At what point in math learning should math facts be memorized?

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I have been actively not trying to have my dd memorize math facts yet because I am afraid that as soon as she does, she won't think about the "why" behind it anymore.  We've been doing Miquon, MM1, and Education Unboxed stuff and I'm fairly comfortable with math teaching, but I have been struggling with this.

Right now, dd can solve an addition or subtraction problem with c-rods, counters, or a picture.  She can't "count-on" or "count-back" a specific amount of times yet (count on from 7 three times to get to 10), but we are working on it and she will grasp that fairly soon, I think.  So I guess I'm just wondering, for you, what are the prerequisites before you will start teaching math facts as such?

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For me, I started teaching math facts once ds understood what addition was ( adding one number to another to get an answer) and could do it in his head if asked to.  I started with the doubles math facts (1+1, 2+2,...) while still working on addition problems visually (using manipulative or drawing it out.)   that way he is memorizing the facts in groups slowly and also still having the concept reenforced.  It has worked great for him because he can now get a new set of facts and memorize them within a day or 2.

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I agree counting on would be prereq also skip counting by 2, 3,4,5 can make subtraction and addition easier. Another prereq would be solving add and subtract on a number line. It's a lot of fun to practice math drills on a hopscotch shower curtain or outside. The main thing I watched was frustration level and time. Sometimes I think mine are ready for a page of 30 long division with remainders only to realize they need 10.

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I personally would not actively work on memorization with a 5 year old. If she "gets" adding and subtracing and enjoys playing math games, that would be fine. My kids have actually done almost all their math fact acquisition from math games. I treat math facts and conceptual maths as 2 different things. Ultimately, as long as they're fluid and fast by the time they get to pre-algebra, I think you're fine. I have a math degree and really came around to my math facts very late (but I was always ahead in concepts). And so did my 7th grader, who is actually accelerated in math, but isn't super fast (he did have his facts by the time he reached pre-alg though). Different kids will come at these skills differently. I'd just watch and be receptive to your child's learning style. Some kids do better with very rote math early on and coming at concepts later.

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I am planning to try for having nailed down the addition and subtraction facts by the start of second grade and the times tables by the end of third. DS has picked up some of each just from repeated exposure, so I figure by that point he'll have done enough conceptually to memorize the rest.

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You've got years to get the math facts nailed down--just keep playing around with numbers. You do want to keep working on the combinations that make a 10--that's important for first grade math and the mental math skills down the road of being able to add say 26+7 ("how many do you need to get to the next 10? 4? Yes, good, now take that 4 from the 7 and you're at 30; how many more are left over from the 7? 3? yes, so you're at 33.") That's where you want to get to (first grade for Singapore math--I don't recommend starting it early as it really is pretty sophisticated thinking. But a great skill to develop). So work on those combinations that make 10, know the combinations that make any number less than 10, and you've got the building blocks to go from there. Five is pretty young--don't stress too much about this. Meet her where she's at and have fun with it.

My youngest did not master facts as quickly as her sister, but I am fine with it being a multi-year process. She wasn't great at addition until maybe 2nd grade, but no problems now. No calculators allowed here in the elementary years, so as she continued to learn skills such as double digit multiplication, her times tables got better and better from all of that multiplying she had to do.

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I've read that by 4th grade kids should have memorized math facts through normal use (word problems, extension problems, etc). If they haven't, then assign practice sheets.

My son is doing 4th grade math now and encountering long division - for which he needs mult facts. He doesn't have them down cold, so I have him do a daily practice sheet. It has not caused a problem before now.

Emily

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I think I might be in a minority, but I think working on facts once a good grasp of the process at hand is beneficial for the kids, especially as they move through conceptual math. It takes all of the emphasis off of something they *should* know already and moves it to something they *are learning.* We try to do some drill ever day. My kids can pick the "fun" way (games) or the "quick" way (running through lists). For my son, it makes a BIIIG difference in attitude when approaching new math subjects.

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We do drill for addition and subtraction (up to a sum of 20) from 1st through 3rd grade most school days.

Multiplication drill with occasional division drill is 2nd through 4th.

It takes a long time to get the math facts down cold, but that is what the kids need in order to be ready for higher level math, or even just for long division.

Of course we also emphasize the math concepts continually as well.

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I like the kid to have facts to ten memorized fairly well prior to starting facts up to twenty. That's because I teach breaking a number up to figure out the rest. Once they understand how to figure out 8+9 by breaking up the numbers 8 +2+ 7 then we work on memorization. Oldest had all her facts memorized fairly well right before hitting MM2b.

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My oldest I never needed to drill addition & subtraction facts with as she just naturally memorized them as she worked through RS B. The times tables she did need to drill on separately from her normal math (I reordered Singapore 3A/B to do all the chapters aside from the ones on multiplication & division while she worked on getting the times tables memorized.

With DS, I did need to have him work through Mindware's "Addition Adventures" and "Subtraction Secrets" workbooks separately from his lessons in Singapore 1 A/B. Like his older sister, he also needed to reorder Singapore 3A/B while memorizing the times tables.

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End of Second grade for addition and subtraction.  End of 4th grade for multiplication and division.  At least that's my rule of thumb.  It gives them time to understand what they are doing and to memorize most of the facts just by using them.

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Some kids learn math facts after seeing them once; others never seem to gain automaticity.

One of mine didn't really have her facts cemented until third or fourth grade, which made long division hard in the program we were using that introduced it rather early in third. Even though we reviewed them constantly, they were "lost" after any short break, like Christmas.

I agree with the others to keep working on it without expected them to be automatic before fourth. Consider yourself especially blessed if they get them after the first exposure and fortunate if they get them by the end of second grade.

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When counting purposefully is fluent and mastered. (counting, the way I mean it, includes counting forward and backward. Fully understanding the connection between counting on and addition and counting back and subtraction.)

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I know it isn't something I need to stress about, but I have been wondering.  I can see the pros for doing it early vs. later.  With dd, I don't think she is seeing the patterns when we do all the discovery stuff.  We keep doing all these neat activities and she is just not putting it all together.  Part of me is thinking that if she has the facts down and then does the discovery stuff, she'll see the connections better.  Sort of like the "peg" theory behind memorization (which really works well for this dd).  I do think I'll wait until she is able to count-on and back well, first.

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Isn't this the type of thing people mean when they talk about whole-to-parts or parts-to-whole learners?

I really think some kids put it together naturally while others need things spelled out to them. That's why it's unrealistic to state categorically that one curriculum is better than another and unfair to judge another parent's choice of curriculum. We have to be open to how our kids' minds work and take advantage of their strengths while working on their weaknesses.

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My son is starting MIF 1B, and at this point I don't see the need to drill math facts. He is very strong in the mental math strategies for addition and subtracting within 20, and I think he will memorize the facts as he uses math. It's pretty quick for him to figure out 8+6 because he regroups it as 10+4. He doesn't need to memorize that 8+6=14. He keeps forgetting that 5+3=8, so each time he starts at 5 and counts up 3 more. He doesn't rely on manipulatives.

In your situation, I would work hard at those mental math strategies until your student no longer needs to use manipulatives to solve. I would not switch over to fact memorization until your student can use those strategies fluently, and then only because you are trying to increase speed. What you could do is use flash cards as an opportunity to practice the strategies. I would not push for speediness, but just work through the problems. I assume that after doing them a while, the answers will get memorized even if that isn't the explicit goal.

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Lots of different philosophies out there on this one! Anyway, we don't start ANY formal math until math facts (all 4 operations) are memorized. My first dd started memorizing at 6 and it took her two years to get them down solid (we only spent 10-15 minutes each day on it). She then started Saxon 5/4 at half pace. Now at 9 she is almost done with Saxon 5/4 (and is working at full speed now). My next 2 just started learning their facts in the last two months (so almost 7 and 5... but same academic level). Of course we do informal things to learn the basics of counting, shapes, simple addition with manipulatives, money, etc. over the years, but nothing really planned, just as they come up. There have been studies done that show that most children cannot really begin to think and understand mathematics (more advanced thinking) until around 8-10 years old, even 11 or 12. So, to spend the early elementary years trying to get kids to "understand" can be difficult at best. Of course some kids are more apt to grasp then others, but these kids are also the same kids who can learn all their math facts in a few months and are then ready for Saxon 5/4 at age 6 or 7! Anyway, that's what we do.

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You know, I think this is different for different kids.  My oldest and youngest worked/are working on memorizing multiplication/division in 3-4th grade.  Addition facts in 1-2 grade.  However, my middle two struggled/are struggling to memorize.  What I've noticed for these two is as we worked on multiplication, the addition and subtraction started to come more easily.  Now, as my dd11 has been working on fractions and decimals her multiplication and division is much better.  I'm hoping this will also happen for my ds10 who struggles memorizing.  For them it's more a process and they needed lots of time.  I'm glad I didn't push with her because she would have refused and it would have been a battle.

I think math is one of those subjects that we have to be flexible in.  Some children just need the gift of time, while others fly through memorization...

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I have been actively not trying to have my dd memorize math facts yet because I am afraid that as soon as she does, she won't think about the "why" behind it anymore. We've been doing Miquon, MM1, and Education Unboxed stuff and I'm fairly comfortable with math teaching, but I have been struggling with this.

Right now, dd can solve an addition or subtraction problem with c-rods, counters, or a picture. She can't "count-on" or "count-back" a specific amount of times yet (count on from 7 three times to get to 10), but we are working on it and she will grasp that fairly soon, I think. So I guess I'm just wondering, for you, what are the prerequisites before you will start teaching math facts as such?

My son is in a very similar place with math and I am not working on math facts yet. When he has a lot of practice counting on and backwards and using number lines I will start on facts. We have started those concepts and he does decent but still needs some hand holding and reminders at times with it. He does great with c-rods, pictures or manipulatives. I am working on math facts with my oldest but it is something that is taking a while. She was fast at adding by counting on and using a number line when I started with her.

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My middle son did Singapore 1A/1B in his K year (turned 6 in November of that year), and I didn't start fact practice until he started 2nd grade math this year in 1st. He knew several just from using the C-rods and from the repetition of doing addition and subtraction in his daily work, but they weren't memorized 100%. This year, he has a 2 minute speed drill every day, plus a quick run through some flash cards (focusing on different sets of facts each day). He's very good with his addition and subtraction facts now. I'm glad I didn't bother worrying about it in K. First grade was a better time for him to learn them.

I plan to do the same with the next kiddo, who will be K next year (though he's a memorizer, so he'll probably not need the fact practice as much).

In particular, I want them practicing things like 8+5=10+3=13 before they start memorizing 8+5=13. It's hard to practice such strategies if the fact is already memorized - the kid skips the strategy portion and just writes the answer, when you're trying to practice a strategy with smaller numbers before applying it to larger numbers where facts aren't memorized.

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