IDEAS FOR TEACHING MULTIPLICATION
from the Homeschooler's Notebook
Encouragement and Advice for Homeschool Families

From Lisa: I really had a lot of help from the Fun with Figures e-book. It is full of little tricks and tips that helped me help my child to multiply (as well as add, etc.) It taught me a lot of things I either had not learned or had not remembered from my growing up.

From Kathleen: This may sound odd, but move on!! Complete mastery/memorization of the multiplication tables is not necessary in order to do division. Really! In fact, provide her with a copy of a filled in multiplication chart and allow her to use it at any time. Yes, this is giving her the answers. Yes, she will look at it often. Encourage it, allow it! Eventually she will learn them and won't need the chart any more. You might wonder how she can do division without knowing her times tables...it'll be slower for her and she will have to do more addition. She doesn't know 8 x 4 = ? but 8 + 8 = 16 and 16 + 16 = 32 and there it is. Or 8 x 7 = ? but she can do 8 x 5 = 40 and 8 + 8 = 16 and 40 + 16 = 56. I'd also suggest having her fill in a blank multiplication chart (up to 12) at least once a week.

Also, realize that it is OK if she doesn't master every concept 100%. Math builds on itself and with each tier you often review many basic concepts. Move on, allow her some "success" in math and see if in 6 months to a year there isn't a huge difference in her math abilities. On a personal note, I can assure you that you can reach adulthood and have a college degree and homeschool your 3 children and STILL not have all your multiplication tables memorized. I'm not proud that I never memorized them, but it has never held me back and has only rarely slowed me down. I also enjoy math and have taken advanced math classes and gotten A's in them in college.

From Becky: Your 9 yr old sounds exactly like my daughter did at this age.

My daughter (14 now) also had problems with subtraction and multiplication. What I did was to show her how to divide. (I know that this sounds backwards, but it made a HUGE difference!)

We use Saxon Math now (she is in 8/7 math). She still does not have all of her multiplication tables memorized as well as I had hoped, but she does not have a problem getting her math done on time and correctly either.

The other thing that really helped with math was to come up with activities that showed them math in everyday uses. I taught my daughter to cook by having her double and triple recipes (multiplication and fractions at the same time) and only making half of a batch of cookies.

This has worked so well that she now wants to be a chef when she finishes school!!!

From Tupelo (who was told all through school that I just wasn't good at math, then pulled an A in summer session calculus in college because the professor taught concepts instead of memorizing!):The problem that she is having is not math, it's memorization. As a "math person" and tutor, I can tell you, knowing the multiplication table has absolutely nothing to do with being good at math! I have tutored many a college student in basic math or algebra because even though they could rattle off the table, they did not understand what it meant, so they could not apply it to fractions, word problems, or algebra. On the other hand, I and many other people I know who are good at concepts and applications, do not know all of their math facts by heart. It is very difficult for most people who are good at math, meaning the concepts and relationships and patterns, to learn math facts through rote memorization. They want and NEED to understand why for every step.

I would recommend focusing on the concepts and letting her figure out the answer each time if she needs to. Go ahead and move on, and leave the flash cards behind. Just using the math facts will help her memorize them far better than the flash cards. It also will give her a better sense of the size of the numbers she is dealing with. Also, keep in mind that the multiplication table is very arbitrary. Why does the table stop at 12's when 13's are much more difficult to figure out? She really only needs the 2's and 3's, because the rest factor into these problems. For example, 8*12 can be factored into 2*2*2*12. Then it can be figured out through doubling (2*12=24*2=48*2=96) Understanding the factors and how the numbers are relating and working together will help your daughter far more, especially in algebra and other higher maths, than the rote memorization of facts ever will. This has worked well for my daughter, who at 7, does not know the table, but can figure out anything on it, or beyond (like 5*16) in her head by visualizing what it means, and factoring. Hope this helps!

From Janet: My daughter had problems grasping the concepts of multiplication as well. I turned to manipulatives to help her see the concept. I did have a few manipulatives on hand to show her that 3x5=15 is actually 3 groups of 5 that add up to 15. However, if you do not have manipulatives, take heart. Pinto beans, paper clips or any other number of small objects available in our homes work just as well.

Initially, I showed her how to group. Thereafter, everytime we had a problem to solve, I simply had her do the grouping and then count out the answer. Since she is a visual/kinesthetic learner, she was able to see multipication as a simpler method of counting and from there she was able (or more likely more willing!) to memorize the facts. I'm a big fan of manipulatives as it helps young children better understand math concepts which they may see as more abstract and hence, beyond comprehension.

Do you know what her primary learning style is? Our homeschooling became a less frustrating experience once I figured out my daughter's learning style. I am able to slightly modify any lesson presentation to accomodate her learning style. A good starting book on the subject of learning styles is The Way They Learn by Cynthia Tobias. Another good read is Understanding Your Child's Personality by Dr. David Stoop, though it has more to do with understanding your child's inner workings.

From Mary Ann:When reading the concern posed by the mother with a 9 year old daughter who is having difficulty learning multiplication facts, I immediately thought of myself at that age. My parents would drill me with the facts and I would break down and cry. I ended up in summer school as a result of my weakness in this area. However, there is a happy ending. I went on to college and majored in chemistry and mathematics. Also, in addition to home schooling, I teach mathematics part time at a community college. Back in my elementary years my parents would have gotten a good laugh if you had told them that I would someday teach calculus.

When thinking back as to why I struggled so much, a couple of things come to mind. First, I now realize that I did not understand the concept of multiplying. I was a product of the era of rote memorization. Once I understood the concept of multiplying, I had such a negative attitude towards math that it was difficult to overcome. I truly believed that I was not good at mathematics, and my parents indeed contributed to this belief.

Now that I have 3 boys of my own, I have taken a completely different approach to teaching mathematics. Every effort is made to concentrate on the underlying concepts. When my two older boys were preschool age, we counted everything. I would say things like, "I wonder how many vanes there are in our vertical blinds?" Also, I employed their help in the kitchen. If I was making iced tea, I would have the boys count out the tea bags. Currently, my three year old is known as the "pancake chef". He helps me put the ingredients in the bowl to mix for pancakes. I emphasize the measurements and amounts and we count together. We also put together collections of 100 items so that they can get a sense of what one hundred “looks” like. Also, teaching the boys to count by 10's, 5's, and 2's was critical to their understanding of multiplication. By the way, this preparation paid off when teaching time and money as well!

Does this mean that we should do away with memorizing facts? Not at all, I think that it is critical for children to learn math facts. I explain to my students that there is only so much space we have in our brains for thinking. If students have to struggle to come up with the answer to 2x3 every time, there will be limited "space" for doing any higher-level thinking.

So, what to do with a nine year old who is struggling? There are other approaches that you did not mention trying. Does your daughter like music? There are some terrific tapes that have been made putting the multiplication facts to music. If your daughter is creative, have her make her own tapes singing the facts or she could even produce a video. In addition, there are math wraps and the Leap Frog Turbo Twists that will allow your daughter to self-quiz rather than you putting the pressure on her.

If your daughter doesn't understand the concept of multiplying, there is also a geometric approach. You can give her grids of varying dimensions and have her count the items in the grid. For example, if you are working on the 3's you could draw a 3x1 grid of flowers, and then a 3x2 grid and so on...have her count the flowers in each grid.

Finally, I would recommend reading Sheila Tobias' book Overcoming Math Anxiety. Some of your daughter's problems may be related to a very common occurrence in this country, math anxiety. I have heard so many parents, particularly mothers, say that they are not good at math and never were. I discourage this type of dialogue, as it seems to give the child the impression that it's okay not to excel in the area of mathematics.

I hope that these suggestions will be helpful to you. I have learned so much from all of the contributors to this newsletter and am so thankful to everyone who has taken time to respond. One more thing, never underestimate the power of prayer! Pray with and for your daughter as she begins a math lesson. God Bless!

From Larry: I had this problem with my son. To be honest, it took us nearly 3 years of work to nail those tables. I still don't know if the problems were developmental, behavioral, or (most likely) a combination of the two. Two things helped. Mathshark was a great help. It was drill with a handheld game feel. Also, we broke down the tables into the facts that you had to know and worked on them exclusively. If you know 2x3 you know 3x2. It made the stack of cards much less intimidating. I had him stop everything and work on the tables but that didn't help much either. I finally figured out that he could do it fast writing or with flashcards but not with the problems given orally. One of these ways-visual, auditory, or hands on will be easier for her. Work with her in this way until she gets the facts down, then work on knowing them as quickly as possible ALL the ways you can do them. Good luck and try not to lose your patience. When something is very difficult to do, your enthusiasm for it is usually less than ideal.

My son is now 14 and has had the tables down for 2 years. It put him behind in his math, but we couldn't move too much farther until he knew them. He is catching up pretty quickly and he now has a much better attitude about subjects that are hard because he knows he can get through it with hard work. He also makes fewer mistakes because he learned how to really tackle math and do his work carefully. I am sure that a lot of people will have some great game ideas so use them and make it as fun as you possible can for her to help overcome the frustration you have both had with it. When it finally clicks you will both be so proud!

From Lourdes: We've been homeschooling now for 7 years. I had the same problem with my son. For him, it was the method that wasn't working for him. Flash cards and speed drills only frustrated him. I was using Saxon at the time, which just didn't seem to "click". My advice would be to try a different teaching method, such as Math-U-See or Miquon, which use manipulatives to illustrate math concepts in a hands-on and visual fashion. Another thing which helped, as a supplement, was a computer program designed to review tables. One free programs available on the internet is: MathTest. Some children might respond well to singing the tables-if your daughter enjoys singing, she may like Musical Math Facts and other similar tapes. Finally, having a large multiplication chart handy was invaluable-he and I made this together, and it really helped him to have a visual representation of the multiplication tables. We made many copies, and he would color in the patterns that each table made.

From Rachael: To help with memorizing multiplication, put up a multiplication chart in one room (on the far side of the house, or in her bedroom upstairs ). When she is doing her worksheets she is allowed to go and look up the answer from the chart. She then has to run all the way to the far side of the house where you have put up the chart, keep saying the answer to herself all the way back, and remember it to write it down on her worksheet! Perhaps she would respond better if you played games when memorizing math facts. Math-It at the LatterDay Resources . Math-It includes a board game for memorizing math.

There are also games and puzzles for kids available on-line at Quia! and Funbrain, A+ Math and Cool Math

From Becky: My son and I had struggled with math for years until I changed to Math-U-See a year ago (he's 9 1/2). It has made all the difference in the world for us. I found that he was a concrete, visual, hands-on learner who thrived using the video and blocks to learn. He is doing great in math now, and actually likes to solve problems. They approach concepts differently than most programs, but it makes things seem so much easier. Here's their website: www.mathusee.com.

Also, I read where visual learners do better with flashcards if the answers are written on the card, so that the child can see the whole problem solved as a picture in their head for better recall later. Right-Brained Children in a Left-Brained World by Jeffrey Freed, M.A.T. and Laurie Parsons has a lot of good ideas for tackling math, too.

From Amy: It sounds like you're using 3rd grade R&S math... that's where we are right now, too... I can't guarantee this is the solution, but it seems to be working for us... my daughter also got *stuck* once we got past 0 and 1 (0 times anything is always zero, so she got that pretty easy... 1 times anything is always itself... pretty easy - what do you mean 2 times something is any different?!?!???) ((we've just completed the 5 times table, btw, with much greater success than what we began with...)) At the suggestion of a friend, we put away our math book for a while, and tucked the flash cards neatly away for later use... I bought a couple packages of 3x5 cards and we practiced by making our own flash cards - individual cards and sets (1 times table on one card, 2 times table on another card, and so on) Then we had her write out the times tables (0x0 through 5x12) three times a day for about a week, to help "drill" it without pressure - she was helped by that, so we brought the math book back out, but still she struggled - though there was some improvement. Our last step was to invest in some cuisenaire cubes from christianbook.com (they are $2.99 for a set of 100 single unit cubes, and they have a choice of orange, blue, or wooden) and I showed her, for example, that 5 times 5 is: 5 blocks lined up in a row, making 5 rows, then add them all together, so that she could visualize it... that's been helping her "see" how it works, since her brain can't seem to wrap around the concept any other way we've tried. An average math assignment, with minimal assistance, now has maybe one problem incorrect - two at the most - though it does take a good hour to hour and a half for her to get through a math assignment - but it is without tears and arguments, and she is doing the work herself and not hating every moment of it! :-) I don't know if this answer would work for your family, but it has helped tremendously in mine :-)

From April: We too had a bit of trouble getting started with multiplication. We began by watching "Schoolhouse Rock" multiplication DVD. That seemed to inspire my son to want to learn. It also got him started on the 3's (because their 3's tunes is very catchy). We then set out very simply, with the 0's, 1's, 2's, 5's, 10's, and 11's. After that we found tricks for almost everything. The following tricks, plus daily repetition (using trianglular flashcards), have worked wonders!

I'm sure that there are more tricks that we haven't mentioned here, but I think once your child starts having success with these, he/she will be encouraged to keep working, and discovering new tricks on the way. For example 56 = 7 x 8 (5,6,7,8). Try an internet search for Multiplication Tricks.

From Christy: I am a private tutor as well as a homeschooling mom and I have taught many children their times tables. I would first recommend building her self esteem about it all by just doing the problems that have a trick to them and are somewhat easy. Teach her: Anything times zero is zero, Anything times one is the other number, Times two is just doubles, Times five is the minute hand on the clock, Times ten is sliding the zero in the ten in back of the other number, times eleven is two of the other number side by side. Then pull out all of these flashcards and just do these for a time until she is confident with them. Keep praising her and showing her the big deck she is able to do. Then add the fours with the trick "double the double" until she is getting those. Add the nines with one of the multitude of 9 tricks. Keep adding one card at a time until she's able to do the stack with only a few reminders!

From Danica: I do not know how the people who receive this newsletter feel about Montessori education, but I think that your daughter would benefit GREATLY from one or two of the math materials. There is a multiplication board that is super simple to make at home that would SHOW her how multiplication works. Here is a link to a picture. Just click on one of the mulitplication tables. I personally like the second one better. she can just use small squares of paper to mark them off or buttons work really well. when doing 1X1 she will only have one spot to place a button, 1X2 she will place two buttons. I'm sure you see what I mean. I hope this is helpful.

From Ann: I also have a daughter who is now 13 years old and who still hasn't memorized her timetables let alone most of her math facts. When she was younger around 10 we had her tested by a learning disabilities specialist. One of her findings was that our daughter had a learning disability - an auditory processing difficulty which meant a difficulty with decoding the symbols of our language which are in the areas of math, grammar, reading, and spelling. I would encourage you to seek out an experienced learning disabilities specialist and have her tested for her sake and yours. Our daughter was so relieved to find out there was a reason and a name for her frustration in so many areas.