Do you teach math tricks?

[madteaparty]

I was sitting at soccer yesterday near a teacher correcting homework. It was mostly worksheets off superteacher or some website, teaching the various 9 tricks with multiplication. 

I’m having a bit of a wobble as I plan her education next year, math especially, so I’m wondering, are these tricks worth teaching? Her school has not covered multiplication yet (2nd grade), so I’ve been teaching at home with a bit of MEP. It’s been slow going (bc we are both lazy, plus it’s afterschool) but it’s also all been basically memorizing. I would have to learn these tricks myself and then teach. Is this worth doing? Or carry on with the drill?

[Sherry in OH]

If by math tricks you mean 

• all even numbers are divisible by 2
• if the digits of a number sum to a multiple of 3, the number is a multiple of 3
• if the last two digits (tens and units) are a multiple of 4 the number is a multiple of 4
• if the final digit is 0 or 5, number is a multiple of 5
• etc.

Yes, they are worth teaching.  It is also worth teaching why the divisibility rules work.   They are very useful when factoring large numbers.  Look ahead in MEP, divisibility rules are covered at some point.  I think 2, 5, and 10 are covered first, followed by 3 and 9 and then other numbers.

 

[Sarah0000]

I'm not sure if you would call these tricks. I show them with rods. I teach:

3s: double then add

4s: double double

7s: 7×7 is the perfect square closest to fifty

9s: multiply by 10 then subtract 

 

[HomeAgain]

Yes to teaching things like above.  No to teaching Russian math or finger tricks - I touch on them, but I don't put emphasis on them.  Yes to using check numbers to make sure the answer makes sense.

I'm actually a little fascinated by ds's math curriculum. Until we got to the second book, I had no idea that c-rods were developed to show number families by specifically color coding the blocks a certain way. The multiplication chart is color coded as well to show the relationship between say, 3x, 6x, and 9x a number.  So there are tricks we teach, but they're not out of place from the study of math and patterns.

[madteaparty]

1 hour ago, HeighHo said:

The student should leave having internalized the associative, distributive, commutative, and  identity properties of multiplication.

I honestly have no idea what this is.

[Tanaqui]

The associative property of multiplication states that it doesn't matter how you group the numbers, you'll still get the same answer. Given 3 x 4 x 2 you'll get 24 regardless of whether you decide to ultimately multiply 12 x 2 or 3 x 8. (This applies to addition as well, where it's the associative property of addition.)

The commutative properties of multiplication and addition state that it doesn't matter how you order the numbers to multiply (or add) them, you'll get the same answer. 2 x 7 = 7 x 2.

The identity property of multiplication just states that any number times one is itself. The corresponding property for addition states that any number plus zero is itself.

The distributive property of multiplication states that n x (a + b) is the same as (n x a) + (n x b). Or, in easier terms, 4 x 15 is the same as 4 x 10 plus 4 x 5.

This is basic pre-algebra material. It's also useful for understanding why our arithmetic algorithms work the way they do. It sounds like you need a brush-up yourself, especially if you intend to teach your child through algebra.

Edited March 14, 2019 by Tanaqui

[madteaparty]

18 minutes ago, Tanaqui said:

The associative property of multiplication states that it doesn't matter how you group the numbers, you'll still get the same answer. Given 3 x 4 x 2 you'll get 24 regardless of whether you decide to ultimately multiply 12 x 2 or 3 x 8. (This applies to addition as well, where it's the associative property of addition.)

The commutative properties of multiplication and addition state that it doesn't matter how you order the numbers to multiply (or add) them, you'll get the same answer. 2 x 7 = 7 x 2.

The identity property of multiplication just states that any number times one is itself. The corresponding property for addition states that any number plus zero is itself.

The distributive property of multiplication states that n x (a + b) is the same as (n x a) + (n x b). Or, in easier terms, 4 x 15 is the same as 4 x 10 plus 4 x 5.

This is basic pre-algebra material. It's also useful for understanding why our arithmetic algorithms work the way they do. It sounds like you need a brush-up yourself, especially if you intend to teach your child through algebra.

Ah, thank you. Right, I know these. I’m talking about teaching the basic facts of multiplication in late second grade and wondering what room there is for these tricks which to me seem to require more mental power than straight memorization 

[alisoncooks]

Yep. I've got a kiddo that struggles to remember multiplication facts but can remember "tricks."  So I do: 

5678 (56=7x8)

School House Rock song for 3s

the 9s fingers

4s table = just double the 2s

12s table = take the 10s and 2s table and add

11s trick (11x any 2 digit # = split that number and stick the sum in between. So 11x34= 3____4. 3+4=7, so 374.)

We use whatever works/helps. I'm sure people will say that if she can remember the above, she can remember just the facts. Sure...if you say so (because why would we choose to add unnecessary work if the other was sufficient?)

Edited March 14, 2019 by alisoncooks

[gstharr]

If you mean like Dr Arthur Benjamin , or the guy on television teaching  kids to do 5 digit multiplication in their head, then the answer is no.  The 8th grader has several of the trick books. He can do some right after he memorizes trick, but a week later cannot.  Some of the rules, especially for that guy on TV are quite complex. Just not worth the effort.  But, you might enjoy Dr. G.  He teaches at Claremont.  He a popular speaker in our area.  The 8th grader gets to see him at least once a year. 

 

[Miss Tick]

If your child is a whiz at remembering the facts after a bit of repetition none of this discussion will be particularly necessary. If, however, you find dc stumbling repeatedly over, say 3x something, you will want a stock phrase to use to remind them how to figure that out. I start by saying, "well, you know what 2x that number is, so you just need one group more than that." As the months pass I let my eyes glaze over as I say this. Eventually I take a deep breath before beginning. At some point they either memorize the facts or the help sentence, doesn't really matter which because now they know it or how to derive it, and eventually they just know it.  Having a stock phrase is really helpful *for my kids*. You may not (be driven to such desperate measures) need that.

[Tanaqui]

41 minutes ago, madteaparty said:

Ah, thank you. Right, I know these. I’m talking about teaching the basic facts of multiplication in late second grade and wondering what room there is for these tricks which to me seem to require more mental power than straight memorization 

 

The basic properties of addition and multiplication are not tricks - and their power lies in that they DO require more mental power than straight memorization. Memory can fail. Understanding doesn't.

Edited March 14, 2019 by Tanaqui

[goldenecho]

Absolutely teach the nines trick!   It not only makes learning the nines easy...it brings some fun into it.   When I was a kid I thought the 9s trick was incredible cool.   It felt like magic.  And I pretty much hated math apart from that so....

As for other tricks, teach them where necessary.  If you have a child who struggles with memorization (my kid, for example), combined with the trick of using a nearby math equation you know to figure out one you don't, those tricks give them keys to fill in gaps in their memorization.  I tried the flat rote memorization method first with addition and my kiddo could only go so far with it.   But while memorization was incredibly hard for him concepts came more easily, so when we started adding in more "tricks" he was able to get through it and move on.   And depending about how the tricks are taught they can really help a child understand math concepts in general better ("Multiplication Facts that Stick" is really good about that...they really help kids understand why the tricks work).  

Edited March 14, 2019 by goldenecho

[Targhee]

For multiplication I think some heuristics are ok, as long as it is no more complicated than actually doing the math and leads to mastery eventually.  When teaching addition we teach counting, counting on, and some tricks like 9 steals one to make ten, etc. with the hopes of them using those trucks only as long as needed to remember their addition facts (or be able to quickly calculate).  We do the same for multiplication. I wouldn’t, however teach “tricks” without teaching the math behind it and showing the kids it’s a short cut to the calculation and not just some random or magical thing.

[Sarah0000]

1 hour ago, madteaparty said:

Ah, thank you. Right, I know these. I’m talking about teaching the basic facts of multiplication in late second grade and wondering what room there is for these tricks which to me seem to require more mental power than straight memorization 

Yes but that's a good thing isn't it? It's built in mental math practice especially when the kid doesn't compute the same way every time.

[madteaparty]

43 minutes ago, square_25 said:

 

Well, the thing about learning these tricks is that you're not really learning tricks: you're learning how to play with the definition of multiplication. That means that you get a very good feeling for when it is that you'd multiply (which whenever you are adding up equal groups.) 

Why jump to straight memorization? What's the benefit? Yes, you'll need them eventually, but why is it a pressing need in 2nd grade? 

There’s no rush but I imagine the multiplication table needs learned, and now is when MEP and Singapore introduce it. Is it not supposed to be learned by heart? Or is it exposure at this point? 

[Sherry in OH]

3 hours ago, madteaparty said:

I honestly have no idea what this is.

 

When you say you are using MEP are you teaching from the lesson plans or just using the worksheets?   Concepts, including various ways to approach multiplication, are taught in the lesson plans.  The worksheets are intended to reinforce rather than replace the lessons.  If you only have time for one, skip the worksheets.   Multiplication and division are introduced in year 2.  Students are not expected to have mastered the table until the end of year 3 or 4 (and most of that mastery is through repeated exposure).

[HomeAgain]

1 minute ago, madteaparty said:

There’s no rush but I imagine the multiplication table needs learned, and now is when MEP and Singapore introduce it. Is it not supposed to be learned by heart? Or is it exposure at this point? 

Yes, it is introduced now, but think down the road to the rest of elementary math.  It's all focused on using the 4 operations, just in different ways.  The kids tend to memorize about half the tables with no problem, and through constant, daily work memorize the rest.  Unless it's my kid.  And then 3x8 and 7x8 will be a pain in the butt no matter how long they've been working on them. 😄 But there really is no rush.  If you wanted a way to do daily reinforcement after a while, though, the Thinkin' Logs multiply game from the Toymaker was a huge hit in our house.

[Sherry in OH]

7 minutes ago, madteaparty said:

There’s no rush but I imagine the multiplication table needs learned, and now is when MEP and Singapore introduce it. Is it not supposed to be learned by heart? Or is it exposure at this point? 

 

2 minutes ago, HomeAgain said:

Yes, it is introduced now, but think down the road to the rest of elementary math.  It's all focused on using the 4 operations, just in different ways.  The kids tend to memorize about half the tables with no problem, and through constant, daily work memorize the rest.  Unless it's my kid.  And then 3x8 and 7x8 will be a pain in the butt no matter how long they've been working on them. 😄 But there really is no rush.  If you wanted a way to do daily reinforcement after a while, though, the Thinkin' Logs multiply game from the Toymaker was a huge hit in our house.

 

It is exposure and understanding what multiplication means.  A child who cannot remember 3x8, may know that the product will be the same as 3x4x2.  Only his 4th grade teacher will ever care which method he uses to find 24.

[HomeAgain]

3 minutes ago, square_25 said:

 

I think learning something by rote before you fully understand what it IS mostly results in kids forgetting what they are doing when they are multiplying. Then they have the table but they don't know what it's for. 

It's more important that your child realizes they are multiplying if you ask "How many legs do 6 dogs have?" than it is for them to remember that 6*4 = 24. You do eventually want the latter, but you're currently working on the former.  

 MEP and Singapore are both very good at teaching the why behind multiplication and not focused on rote memorization.  I know that MEP will add in practice after concepts have been explored, puzzled through, skip counted, and so forth.  I was a little puzzled at the OP insinuating it's memorization at this point, but we loved year 2 of MEP and the various methods it brought together (we also used MUS blocks that year for the more complex problems as a hands on aid).  Towards the end of year two there is a lot more focus on the memorization aspect, so maybe that is where they are.

[HomeAgain]

5 minutes ago, Sherry in OH said:

 

 

It is exposure and understanding what multiplication means.  A child who cannot remember 3x8, may know that the product will be the same as 3x4x2.  Only his 4th grade teacher will ever care which method he uses to find 24.

True that.  He developed his own method of grouping into 5s for numbers above, so 7x8 is 5x8 + 2x8.  Eventually I'm hoping these last two facts stick, though, because it does slow him down and/or cause him to have mistakes in his work.

[madteaparty]

20 minutes ago, square_25 said:

 

I think learning something by rote before you fully understand what it IS mostly results in kids forgetting what they are doing when they are multiplying. Then they have the table but they don't know what it's for. 

It's more important that your child realizes they are multiplying if you ask "How many legs do 6 dogs have?" than it is for them to remember that 6*4 = 24. You do eventually want the latter, but you're currently working on the former.  

Oh, yes, most problems we do are like that. Fill this table with the number of legs, etc. 

[madteaparty]

11 minutes ago, square_25 said:

You know me, I'm really very unworried about memorization, but then my kid acquires things very well through exposure :D. 

I really need to print off some MEP worksheets... not having a printer at home makes me lazy. 

 

A real downside to having quit my job is inability to print the random MEP worksheet 🙂. I think I need to have them printed and bound. I wonder if Lulu does that.

[madteaparty]

 

30 minutes ago, Sherry in OH said:

 

When you say you are using MEP are you teaching from the lesson plans or just using the worksheets?   Concepts, including various ways to approach multiplication, are taught in the lesson plans.  The worksheets are intended to reinforce rather than replace the lessons.  If you only have time for one, skip the worksheets.   Multiplication and division are introduced in year 2.  Students are not expected to have mastered the table until the end of year 3 or 4 (and most of that mastery is through repeated exposure).

As afterschool, I have been using MEP worksheets, Singapore Intensive Practice (just finished 2A) and also Process Skills in problem solving (just finished 2). I think it goes without saying we do not do every single problem...Maybe 60% in some and 80% in others. 

[madteaparty]

3 minutes ago, square_25 said:

 

Yeah, my husband will print them at the office for me, I think... 

Yeah but mine won't bind and collate. I've found his limits 🙂

Edited March 14, 2019 by madteaparty

[madteaparty]

7 minutes ago, square_25 said:

 

That seems good :-). Maybe talk to her about how she could do it? How does she compute something like 6*4, do you know? 

Yes, we do talk about stuff like mentioned upthread, like 6x9 is one 6 less than 6x10

Edited March 14, 2019 by madteaparty

[sweet2ndchance]

I think teaching tricks is fine IF AND ONLY IF, the child fully understands what multiplication is and how it works and how to manipulate it. I don't think it is helpful to teach tricks to 2nd and 3rd graders who are just getting started with multiplication and its meaning and uses just so they can pass a timed test. Memorization of the facts will come to most kids in time with lots of low stress (i.e. untimed) opportunities to practice them. But there are some kids who are either very visual learners or have some degree of dyscalculia or memory issues or what have you. Once they thoroughly understand the hows and the whys and the meanings of multiplication, if recall of facts is still causing them to struggle, I see no reason not to try some tricks. I can visualize the finger trick for the 9s in my head (even though I still have to pause a second to remember my right and left) much faster than I can try to add that many 9s in my head. If I had had access to Cuisenaire rods or MUS blocks as a child, I might have been able to visualize those much easier than trying to simply memorize facts like my parents and teachers tried to make me do when I was a child.

I can still visualize the two anthropomorphized number 8s struggling to roller skate on a sticky floor in a picture that someone showed me. The caption was "skate x skate = sticky floor" Up until someone showed me that, I couldn't remember 8x8 to save my life but for some reason that little comic stuck with me and I've never forgotten since then that 8x8=64. Is it a little extra information to remember? Yes but for some reason that comic was so much easier for me to instantly visualize than just numbers and I could visualize that picture faster than I could add eight 8s in my head. For full disclosure, I do have moderate dyscalculia and I was shown that comic in jr high because while I could understand pre-algebra concepts just fine, calculation errors kept me from doing very well. I understood multiplication just fine and everything about it but just flat memorizing numbers, I've never been good at it even if I do understand the logic behind them.

[sweet2ndchance]

Well see, the thing is, in order to be able to double 4x8, I would have to remember what 4x8 was lol! Many teachers and my parents tried to get me to just straight memorize the times tables and it never, never happened no matter how hard I tried. I can remember being in tears over it on more than one occasion. When teachers or my parents caught me using any kind of trick to try to remember, even just skip counting to get to the answer, I was reprimanded and told if I would just memorize the facts it wouldn't be so hard but with dyscalculia, it really can be that hard to memorize number patterns. It's not that I can't see the patterns, I can see them everywhere but to memorize was a whole 'nother can of worms. So my parents and my teachers were frustrated with me because I was obviously smart, I could see the patterns and understood the concepts and I excelled in every other part of school but, and these are their words, I "refused" to memorize my math facts. And then I was frustrated and felt like a failure because I couldn't do what they wanted me to do no matter how hard I tried. It took a very long time and some amazing teachers that understood that not everyone is wired to learn the same way to find my way into loving math again.

Today, yeah sure I can just double 8x4 to get 8x8. I can also see the relationship with 8x5 and 8x3 and how adding them together will get me the same answer. But when I was a child, feeling pressured by teachers and my parents to produce a correct answer instantly, I would inevitably miscalculate trying to do it quickly or overthink it  and get it wrong. With the word play mnemonic and picture that I could instantly produce in my head, I could produce the instant answer they were looking for.

[sweet2ndchance]

I wasn't diagnosed as having dyscalculia until I was an adult. I also have many signs of high functioning autism but I've never been formally diagnosed, just many professionals that I've met as an adult that agree I probably qualified for diagnosis as a child (and still do). But even if I were completely neurotypical, I still agree that understanding concepts is much more important than instant recall of math facts. I never made any of my children do timed tests, not only because they traumatized me but because I don't see a point. I let them use multiplication tables and manipulatives for as long as they needed them. I would much rather they came up with the right answer than a quick answer.

[Sarah0000]

My kid loosely finished 4th grade math and still does not have instant recall of every single multiplication fact. You can still move forward, whenever she's otherwise ready, into multidigit multiplication and division and that will be continued practice of the facts. About every 3-4 months I spend a couple weeks doing drills of the facts and each time there seems to be a few more facts that he's internalized. Sometimes he forgets one that was previously learned but he relearns it quickly. When I first started teaching him multiplication I had to compute quite a lot of the facts first myself to jog my memory.

[Farrar]

The pattern of the 9's table is something you need to know in a sense, just because it reflects the nature of 9 as being like adding 10 and taking one away. The "trick" with the fingers... not so much. But whatever works to help kids memorize them. Rhymes, finger tricks, weird video stories, whatever. Some people on this board talk a lot about concepts leading the way, but honestly, I think it's fine for kids (especially younger kids like this) to memorize first and have the concepts fall in place more fully afterward. Sometimes memorizing first helps the concepts solidify and take on meaning.

The photocopier should collate! And you can get things bound at Staple/Office Depot/FedEx/etc. for a lot cheaper than getting the whole thing done and bound.

[Sherry in OH]

21 hours ago, madteaparty said:

 

As afterschool, I have been using MEP worksheets, Singapore Intensive Practice (just finished 2A) and also Process Skills in problem solving (just finished 2). I think it goes without saying we do not do every single problem...Maybe 60% in some and 80% in others. 

 

I am guessing that you are looking at worksheets with directions such as “complete the 6 times table and learn by heart.”  What you aren’t seeing are the teacher notes indicating that this is a group activity. The class completes the table together – a student or the teacher writes on an overhead while the rest of the class fills in their own tables.  The students are given a few minutes to look over the completed table before being instructed to close their books.  Then as a class they recite the table forward and back.   (This oral recitation is repeated as part of future lessons.) 

You also aren’t seeing the skip counting and extensive use of manipulatives, number lines, and games imbedded in the lesson plans.  Nor are you seeing that some of the problems on the worksheets are intended to keep advanced students busy while the teacher works with students who need more help.  

Since you are afterschooling ahead of her school curriculum, I would disregard any instructions on worksheets indicating that facts should be memorized. If she likes flash cards and drill, certainly do them. If you want to teach ‘tricks,’ teach them. Otherrwise, they can wait.  If she hasn't already learned to skip count, work on that.  Have her use manipulatives until she is comfortable with multiplying.  Given time and practice, most likely your daughter will either memorize most of the basic multiplication facts or become proficient at calculating on the fly.