7 days a week, and 3 months later, that kid FINALLY knows every fact up to 12s.  She is still reviewing at least once daily (unprompted by me), bc she is so afraid she will forget and have to relearn them!  

We used Big Brainz Timez Attack once a day, MobyMax once a day, and the math game app of their choice once a day.  She also did a 100 problem mixed operation speed drill once day.  I printed them to only include the facts I knew she had practiced (I could see with MobyMax).  I told her the goal was to do the drill in under 15 minutes.  (The goal is actually supposed to be 5 minutes, but I didn't want her to freak out.)  She easily beat my 15 minute time, and kept improving - by the end of the summer she could do it in under 3 minutes!   :)  So it was a long hard summer in that respect, but she is SO proud of herself and has really learned that hard work pays off!  This monkey is FINALLY off our backs!

 

Edited by MeganW
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My kids are essentially neurotypical, just a little advanced, and we used Big Brainz, which had both girls through division by the end of second grade. It makes third and fourth grade math go a lot more smoothly.

Edited by Arctic Mama

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It may help to not think of the facts as being for "4 different operations." For many it may be easier to take a more big-picture, three-dimesional perspective of number composition, with subtraction just being addition backward and division being multiplication backward.

Yes, the holistic, fact family, manipulating numbers approach to fact acquisition helped my kids. They'd have probably gotten them sooner but I wanted them to be completely concrete on the operation and why/how it worked first, which is somewhat developmental. Once they got it the rest was just practice.

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Ds9 did know them when he was 8 and had to do speed drills. He seems to have forgotten a few though.

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I'm 42 and have a BS in math and am a high school math teacher by trade... To this day I *still* cannot seem to memorize the answers to 6x7, 6x8, and 7x8. I always have to go back to answers I know (6x6 or 7x7) and then add up. It baffles me that this still happens, but I do the calculations so fast that no one ever has noticed. 

 

Ditto. I've always been a straight A math student, too. I just worked out the problems a little slower than those who have their facts down cold.

 

It is possible that had math facts continued to be drilled beyond elementary school, I may have learned them all before high school. I may not have been developmentally ready to really learn math facts until I was 14 years old despite all of the drilling and flash cards in elementary school. 

 

With my son, we will work on math facts a little every day until 12th grade if we have to, until he knows them all. He's making slow but steady progress on math facts, but otherwise he is doing great in math.

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I'm 42 and have a BS in math and am a high school math teacher by trade... To this day I *still* cannot seem to memorize the answers to 6x7, 6x8, and 7x8. I always have to go back to answers I know (6x6 or 7x7) and then add up. It baffles me that this still happens, but I do the calculations so fast that no one ever has noticed. 

 

 

Physics major, same story.  :-).  My 6s, 7s, and 8s are all hazy, and I simply work form either a x5 or from a square to get to the answer.  

 

OP, I would worry less about age and more about math level.  For my son, 4th and 5th grade Singapore books would have been very long and tedious without being able to recall or calculate his facts relatively quickly.  Whatever grade your math curriculum starts multi-digit multiplication is probably the grade level the child should have multiplication facts down pretty well, otherwise one problem could take quite a while and be very frustrating.  Another indicator would be long division.  I'd hate to have to teach a child long division if they weren't relatively solid on all four operations.    

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In PA at the b&m school, our 3rd graders are expected to know their facts by the end of the year. We are asked to spend 5 minutes a day, 5 days a week, working on them with our kids.

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I would say to focus on mastering the facts within 6-12 months of FULLY understanding the operations.

 

There are at least a dozen ways to master them and all of them are valid.

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I think by 10. The earlier they are memorized, the easier math will be later for them. When I taught at a private school the goal was all multiplication and division mastered by the end of 3rd grade, but there was an understanding that August - October in 4th grade it had be reinforced. It was an easy concept to covey to parents as well. 

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I have kids that were tramatized by timed math facts test is school, so I have not pushed the memorization of math facts.

Yes, it makes kids faster, but as long as they can figure out the correct answer, I don't care.

 

My son developed rapid recall of multiplication facts in 6th grade when he had to complete many, many problems of multi digit multiplication.

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