# Help me see this - math - facts vs concepts

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I've been reading in some math threads about kids struggling with facts. A lot of mamas recommend continuing on in concepts while doing fact practice separately. For some reason, I am not visualizing how this looks. DS is in 3rd. We are working through MM2 because he just doesn't know his facts easily. Yesterday we were adding 43 + 20 and it took him 5-10 minutes to figure out 4+2=6. And the whole time, he's fidgeting, pulling on his hair, holding his head, etc.

He enjoys story problems and loved the geometry intro we had last year in CLE. I started him in MM2 because of the facts.

So if I want to continue in concepts, how will that work? I think lack of sleep is making this hard than it really is.

Should I work on MM3 instead? Math is an everyday struggle. I'm at a loss.

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For multiplication, facts may be knowing the multiplication table at their fingertips through drill. Concept would be knowing that e.g. 4 x 4 = 4 + 4 + 4 + 4.

So a child that understand the concept of multiplication could continue to the next topic in math but drill on the side to improve on speed.

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I have, at times, done a few minutes of flash cards with a child, in addition to the regular conceptual lesson. My daughter learned her multiplication tables by simply looking them up on a chart as needed; at first, she looked up a lot, and over time, she needed the chart less and less. We also use the Saxon timed facts practice tests to build speed with memorizing the basic facts.

My son does the mental math exercises in the HIG for Singapore. I think games could also be useful for learning facts. If the child understands what 6 x 4 means, I'm fine with moving to the next concept even if the child doesn't always come up with 24 quickly when encountering 6 x 4.

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How did he come out 4+2? Do u feel he understand it? It seems 10 mins to come out 2+ 4 is a bit much. I will not move him on because it will just add frustration. I moved my kids on when they at least have some proficient. 5-10 mins just a bit much

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We separate arithmetic and math, but I wouldn't consider 4 + 2 and 43 + 20 to be different concepts; they're both addition, and I wouldn't move on to the latter with a child who was struggling with the former. I suppose if the latter were part of a lesson in place value, and the child was focusing on the idea that 4 tens and 2 tens uses the same arithmetic as 4 beetles plus 2 beetles, then I would just tell him that they made 6 tens. We often help out with the arithmetic in a math problem so that the concept being taught isn't derailed by "brain blinks."

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Taking that long to figure that out isn't a lack of understanding per se... it's a complete lack of focus. I've seen my kids do that a few times. I don't take it to mean they don't get the math. More that they need to eat, sleep, run, or SOMETHING before they can do any more math for the day. :tongue_smilie:

I think of it as going sideways. If I just kept at ds to learn his times tables, we'd probably be at that all year long. But I know he understands how to calculate them. If I give him paper or manipulatives or just a little time, he can figure them all out - he just isn't at the automatic stage... yet. In the meantime, we can keep practicing them on the side and do something else... some place value, some adding time, some introduction to division, some word problems, and so forth.

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Well for my 2 ds not knowing the facts well enough kept causing melt downs during math because the larger the problems got the more time it took them to do each problem because of not knowing the facts well enough. We are doing mm2 moved over from MUS, because there is alot of fact review in MM2 but I printed out some of the sheets for MM3 like clocks, calendar etc. I am going to throw those in, so partly they will be moving ahead while still working on the facts. We also got a flashmaster and I have seen improvement with it.

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He understands the concept of addition - that 4+ 2=6 but just struggles to get to the answer. He does gets easily distracted by brothers., hunger, wanting to play, etc.

Thanks all. I will go back and reread again.

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For what it is worth:

• Try doing math as the first subject of the day.

• Taking that long to figure out 4+2 is concerning. How is your DS at mental math? Along with my first point, does your DS do better at different times of day?
• Practice skip counting in the car.
• I am a firm believer in math drill once a concept is understood. For example, Singapore Math teaches the concept of number bonds for faster computation, but to get that concept put into use, it needs to be practiced until it becomes second nature.
• You need to look at your son holistically in an effort to determine if you have a "lack of focus" issue or something more. Just so you don't feel alone, my DD has a "Whole lotta attitude" issue that gets in the way everyday. If memory serves, my DD too might have had difficulty getting 4+2 at the beginning of 3rd grade.
• I'd refrain from moving on in math too quickly. To me, moving would be a recipe for building huge learning gaps and frustration. Work on number sense, simple addition to 10 and not just computation but using it everyday adding cans to the shopping cart type of thing. I have my older kids always do the tip in restaurants.

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Can he use his fingers? I think a hands on manipulative, since he understands the concepts, could make things much less frustrating.

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I think it is an error to focus on concepts while ignoring memorizing basic arithmetic facts. You can see this yourself in your ds's example.

Back in the 60s, the professionals started that whole New Math debacle. I spent six weeks in a new school with that stuff.:glare: Then, instead of saying to themselves, "wow--that was dumb. We should go back to what used to work," they decidedd that the problem was that children weren't understanding concepts, and that all childrenn needed process math (manipulatives). So off they went in that direction.

But the thing is that traditional math--memorizing basic arithmetic facts and learning how to use them IRL--actually works. Not memorizing math facts and never learning how to use them, or not ever using manipulatives when appropriate.

See, all that time was sucked out of your ds's life that he'll never get back, because some Math Expert decided that children must understand the whys of math at all times in all situations. The truth is that they just need to know that 4+2-6. You can show them what that looks like with manipulatives, and you can have discussions with them about how many apples you'd have if you started with four and your friend gave you two more, but to spend a great deal of time right off the bat making children "understand" what that means is just counterproductive, IMHO.

That's one reason I like R&S's arithmetic so much. It spends the first three years on basic arithmetic before moving into more advanced concepts, so the children are truly ready for them because their arithmetic is solid.

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Yesterday we were adding 43 + 20 and it took him 5-10 minutes to figure out 4+2=6.

Does he not understand place value? When my kids see 43 + 20, they don't see 4+2. They see 40 (4 tens) + 20 (2 tens) and 3+0. They also have a visual abacus in their minds.

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For us separating out fact drill while moving on means rearranging the chapters in Singapore when necessary. There are a lot of self-contained measurement and geometry chapters. So a student who is still working on mastering the facts can be working on some unrelated topic like telling time on an analog clock, or what have you.

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He sounds like he may be a visual learner. Have you given him a manipulative to work with? Visual learners often take a longer time to learn facts, and it helps to give them a visual representation. C-rods worked for my VSL. He now has pictures of C-rods in his head to recall his facts.

For a problem like you described, I would have the bucket-o-C-rods sitting next to my son, and say, "If you need to use the rods, you can." So if he's stuck computing 4+2, he can pull out the rods and compute it quickly. (and I disagree that he necessarily has an issue with place value - adding 4 tens and 2 tens is still a problem of 4+2=6)

Math Mammoth has tons and tons of fact practice, though it sounds like you're needing the grade 1 level fact practice. Or you could just print out sheets from math-drills.com to practice them. Just work for 5 minutes, stop where he is, then pick up there the next day. Let him use manipulatives in the process.

You could skip ahead to the geometry section of the 3rd grade book while continuing to practice basic addition/subtraction facts in the 1st grade book or via drill sheets. But definitely make sure he has a manipulative to use... sounds like he needs it. My oldest kid never needed manipulatives, so I don't use them with him, but my middle kid definitely needed them - he thinks in pictures, so jumping to abstract symbols wasn't going to work. He needed to SEE that 4+2=6 first.

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