# How do I teach math facts?

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DD is in 1st grade in a small, private school. One month in and it is painfully obvious that she needs to be AS in math. The teacher sends home flash cards every night, but DD is clueless and completely guessing. So my question is this: Is learning the match facts simply a matter of memorization or is there some work I can do with DD to help her along? I would love some suggestions of straightforward curriculum we could do together; however, DD is very much a 'do-it-yourselfer' and would do well with computer based learning too.

Thanks for any suggestions!

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Dd (6) just spent 3 weeks learning her math facts. I first went through the stack of flash cards (0+ through 9+ cards) to see what she knows. Then we started to memorize them one set at a time. For some there are tricks I told dd, maybe not standard ones but they helped dd: jump 2 ahead in your head for the +2s, count on for each point on the 3 on +3, doubles you count by 2s, +9 I told her to subtract 1 from the number and then put a 1 in front of the number, and for near double cards I told her to figure out the double for the smaller number and add 1. We also memorized the addition facts that equal 10. By the time she had these cards down there were only about 8 she is having trouble with, for those we are just going over them every day and writing them.

We are about to start the subtraction set of cards, but for these I will begin to introduce families. Since she will know her addition facts, the subtraction wont be so hard.

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I used Saxon 1 last year for dd6 (K at that time) and they had a great system for teaching math facts. I liked it because it made sense.

They teach doubles, then doubles plus one, etc. There is a timed drill every lesson for Saxon 2 (also did that for dd8- first grade at the time).

Honestly, you wouldn't have to buy Saxon to figure it out. Just get some good cards, work in a systematic manner, and drill. Also, get some music to listen to with the facts. It's amazing what kids will remember with songs.

Though we don't officially do Saxon math this year (probably go back to it next year), I still love those cards and timed drill sheets, and we use them every other day to review.

Math facts have to be drilled often for short periods of time. At least that is how my dd6 keeps up.

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Don't aim for mere memorization. It's much more important your daughter understands what is going on first. Start with manipulatives, eventually having her teach you the concept. For example, once she understands how 5 + 3 = 8, ask her if she can teach it to you. Teaching math concepts helps to cement the ideas. Initially, keep lessons short and fun and try to do them often, maybe 5" and twice a day. Once she understands what is going on, then have her work on memorizing.

Besides the other suggestions mentioned, we liked using the triangular flash cards:

My youngest also loved this DK book which we'd read as part of his bedtime routine.

http://www.amazon.com/First-Math-Book-David-Clemson/dp/1564584577/ref=sr_1_3?s=books&ie=UTF8&qid=1316007063&sr=1-3

Good luck. :)

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We used SM and I really like it. I would highly recommend it. I don't think memorization is any good without understanding.

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I'm currently working with all 3 of my girls to learn their math facts. One of the things I do is print a set of worksheets from this site: http://www.math-drills.com/addition.shtml that focuses on one number - adding 2's or 9's etc. My girls work for 30 minutes a day going through the set of 10 worksheets, and they check their own work as they finish each sheet. After the 2nd or 3rd sheet they are usually working very fast and by the 10th they've memorized the facts for that number.

We downloaded a math facts program called Sterling Math Facts (there is a 7-day free trial and then it's \$10) and I set which facts they work on, how many, how long before showing the answer, etc. They do this daily as well, and it only takes about 4 to 5 minutes to go through 50 facts or so. If they get any of the facts wrong they copy those down about 3 times. Now all the girls are making 98 to 100% each day.

This method has been very effective for us.

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These are some very helpful ideas. DD is reading like a champ, but is definitely lagging in math. I just want to get her off to a good start so she doesn't get it in her head that she's 'bad' in math!

Thank you all again!

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Memorizing + knowing some of the mental tricks is great. My daughter (3rd grade) intellectually knew the tricks, but was still very slow at her math facts. We're speeding through using xtramath.org and it's helping a TON! Just drill, very plain, no frills. It only takes about 10 minutes per day. All of my kids really like using it and seeing their daily progress.

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Memorizing + knowing some of the mental tricks is great. My daughter (3rd grade) intellectually knew the tricks, but was still very slow at her math facts. We're speeding through using xtramath.org and it's helping a TON! Just drill, very plain, no frills. It only takes about 10 minutes per day. All of my kids really like using it and seeing their daily progress.

Does xtramath help with learning the math facts or just drilling once they are already memorized? At this point, DD needs to learn the facts *cold* so that she doesn't fall behind in school. Once she gets comfortable with the facts, I will AS with more of a mental math kind of program.

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My only success recently is with card games. She's loving these.

I'm talking a basic playing deck of cards and adapting games to them.

We might sit for an hour and play and then I hear this from her:

"Okay, I'm bored with this one, let's make up a new game..."

I get new ideas and rules off the web, they seem pretty endless.

http://www.pepnonprofit.org/uploads/2/7/7/2/2772238/acing_math.pdf <--this is our favorite one

Edited by one*mom
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My only success recently is with card games. She's loving these.

I'm talking a basic playing deck of cards and adapting games to them.

We might sit for an hour and play and then I hear this from her:

"Okay, I'm bored with this one, let's make up a new game..."

I get new ideas and rules off the web, they seem pretty endless.

http://www.pepnonprofit.org/uploads/2/7/7/2/2772238/acing_math.pdf <--this is our favorite one

The list IS endless! This will be perfect for DD!!!

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I really like http://www.more.starfall.com There is an annual fee though.

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Skip counting really helped my kids.

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Does xtramath help with learning the math facts or just drilling once they are already memorized? At this point, DD needs to learn the facts *cold* so that she doesn't fall behind in school. Once she gets comfortable with the facts, I will AS with more of a mental math kind of program.

She did not know them well. She would count on her fingers, etc. It's basically a flash card program that can be done independently. We had long been at the point where not knowing her facts COLD was holding us back in math. I didn't want to move on until she really had them. This is finally what has zoomed us ahead.

She had already learned the "tricks" for doing the math in her math program (Singapore, then Mammoth Math), but was not fast at applying the tricks. In fact, I think cold memorization works much better for her than tricks.

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Memorizing "math facts" is a terrible way to learn math. Flash-card type knowledge is as thin as the card it is written on.

It would be far better to use one of the fine math programs available to home educators that emphasizes developing mathematical understanding, otherwise you may only achieve a false perception of competence through memorization, but with out true understanding it will be hollow in the long run.

Read Liping Ma's "Knowing and Teaching Elemental Mathematics" to see the difference between teaching for understanding and not.

Best wishes,

Bill

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I'll admit up front that I'm not a "math person" and I have never read Liping Ma's book. Take that for what it is worth here . . .

While I agree that ONLY memorizing math facts is not sufficient, I am wondering if there should an expectation of quick recall for ease of use?

Using drills and math fact cards ONLY would never work for true comprehension, but could it help for ease of use?

I've seen Asian kids (both from China and Singapore- living in Indonesia now) who were sent to Kumon from young ages and they are flying through calculations because of the memorized facts. The same school has expat (American, Australian, etc.) kids who were never drilled and forced to memorize and continually struggle because they just haven't memorized the basic fact tables.

This is certainly a bigger question- I don't want to distract from OP. Just thinking out loud.

ETA: I will certainly be getting Liping Ma's book now!

Edited by 3Blessings
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Memorizing "math facts" is a terrible way to learn math. Flash-card type knowledge is as thin as the card it is written on.

It would be far better to use one of the fine math programs available to home educators that emphasizes developing mathematical understanding, otherwise you may only achieve a false perception of competence through memorization, but with out true understanding it will be hollow in the long run.

Read Liping Ma's "Knowing and Teaching Elemental Mathematics" to see the difference between teaching for understanding and not.

Best wishes,

Bill

I completely agree. If you were referring to my most recent message above, I do teach for understanding. My DD knew that, for example, to do 9+8 you can take 1 from 8 and make the 9 a 10 to get 17. (Singapore and Math Mammoth are very thorough in teaching mental math.) My DD was just very slow at that sort of process and would revert to finger counting. Now, she's learning that it's actually FASTER to do the mental trick rather than count on fingers and she can beat the timer more easily and consistently. The flashcards (and those Xtramath smiley faces!) have been her motivation to speed up. I would not teach flashcards and then go back and teach the underlying process. She HAD the process; she needed to speed it up.

The end goal is yes, understanding, but it must also be speed and memorization.

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I completely agree. If you were referring to my most recent message above, I do teach for understanding. My DD knew that, for example, to do 9+8 you can take 1 from 8 and make the 9 a 10 to get 17. (Singapore and Math Mammoth are very thorough in teaching mental math.) My DD was just very slow at that sort of process and would revert to finger counting. Now, she's learning that it's actually FASTER to do the mental trick rather than count on fingers and she can beat the timer more easily and consistently. The flashcards (and those Xtramath smiley faces!) have been her motivation to speed up. I would not teach flashcards and then go back and teach the underlying process. She HAD the process; she needed to speed it up.

The end goal is yes, understanding, but it must also be speed and memorization.

I actually wasn't picking on your post, and was trying to speak to the OPs original question. I get why one might, after working repeatedly through re-grouping strategies and math concepts, want to work on "speed." I get it.

I just think (as I believe we both agree) that too many people get the idea that simply memorizing "math facts" is the way to learn or teach math. And that is what I'm speaking about. It is insufficient, and potentially counter-productive if it gives a false sense of competence.

I think the analogy with reading is pretty sound. Most people in this community would probably shrink in horror if someone posted that they had a big pile of flashcards that they intended to drill their child with until they had them "memorized", rather than bothering with the hard work of phonics instruction.

Yet, many people use exactly the same approach they would abhor with reading to "teach" math. I think it is a huge mistake.

Bill

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Flash-card type knowledge is as thin as the card it is written on.

Ha ha! I really like this sentence. :)

To the OP,

You have gotten good ideas from prev. posters. I will only add, work with manipulatives for understanding, then give lots of practice, and finally, wait a few months. My dd is the same; she needs more time to understand and own maths concepts. Whatever it is that we are trying to teach her, we found that she generally gets it easily after about 6 months (!) Don't worry about her "falling behind" in school. As long as she catches up by the time the standardized test comes up, she'll be fine. Here, in Singapore, we have a big standardized test in grade 6. So I am hoping that my dd will get all necessary concepts by then.

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I will take all of this great advice into consideration. I do realize that there is alot more to it than just drilling math facts and now just need to decide the best way to proceed with DD.

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So is there a curriculum that anyone could suggest that would accomplish both goals (facts and the 'why's' behind them)? I realize there is no one magic bullet, but for a variety of reasons, I need to keep it as simple as possible. FWIW - DD is using Houghton-Mifflin (sp?) at school.

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So is there a curriculum that anyone could suggest that would accomplish both goals (facts and the 'why's' behind them)? I realize there is no one magic bullet, but for a variety of reasons, I need to keep it as simple as possible. FWIW - DD is using Houghton-Mifflin (sp?) at school.

The program we use (and one I highly recommend) is Primary Mathematics (Singapore).

But others to consider that may (or may not) better suit your style are Math Mammoth and Math in Focus. Both of these use a Singapore approach in a different format than Primary Mathematics. RightStart is another whole-parts maths program that many people love, especially in the early years.

You may need to do some research and make an "educated guess" on which program might fit your teaching and learning needs best. I have only used Primary Mathematics (which I love) but any of these a known solid programs, and each has reasons to appeal to different users.

Best wishes.

Bill

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I like this book:

Once they understand what addition is, of course, which isn't really a difficult concept.

The book takes you though a systematic way of learning the facts. It's not quite as conceptual as Singapore (which is a great curriculum, I used it--it's not strictly good for learning facts. In fact most people complain that Singapore doesn't teach facts. Not true, but it's not contained in the curriculum.) I like Singapore, but we don't have time to after-school a full curriculum during the school year. That's a trade-off we made, when we decided to put her in school. My plan IS to use Singapore over the summer and use the school year to support what she's doing in school. That works for us, because I feel their math program is solid. Not terribly imaginative or conceptual, but it's solid. I won't name it, lest Spy Car suffers a case of apoplexy. :)

Back to the book, Once they learn doubles, for example, it teaches "near doubles" or "the one in between". So, 4+6----- the number in between is 5 and if you double 5, you get 10. It teaches the trick, does some drill sheets, and instructs you which flashcards to use. It also teaches subtraction as a natural offshoot. If they know 4+6, then have them learn 10-6 soon after.

Along with the book, we play a board game called "Sum Swamp", we play Right Start games, we have math games on my I-pad, etc., etc., etc.,

I just bought the multiplication version of the book to start with older dd.

Edited by snickelfritz
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We have enjoyed games like Sum Swamp and Dino Math Tracks. Yahtzee is a little harder but also fun.

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I agree with so much posted. Skip counting definitely helps prior to memorization. You can do this while tossing bean bags, balls, yarn balls, etc. Some Manipulatives are great - try flat marbles (the type that go in vases) ,group them and then count the groups. The little groups are beautiful to touch and appeal to boys and girls. We call them pirate treasure. Use cuisenaire rods and Miquon puzzle books. YOu could try Rudolf Steiner Waldorf stories about the squirels that collect the groups of nuts and then lose some groups. The stories can be drawn and colored and it helps create memory hooks. Or create stories about King Minus (with holes in his pocket, King Plus (always has an abundance), King Divise(likes to share with others), King Multiply (hangs on to what he has) - again drawing and illustrating help. It all depends on the childs learning type. My ds and dd are great mathematicians but they did not understand why they needed to memorize things when they were younger. Give it some meaning.

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I agree with so much posted. Skip counting definitely helps prior to memorization. You can do this while tossing bean bags, balls, yarn balls, etc. Some Manipulatives are great - try flat marbles (the type that go in vases) ,group them and then count the groups. The little groups are beautiful to touch and appeal to boys and girls. We call them pirate treasure. Use cuisenaire rods and Miquon puzzle books. YOu could try Rudolf Steiner Waldorf stories about the squirels that collect the groups of nuts and then lose some groups. The stories can be drawn and colored and it helps create memory hooks. Or create stories about King Minus (with holes in his pocket, King Plus (always has an abundance), King Divise(likes to share with others), King Multiply (hangs on to what he has) - again drawing and illustrating help. It all depends on the childs learning type. My ds and dd are great mathematicians but they did not understand why they needed to memorize things when they were younger. Give it some meaning.

I was browsing around the Parent-Teacher Store yesterday and started chatting with a woman who has just opened a Montessori-based Enrichment Center near our home. She basically said that dd probably needs some real life application in order to make it stick - ie, 'give it some meaning'.

Thanks!

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Abook call outliers, also, briefly mentions giving math some meaning. The content of the chapter really discusses why Asians are ahead of the US in math.

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