Initially teaching multiplication facts

[Sarah0000]

What are the different ways to approach the stage between conceptually understanding multiplication and rote drill for speed? I haven't really found any threads on this topic. Do folks go straight to drill?

 

So I've been approaching it by teaching DS strategies for easy mental arithmetic rather than just memorizing the fact. Do most people do this? Why or why not? Which curriculums approach it this way? We're not using a curriculum (for this) right now, but here's what we've been doing so far:

 

1x : Obvious

2x : Just doubles addition facts

3x : The double fact plus one more group (3x7=2x7+7)

4x : The double fact doubled (4x7=2x7+2x7)

5x : Divide the next lowest even number by two and that's how many tens plus the left over group (so 5x6=6/2=3 tens and 5x7=6/2=3 tens plus one more 5)

6x - 8x : Haven't gotten there yet. Ideas? Might just wait until the others are memorized then encourage doubling and adding on other facts.

9x : Multiply by ten then subtract one group (7x9=7x10-7)

10x : Obvious

11x : Mostly obvious

12x : Haven't gotten there yet. Probably do ten facts plus two groups.

 

After he gets more practice calculating these (mostly from playing Mythematical Battles) I figure he'll start memorizing them, then that's probably a good time for the usual drill options for speed.

[Kiara.I]

RS does some tricks.  A lot of it is using the abacus to SEE what 6 taken 8 times is (you can see that it's a full 25 of the blue beads, plus another 15 of the yellows and another 8.  And then a good deal of creating a multiplication chart, and then using the multiplication chart.  And lots of games for practice.  They don't really do rote drill at all.

[fourisenough]

I basically used your way (deriving the facts) + memorizing skip-counting songs. My DDs could usually figure-out the facts one way or the other. As they did it more often, they picked up speed, but all eventually needed drill to move them toward automaticity. For drill we used everything from Calculadders, to Wrap-ups, to Xtra-Math, to old-fashioned flash cards. Sounds like you're on the right track.

[Sarah0000]

I did make a few RS abacus inspired dot flashcards for a few of the 6x facts. But when he needed to multiply he will derive the answer some way rather than remembering the way the dots look. I do have Activities for the Al Abacus though and I'll take a look for multiplication.

[MeganW]

We did skip counting songs, then deriving, then memorization.

[Monica_in_Switzerland]

Personally OP, I think you are on the right track to teach fast calculation rather than skip counting or rote memorization.  

 

I say this because I have discovered that my 9yo (using SM5) is still skip counting often for facts, even though he has beaten TimezAttack (a rote memorization game) many times, and even though I have belatedly shown him the tricks you listed in your OP.  He goes to skip-counting as his first strategy if he doesn't immediately recall the fact, and unfortunately, he regularly comes up wrong from making a skip-count error of one kind or another.  He also occasionally mis-remembers a "rote memorized" fact.  It's really aggravating for me!!!  LOL.  A lot of what we did earlier in SM5a has been factoring numbers, and he cannot "see" the factors quickly and easily.  

 

So, I find myself remediating this by really drilling the calculation tricks you have listed.  We are really spending a lot of time on this and I regret not teaching him the fast calculation way from the start.  We are also doing something called the 60-second sweep (google it) which is a great way to get kids going faster on factoring and division.  

 

My dd, in SM2, is now in the multiplication chapters, so we are going straight to the fast-calculating method, rather than skip counting or rote.  Once I can see that she can do fast calculation for all her facts (so probably not until we're in SM 3 or 4), I will put her in front of TImezAttack if I feel she needs some speeding up.  But I really doubt that she will.  

 

As an aside, I have a degree in physics, and so am obviously very mathy.  I have never, ever, memorized my facts.  I do fast calculation each and every time.  Every Time.  7x8 will forever by 7^2+7 for me.  6x8 will forever be 5x8+8.  Now, I've done that fast calculation so many times in my head that I can pull out the answer in the same time it might take a normal person to pull up the relevant fact, so it's not big deal. 

 

I truly regret not using the fast calc method to teach multiplication initially with ds, and have changed my ways with dd.  And of course, doing a fast calc is also going to help some of the properties of multiplication become ingrained before they necessarily learn things like distributive property and the like.  

[Laura Drexler]

1.  I found a full set of Cuisenaire rods very helpful in explaining what, e.g., 6x8  physically looks like.

 

2.  I had my child fill out a written grid multiplication chart at least once a week. Overwhelmed at first, she relaxed visibly once I took a highlighter marker and struck a line through the 1's (because they are given), then struck lines through anything she could skip count (2's, 10's, 5's, 3's).  She was able to tell me 4's through 4x5. By then the number of completely empty spaces without markings was reduced to less than a dozen math facts.

That was much more doable.

 

As her first missed 4 was 4x6, I took a fine point Sharpie and wrote it on the inside of her arm, which she thought was pretty cool. I then asked her, how much is 4x6? When she said she didn't know, I told her to look at her arm. This was 6 months ago. To this day, when asked for 4x6, I can ask her to look at her arm and she suddenly remembers the answer (and yes, the Sharpie was washed off that evening).

 

For the rest of the year, I let her strike through the 1's, then complete the grid to the best of her ability, leaving blank the ones she didn't know. This helped me to know where to focus. 

 

3.  When it seemed that she couldn't remember 6x7, 7x8, 6x8, and 8x8, I looked for a more kinetic approach than I'd been using.

I took chalk to the pavers and created a random grid with the numbers: 5,6,7,8, 9, 35, 45, 48, 54, 56, 63, 64. We enlarged it later, but I found the smaller grid was preferable.

Grid might be:

64  56  63   9 

 7   6   5   54

35   8  48  45  

 

The Math Hopscotch Game:

Write the numbers you'll be using with chalk in a random 4x3 grid. 

Have the equations written out or choose the flash cards you will be using. 

Player 1 takes a flash card and calls the two multipliers to Player 2.

Player 2 jumps to first multiplier, then to next, then to the answer. A correct answer yields a point. Winner gets to... (name your prize)

Player 2 then calls out the multipliers to Player 1. 

Game is played till all flash cards are done.

 

I suppose this could also be done with a Twister board and number assignments!

 

After going though all the combinations we had, her assignment was to go through the flash cards twice again on her own. She loved it. It was glorious, it turned the key for her to memorizing her math facts through the 9's, and she got to jump around during math session for 20 minutes.

 

Hopefully these ideas help. :)

[Holly]

MUS teaches lots of little tricks like this.  Some of them I hadn't heard before.  Gamma is completely on multiplication, and teaches a mix of skip counting (with a CD you can buy) and strategies for some facts.  With some facts like 2s, 3s, 5s, and 12s, I think skip counting is helpful.  However, I don't think teaching them some shortcuts will do harm either.  We do a bit of both.  

 

I can't remember too many of them myself, since we haven't done Gamma in awhile--I'll have a Gamma student next year.

Edited June 26, 2016 by Holly

[Elizabeth 2]

I had an awesome teacher for 4th and 5th grade that taught me lots of initial calculations and memory triggers.  Then it was just drilling it until it became second nature. The above suggestions, plus random things that helped me and DS were:  

 

Give a week, at least between each family, drilling on the fresh one daily through skip counting and quick mixed quizzes.  Focusing on learning the majority of one family before throwing in another.  

 

Saxon recommended drawing out the pattern for each family on a 100s chart, and that made a *huge* difference for DS.   (That was probably the best thing to come out of that program. :D)  His brain recognized how the tens and units changed with addition of each group.  We did it together, but I let him look and see if he finds something that makes sense to him.  If not, then see if the pattern you see makes sense to him.  

 

Anchor facts: 1x, 2x, 5x, 10x, 11x, and Squares.  These become points of reference for quick calculations.

 

7x3 is 21.  (I have no idea why this was important, but it became an anchor for the 3s that I could then calculate from.)

 

Phrases to trigger memory:

 

six times eight is fourty-eight (rhythmic chant)

 

7x7 is 49, less 7, is 42. The answer to the universe and everything in it.  

 

 

9x: the digits always add to 9.  use fingers for under 9x12, then memorize that 9*12 is 108.  

 

12x: learn it last.  It can became a continuation of the fact family.  So 9x12 = 99 + 9, 12x8 = 88+8, etc.  Or, see if DS finds his own pattern to them.  

 

Perhaps out of one of these random ideas, something will help. :)

 

Edited because I haven't had coffee and my brain isn't cooperating. 

Edited June 26, 2016 by Elizabeth 2