Resources for multiplication tables

This time of year many students tackle multiplication tables. These resources can be of help:

1. This video explains my method for "structured drilling" of multiplication tables. We don't start with random drill (that comes later) but with drill that is using the structure of the tables. The tables ar ealso practiced "backwards", which will facilitate the learning of basic division facts.
   
   Over the years I have hears from many individuals who have gotten their child to learn the tables using this method, but recently  I got word from a a principal of an English medium school in Pune, India, that they have already implemented my multiplication drilling method and it is working beautifully with their children! I feel flattered a whole SCHOOL is using it... and glad it is working.
   
   
2. Math Mammoth Multiplication 1 book. First it has a long section that concentrates on the concept of multiplication, and then the last part has lessons to faciliate the same drilling as explained in the video.
   
   
3. There is a place for random drill, and you can use flashcards, or the way shown in the video, and/or GAMES. I have compiled a list of online multiplication games here.
   
   This card game is also noteworthy  (the "Product War" version). Essentially, each player is dealt two cards face up, players multiply those, and the person with highest product captures all cards in that round.
   
   Or, try a dice game called Damult Dice.

I feel that learning the multiplication tables well is more important than even mastering addition and subtraction facts. Why? Because knowing the tables well facilitates the learning of basic division facts, multidigit multiplication, long division, most fraction math and factoring. Even in algebra you still need to be able to simplify rational expressions and factor polynomials, perhaps even multiply matrices.

Or, we can say it this way: if you child does not know the tables, he/she will have a terrible time mastering all those topics. I'm not saying children won't learn those topics conceptually -- I mean they will have hard time completing the problems and exercises quickly, and can instead get all "bogged down" just by the multiplications.

That is why I feel every teacher/parent should put forth a good effort for their students to learn the times tables. Spend 1-2 months on it. It can pay off!

That said, there is a BALANCE, as in everything. IF you've already expended a considerable amount of effort and the child is not retaining them, please don't make the multiplication tables to be the reason why your student hates math. You can back off and try again later. Some give their students a "crutch" -- tables written out -- and eventually the kid notices how slow it makes him/her having to check the answers in the table instead of knowing them, and decides to memorize them.

Resources for multiplication tables

This time of year many students tackle multiplication tables. These resources can be of help:

1. This video explains my method for "structured drilling" of multiplication tables. We don't start with random drill (that comes later) but with drill that is using the structure of the tables. The tables ar ealso practiced "backwards", which will facilitate the learning of basic division facts.
   
   Over the years I have hears from many individuals who have gotten their child to learn the tables using this method, but recently  I got word from a a principal of an English medium school in Pune, India, that they have already implemented my multiplication drilling method and it is working beautifully with their children! I feel flattered a whole SCHOOL is using it... and glad it is working.
   
   
2. Math Mammoth Multiplication 1 book. First it has a long section that concentrates on the concept of multiplication, and then the last part has lessons to faciliate the same drilling as explained in the video.
   
   
3. There is a place for random drill, and you can use flashcards, or the way shown in the video, and/or GAMES. I have compiled a list of online multiplication games here.
   
   This card game is also noteworthy  (the "Product War" version). Essentially, each player is dealt two cards face up, players multiply those, and the person with highest product captures all cards in that round.
   
   Or, try a dice game called Damult Dice.

I feel that learning the multiplication tables well is more important than even mastering addition and subtraction facts. Why? Because knowing the tables well facilitates the learning of basic division facts, multidigit multiplication, long division, most fraction math and factoring. Even in algebra you still need to be able to simplify rational expressions and factor polynomials, perhaps even multiply matrices.

Or, we can say it this way: if you child does not know the tables, he/she will have a terrible time mastering all those topics. I'm not saying children won't learn those topics conceptually -- I mean they will have hard time completing the problems and exercises quickly, and can instead get all "bogged down" just by the multiplications.

That is why I feel every teacher/parent should put forth a good effort for their students to learn the times tables. Spend 1-2 months on it. It can pay off!

That said, there is a BALANCE, as in everything. IF you've already expended a considerable amount of effort and the child is not retaining them, please don't make the multiplication tables to be the reason why your student hates math. You can back off and try again later. Some give their students a "crutch" -- tables written out -- and eventually the kid notices how slow it makes him/her having to check the answers in the table instead of knowing them, and decides to memorize them.

Multiplication Mountain songs CD - a review

It has been proven that music can help children memorize things. There is something about the music or the rhythm or both that changes or improves the way our brain works. I haven't studied this effect in-depth; I'm just familiar with the general idea.

So, using music to memorize math facts—or in this case, multiplication tables—is definitely a sound idea.



Multiplication Mountain is a CD by Hap Palmer, filled with songs for the multiplication tables. For each table, there is one song, but it is presented twice on the CD: once sung completely, and the second time without the answers sung. That way, the child can try to fill in the answers while listening to the song from the second track.

I found the songs to be pleasant and jolly, easy to listen to. The musical style varied somewhat so that one song was more jazzy, another was bluegrass, another a waltz, and so on. But they all were melodic, harmonic, and had a medium beat—easy to sing along. My favorite was the song for the sixes times table.

The songs are presented in a particular order: the easiest tables first. Learning all the tables is compared to climbing a mountain: you start at the bottom with the 2s, 5s, 10s, and 11s. You gradually climb up till you reach 7s as the top of the mountain — and then you reach for the sun (the 12s)!

You can listen to samples at www.myspace.com/happalmer (the songs for nines and twos) and at CdFreedom website.

Here's yet another sample of his music from YouTube. It's called Bean Bag Alphabet Rag. It's not from the Multiplication Mountain CD. I just put the link here in case you want to check out the musical and singing style of this artist.
Bean Bag Alphabet Rag by Hap Palmer .

Multiplication Mountain is not the only CD I have that has songs about multiplication tables. I have gotten one other CD in the past, but much disliked that one, because its musical style was rap with quite heavy beats - reminded me of heavy rock. Hap Palmer's music is quite the opposite of that, so I liked it much better (of course, all of us have VERY varying tastes of music).

My older child already knew the multiplication tables when I got the CD, so I could not test how much she would learn with it, and the younger one is not quite ready for that yet. But, in a nutshell, I feel the CD is well done and there is no reason why it wouldn't be effective in helping children to learn the tables.

I would definitely recommend it for anyone interested in trying musical approach to learning the tables and for elementary teachers & tutors in general. Also, if your child has ADD/ADHD or any learning disability, I would suggest that you try music-enhanced learning simply because of the special effect music has on our brain.

Here's a link to Multiplication Mountain CD at Amazon.com.

Disclaimer: I was given this CD for free to review it. I'm not receiving any monetary gain from the company, however.

Multiplication Mountain songs CD - a review

It has been proven that music can help children memorize things. There is something about the music or the rhythm or both that changes or improves the way our brain works. I haven't studied this effect in-depth; I'm just familiar with the general idea.

So, using music to memorize math facts—or in this case, multiplication tables—is definitely a sound idea.



Multiplication Mountain is a CD by Hap Palmer, filled with songs for the multiplication tables. For each table, there is one song, but it is presented twice on the CD: once sung completely, and the second time without the answers sung. That way, the child can try to fill in the answers while listening to the song from the second track.

I found the songs to be pleasant and jolly, easy to listen to. The musical style varied somewhat so that one song was more jazzy, another was bluegrass, another a waltz, and so on. But they all were melodic, harmonic, and had a medium beat—easy to sing along. My favorite was the song for the sixes times table.

The songs are presented in a particular order: the easiest tables first. Learning all the tables is compared to climbing a mountain: you start at the bottom with the 2s, 5s, 10s, and 11s. You gradually climb up till you reach 7s as the top of the mountain — and then you reach for the sun (the 12s)!

You can listen to samples at www.myspace.com/happalmer (the songs for nines and twos) and at CdFreedom website.

Here's yet another sample of his music from YouTube. It's called Bean Bag Alphabet Rag. It's not from the Multiplication Mountain CD. I just put the link here in case you want to check out the musical and singing style of this artist.
Bean Bag Alphabet Rag by Hap Palmer .

Multiplication Mountain is not the only CD I have that has songs about multiplication tables. I have gotten one other CD in the past, but much disliked that one, because its musical style was rap with quite heavy beats - reminded me of heavy rock. Hap Palmer's music is quite the opposite of that, so I liked it much better (of course, all of us have VERY varying tastes of music).

My older child already knew the multiplication tables when I got the CD, so I could not test how much she would learn with it, and the younger one is not quite ready for that yet. But, in a nutshell, I feel the CD is well done and there is no reason why it wouldn't be effective in helping children to learn the tables.

I would definitely recommend it for anyone interested in trying musical approach to learning the tables and for elementary teachers & tutors in general. Also, if your child has ADD/ADHD or any learning disability, I would suggest that you try music-enhanced learning simply because of the special effect music has on our brain.

Here's a link to Multiplication Mountain CD at Amazon.com.

Disclaimer: I was given this CD for free to review it. I'm not receiving any monetary gain from the company, however.

Carnival picks

I have a collection of interesting links for you today; mostly some picks from Math Teachers At Play #2 blog carnival, which you SHOULD visit. Denise always has good stuff and really nice photos to spice up the reading.

Here's a neat way to practice multiplication tables by Math Mojo.

I also liked some simple dissection puzzles; you'll even get a free worksheet download.

Nick has posted two geometry "Wrapper" problems

This one is hilarious - lots of pictures of mathematical clocks!

Those were all from the carnival; please check out all the other posts as well; it is a good carnival!

Lastly, I visited this yesterday, and I think ALL of us should check out what a trillion dollars looks like.

Carnival picks

I have a collection of interesting links for you today; mostly some picks from Math Teachers At Play #2 blog carnival, which you SHOULD visit. Denise always has good stuff and really nice photos to spice up the reading.

Here's a neat way to practice multiplication tables by Math Mojo.

I also liked some simple dissection puzzles; you'll even get a free worksheet download.

Nick has posted two geometry "Wrapper" problems

This one is hilarious - lots of pictures of mathematical clocks!

Those were all from the carnival; please check out all the other posts as well; it is a good carnival!

Lastly, I visited this yesterday, and I think ALL of us should check out what a trillion dollars looks like.

Multiplication tables video

I have finished my very first YouTube video ever... It's about using a structured drill to learn multiplication tables.



I'm a bit excited, but of course I have room to improve! I hope the method is understandable : )

Multiplication tables video

I have finished my very first YouTube video ever... It's about using a structured drill to learn multiplication tables.



I'm a bit excited, but of course I have room to improve! I hope the method is understandable : )

Mnemonic helps for multiplication tables?

...regarding my third grader. We are still slogging through learning the times tables. To liven it up, I decided to order Times Tales (I ordered the deluxe version that includes division as well).

I have read different opinions about using mnemonic devices to learn math facts. Some say that mnemonic devices actually slow the student down, and one even went as far to say it was like counting on fingers. I don't want to use Times Tales if it's going to slow her down, and I do want to make sure she knows her math facts cold.

I, myself, remember I didn't know 8x8=64 in seventh grade, and I just figured it in my head, 8+8=16, 16+16=32, 32+32=64 -- 8x8=64. I did this until I realized how slow I was and decided to commit the facts I didn't know to memory. What do you think about Times Tales and other "helps" for math facts?

Mnemonic helps in themselves are not bad. We use them all the time, in everyday life situations. You have a phone number, you divide it to 2-digit numbers, maybe remember it has successive numbers, or doubles, etc.

I once memorized a certain 4-digit pin number by dividing it to two 2-digit numbers, and remembering that the latter was 9 less than the first... but after a while I remembered it without that.

On Times Tales. It's a fine program in itself. It associates a silly story and picture with each "difficult" upper times tables fact. You've probably seen samples. I don't think it is going to hinder... Basically, if it works for your kid, let's say you will show 8 x 7 to your your kid. He will see 8 x 7 and suddenly also see the silly picture of lady eight and the character 7 driving in a car, in his mind, and remember "It's 56."

It's not too much different from using a rhyme such as "5, 6, 7, 8, fifty-six is seven times 8."

Such a program can be a confidence booster as well.

Now, for some kids it doesn't work because they don't easily remember silly stories, and then it can cause frustration. Or, they're older and don't enjoy the silly stories anymore.

All these "helps" are fine in their place, but you have to be sensitive to your child so that the mnemonic "help" does not end up being an additional burden in itself... such as if the child cannot easily remember the stories or the song or whatever the "help" is.

So it's totally up to you. Try it first with the free sample they offer on their website... and see how your child reacts.

That program is an additional resource of course, and doesn't replace studying multiplication concept itself.

Mnemonic helps for multiplication tables?

...regarding my third grader. We are still slogging through learning the times tables. To liven it up, I decided to order Times Tales (I ordered the deluxe version that includes division as well).

I have read different opinions about using mnemonic devices to learn math facts. Some say that mnemonic devices actually slow the student down, and one even went as far to say it was like counting on fingers. I don't want to use Times Tales if it's going to slow her down, and I do want to make sure she knows her math facts cold.

I, myself, remember I didn't know 8x8=64 in seventh grade, and I just figured it in my head, 8+8=16, 16+16=32, 32+32=64 -- 8x8=64. I did this until I realized how slow I was and decided to commit the facts I didn't know to memory. What do you think about Times Tales and other "helps" for math facts?

Mnemonic helps in themselves are not bad. We use them all the time, in everyday life situations. You have a phone number, you divide it to 2-digit numbers, maybe remember it has successive numbers, or doubles, etc.

I once memorized a certain 4-digit pin number by dividing it to two 2-digit numbers, and remembering that the latter was 9 less than the first... but after a while I remembered it without that.

On Times Tales. It's a fine program in itself. It associates a silly story and picture with each "difficult" upper times tables fact. You've probably seen samples. I don't think it is going to hinder... Basically, if it works for your kid, let's say you will show 8 x 7 to your your kid. He will see 8 x 7 and suddenly also see the silly picture of lady eight and the character 7 driving in a car, in his mind, and remember "It's 56."

It's not too much different from using a rhyme such as "5, 6, 7, 8, fifty-six is seven times 8."

Such a program can be a confidence booster as well.

Now, for some kids it doesn't work because they don't easily remember silly stories, and then it can cause frustration. Or, they're older and don't enjoy the silly stories anymore.

All these "helps" are fine in their place, but you have to be sensitive to your child so that the mnemonic "help" does not end up being an additional burden in itself... such as if the child cannot easily remember the stories or the song or whatever the "help" is.

So it's totally up to you. Try it first with the free sample they offer on their website... and see how your child reacts.

That program is an additional resource of course, and doesn't replace studying multiplication concept itself.

I get these questions a lot...

I've recently embarked on something new... I let people request a package of over 100 free worksheets and over 180 sample pages from the Math Mammoth books and worksheet collections.

In it, I included one question along with the name & email that people can fill in: "What is your most pressing math teaching question?"

I did that because I saw some other people had done something similar, and I thought that's a great idea - I would get to know what kind of math teaching related problems people have.

I also wanted to give people a chance to communicate a little with me... You know, we all go visit these multitudes of websites, and we show up as numbers on the website statistics program. It all can seem so impersonal, so "machinistic" sometimes.

But the reality is, behind every website are people. On school days, over 10,000 people visit HomeschoolMath.net. Over 1,000 people visit MathMammoth.com. I never hear from most.

If I had a physical store, I would see those people, talk to many. With a website, I still want some COMMUNICATION with my visitors and customers.

So that's what that little box with the question is about. Communication.

In this blogpost I want to answer TWO popular questions or themes that people keep writing into that little question box.

Interestingly - though not surprisingly - these two most popular themes correspond to the two best-sellers of my Blue Series books.

The two themes are:
1) Multiplication tables and
2) Fractions.

****************************************************

1) I've gotten questions such as (copied and pasted here verbatim):

"multiplication & division of one and two-digit numbers"

"How can i get my students to learn all of the multiplication tables?"

"What is the easiest way to teach the times tables?"

"It is very tough for me to learn tables. Please help me"


I believe in the methods I've put into my book Math Mammoth Multiplication 1:

****************************************************
* First teach the concept of multiplication well down pat.
* Then the tables in a specific order, with a systematic drill approach and 12x12 grid.
****************************************************

Let me explain a little more.

* First teach the concept of multiplication well down pat.

In the book, I have written not 1 or 2, but all these lessons about multiplication concept itself, to be studied BEFORE the drills:

Multiplication is Repeated Addition ............ 6
Multiplication as an Array ..................... 11
Multiplication on a Number Line ................ 14
Multiplication in Two Ways ..................... 17
Multiplying by Zero ............................ 22
Understanding Word Problems .................... 25
Order of Operations ............................ 27
Understanding Word Problems, Part 2 ............ 30

There are total of 28 lesson and practice pages in the book before the drills.

Studying the concept super well helps children to understand, become very familiar and at ease with multiplication.

While they study through these, they will probably memorize a few facts already - AND they will start seeing the need of having an effective and quick way to multiply (which is of course, knowing the facts by heart).

* Then the tables in a specific order, with a systematic drill approach and 12x12 grid.

The tables in my book are studied in this order:
table of 2
table of 4
table of 10
table of 5
[More Practice and Review]
table of 3
table of 6
table of 9
table of 11
[More Practice and Review]
table of 7
table of 8
table of 12

So it's the easiest first. Not only that, but in each lesson the student fills in a 12x12 grid to those facts he already knows. The "blacked out" unknown facts territory gets smaller really fast - and they can SEE it!

AND... that's not all. I feel it is VERY important kids learn their tables "both ways" - so they not only know that 5 x 6 is 30, but that they also know that 30 IS in the tables of 5 and 6.

To that end, I include specific instructions how you can "drill" or help the memorization of first the ANSWERS (skip-counting list), then associating each answer with a problem.

(This guide to oral drill is available online.)

All this multiplication info and practice is yours for only $4.50 :

=> Math Mammoth Multiplication 1

****************************************************

Well, this got to be long. I better save the fractions questions for another post.

Maria

P.S. If you go ahead and request that package of free worksheets, don't then be too surprised to get this blogpost as an email as well... I'm sorry but I just have to use what I write in multiple places, let many people read it. You know, sometimes I put my blogposts to an article to the website, I always pull my newsletter content from my blogposts - this time one of my email series emails ended up to be a blogpost.

I get these questions a lot...

I've recently embarked on something new... I let people request a package of over 100 free worksheets and over 180 sample pages from the Math Mammoth books and worksheet collections.

In it, I included one question along with the name & email that people can fill in: "What is your most pressing math teaching question?"

I did that because I saw some other people had done something similar, and I thought that's a great idea - I would get to know what kind of math teaching related problems people have.

I also wanted to give people a chance to communicate a little with me... You know, we all go visit these multitudes of websites, and we show up as numbers on the website statistics program. It all can seem so impersonal, so "machinistic" sometimes.

But the reality is, behind every website are people. On school days, over 10,000 people visit HomeschoolMath.net. Over 1,000 people visit MathMammoth.com. I never hear from most.

If I had a physical store, I would see those people, talk to many. With a website, I still want some COMMUNICATION with my visitors and customers.

So that's what that little box with the question is about. Communication.

In this blogpost I want to answer TWO popular questions or themes that people keep writing into that little question box.

Interestingly - though not surprisingly - these two most popular themes correspond to the two best-sellers of my Blue Series books.

The two themes are:
1) Multiplication tables and
2) Fractions.

****************************************************

1) I've gotten questions such as (copied and pasted here verbatim):

"multiplication & division of one and two-digit numbers"

"How can i get my students to learn all of the multiplication tables?"

"What is the easiest way to teach the times tables?"

"It is very tough for me to learn tables. Please help me"


I believe in the methods I've put into my book Math Mammoth Multiplication 1:

****************************************************
* First teach the concept of multiplication well down pat.
* Then the tables in a specific order, with a systematic drill approach and 12x12 grid.
****************************************************

Let me explain a little more.

* First teach the concept of multiplication well down pat.

In the book, I have written not 1 or 2, but all these lessons about multiplication concept itself, to be studied BEFORE the drills:

Multiplication is Repeated Addition ............ 6
Multiplication as an Array ..................... 11
Multiplication on a Number Line ................ 14
Multiplication in Two Ways ..................... 17
Multiplying by Zero ............................ 22
Understanding Word Problems .................... 25
Order of Operations ............................ 27
Understanding Word Problems, Part 2 ............ 30

There are total of 28 lesson and practice pages in the book before the drills.

Studying the concept super well helps children to understand, become very familiar and at ease with multiplication.

While they study through these, they will probably memorize a few facts already - AND they will start seeing the need of having an effective and quick way to multiply (which is of course, knowing the facts by heart).

* Then the tables in a specific order, with a systematic drill approach and 12x12 grid.

The tables in my book are studied in this order:
table of 2
table of 4
table of 10
table of 5
[More Practice and Review]
table of 3
table of 6
table of 9
table of 11
[More Practice and Review]
table of 7
table of 8
table of 12

So it's the easiest first. Not only that, but in each lesson the student fills in a 12x12 grid to those facts he already knows. The "blacked out" unknown facts territory gets smaller really fast - and they can SEE it!

AND... that's not all. I feel it is VERY important kids learn their tables "both ways" - so they not only know that 5 x 6 is 30, but that they also know that 30 IS in the tables of 5 and 6.

To that end, I include specific instructions how you can "drill" or help the memorization of first the ANSWERS (skip-counting list), then associating each answer with a problem.

(This guide to oral drill is available online.)

All this multiplication info and practice is yours for only $4.50 :

=> Math Mammoth Multiplication 1

****************************************************

Well, this got to be long. I better save the fractions questions for another post.

Maria

P.S. If you go ahead and request that package of free worksheets, don't then be too surprised to get this blogpost as an email as well... I'm sorry but I just have to use what I write in multiple places, let many people read it. You know, sometimes I put my blogposts to an article to the website, I always pull my newsletter content from my blogposts - this time one of my email series emails ended up to be a blogpost.

Do you need drill to learn multiplication facts?

Continuing on the same lines as my previous post, what about multiplication facts and drill?

Well, the principle is similar: show them first the concept and patterns.

Then can come some plain drill.

But, I want to share with you a few more detailed points.

1. The main "patterns" in various multiplication tables of course follow from the concept of multiplication. For example, table of 2 is counting by 2's. You get table of 4 by doubling the answers in table of 2. You get table of 8 by doubling the answers in table of 4.
   
   Table of 10 is counting by 10s. Table of 5 - just take half of what the 10 ×
   
   Here are some resources to give you ideas about these kind of patterns and little "tricks".
   
   * Michele's Math
   * Times Tables' factsheets
   
   


2. We ALSO need them to know the tables "backwards".
   
   Let me explain.
   
   It's not enough to know that 8 × 7 is 56, when someone asks what is 8 × 7. The students ALSO need to know that 56 is 8 × 7, when given just the answer 56.
   
   This is very important. Students need this fairly soon when they start learning division. Later on it will be important when simplifying fractions or factoring.
   



3. Since it's important to know the tables backwards, I do not feel it's enough if the child is able to "figure out" the multiplication problems. I feel they need to memorize them, period, and not just be able to count or use some other method to find the answers.
   
   It's fine initially, and indeed very helpful, if the child figures out 8 × 8 by first going 8 × 2 and doubling that twice.
   
   But this fact also needs memorized so that later on, when she comes to the problem 64 ÷ 8, it won't take her 10 seconds to find the answer.
   
   Now you might ask why is that important? Because of long division, for example. It's going to be a pain to learn long division if you don't know your division facts by heart.
   
   Here's another reason: soon the student is going to have fractions to simplify. If you know your division facts, then simplifying 35/56 will be a breeze, otherwise a pain.
   

See how it all builds on the previous topics? You need to get a good foundation, and multiplication facts "both ways" is part of that foundation.

I have posted online the entire guide to effective oral drilling from one of my books.

The guide explains how the teacher and student can achieve memorizing multiplication tables in this manner where they know the answers and they know which answer goes with which multiplication problem.

Check also a list of online games that practice times tables. These are great after you've done some basic drill and the child needs reinforcement (practice!!!).

Do you need drill to learn multiplication facts?

Continuing on the same lines as my previous post, what about multiplication facts and drill?

Well, the principle is similar: show them first the concept and patterns.

Then can come some plain drill.

But, I want to share with you a few more detailed points.

1. The main "patterns" in various multiplication tables of course follow from the concept of multiplication. For example, table of 2 is counting by 2's. You get table of 4 by doubling the answers in table of 2. You get table of 8 by doubling the answers in table of 4.
   
   Table of 10 is counting by 10s. Table of 5 - just take half of what the 10 ×
   
   Here are some resources to give you ideas about these kind of patterns and little "tricks".
   
   * Michele's Math
   * Times Tables' factsheets
   
   


2. We ALSO need them to know the tables "backwards".
   
   Let me explain.
   
   It's not enough to know that 8 × 7 is 56, when someone asks what is 8 × 7. The students ALSO need to know that 56 is 8 × 7, when given just the answer 56.
   
   This is very important. Students need this fairly soon when they start learning division. Later on it will be important when simplifying fractions or factoring.
   



3. Since it's important to know the tables backwards, I do not feel it's enough if the child is able to "figure out" the multiplication problems. I feel they need to memorize them, period, and not just be able to count or use some other method to find the answers.
   
   It's fine initially, and indeed very helpful, if the child figures out 8 × 8 by first going 8 × 2 and doubling that twice.
   
   But this fact also needs memorized so that later on, when she comes to the problem 64 ÷ 8, it won't take her 10 seconds to find the answer.
   
   Now you might ask why is that important? Because of long division, for example. It's going to be a pain to learn long division if you don't know your division facts by heart.
   
   Here's another reason: soon the student is going to have fractions to simplify. If you know your division facts, then simplifying 35/56 will be a breeze, otherwise a pain.
   

See how it all builds on the previous topics? You need to get a good foundation, and multiplication facts "both ways" is part of that foundation.

I have posted online the entire guide to effective oral drilling from one of my books.

The guide explains how the teacher and student can achieve memorizing multiplication tables in this manner where they know the answers and they know which answer goes with which multiplication problem.

Check also a list of online games that practice times tables. These are great after you've done some basic drill and the child needs reinforcement (practice!!!).

Need multiplication tables practice or games?

Remember, I have created a list of the best online activities, games, tutorials, etc. for this (and other topics as well).

All kids love games, and with multiplication tables, it's one way to give them more practice.

The complete list of online activities is here, but I'll copy and paste a sample to this blogpost:

---

Multiplication grid
Drag the scrambled answer tiles into the right places in the grid as fast as you
can!

Multiplication.com
Strategies, worksheets, games just for times tables.

The Times Tables at Resourceroom.net
Fill in the multiplication chart - partially or the whole thing - or take quizzes, and get graded.

Explore the multiplication table
This applet visualizes multiplication as a rectangle.

Table Mountain
Climb the mountain with 20 questions from a selected table.

Multiplication table Challenge
100 questions, timed.

Multiplication mystery
Drag the answer tiles to right places in the grid as they are
given, and a picture is revealed

Mr. Taylor's Multiplication Facts Drill
Simple practice (click on the right answer) for the easy ones, the hard ones, the monsters, or them all.

Multiplication memory game
Click on corresponding pairs (problem-answer).

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You will find a few more here, plus some recommended books and software.

Need multiplication tables practice or games?

Remember, I have created a list of the best online activities, games, tutorials, etc. for this (and other topics as well).

All kids love games, and with multiplication tables, it's one way to give them more practice.

The complete list of online activities is here, but I'll copy and paste a sample to this blogpost:

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Multiplication grid
Drag the scrambled answer tiles into the right places in the grid as fast as you
can!

Multiplication.com
Strategies, worksheets, games just for times tables.

The Times Tables at Resourceroom.net
Fill in the multiplication chart - partially or the whole thing - or take quizzes, and get graded.

Explore the multiplication table
This applet visualizes multiplication as a rectangle.

Table Mountain
Climb the mountain with 20 questions from a selected table.

Multiplication table Challenge
100 questions, timed.

Multiplication mystery
Drag the answer tiles to right places in the grid as they are
given, and a picture is revealed

Mr. Taylor's Multiplication Facts Drill
Simple practice (click on the right answer) for the easy ones, the hard ones, the monsters, or them all.

Multiplication memory game
Click on corresponding pairs (problem-answer).

---

You will find a few more here, plus some recommended books and software.