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Here are a sequence of steps for teaching multiplication tables.
STEP#1: Teach the concept kinesthetically. The kitchen is an ideal place. Start doing this as soon as the child can talk. If you have an older child who is struggling with multiplication, step away from the book for a while and have math lab every day instead.
Make cookies. Look at the egg carton: rows and columns of eggs. 3 x 6 = 18 and 6 x 3 = 18 (or 2 x 6 = 12, if you buy the dozen size). Take out 3 eggs for cookies and you now have 3 x 5 = 15. Put the cookies on a sheet in neat rows and columns. 3 cookies across x 4 cookies down = 12 cookies per sheet. What happens if we put 4 across or 5 down? Take the cookies out of the oven and put them on cooling racks in rows. When the are cool, stack them: 6 cookies in a stack, 4 stacks... 4 x 6 = 24. Pack the cookies in storage bags, 10 to a bag... 40 cookies, but we have some left over... let's add 2 more to each bag now we have 48 because 2 x 4 = 8 and 40 + 8 = 48; now we have a dozen in each bag... 4 x 12 = 48. Wow! We get the same number! Isn't math great?! You always get the same answer no matter how you do it!
Do you have a clothesline? (If not, use a length of twine or small rope.) Get those plastic baggies again. Have him put 5 peanuts in each bag and pin the bags on the clothesline. (If you don't have clothespins, use binder clips or giant paper clips.) Now help him count by fives. When he can count them and tell you that 6 x 5 = 30, he gets to shell and eat peanuts. Do it with different numbers, different contents.
Get out a big bowl, bucket or dishpan, a 4-cup liquid measuring cup and a 1-cup measure (dry will be easier, but let him pick for the 1-cup). Send him to the kitchen sink to see how many cups of water it takes to fill the quart measure to the 4 cup line... seems obvious, I know, but he needs to experience it. (Make sure he knows to keep the quart measure flat on the counter). Now have him pour 4 quarts of water into a big bowl. How many cups are in the bowl? He can prove it by measuring them back out with the 1-cup. (Watch to be sure he gets the measuring right: 2 tablespoons shy on each cup will quickly spoil this!)
How many cups in a gallon of milk? How many in a quart; what's a quart? Well, quart means one-quarter or one-fourth which means four of them. 4 x 4 is 16. How long will it take him to drink a gallon of milk? Cups per days times days...
How many tablespoons in a cup? Let's find out by measuring water and counting. Is there a faster way to do it? Measure tablespoons into a 1/4 cup. 4 in a quarter cup... what's a quarter? Prove it: pour quarter cups into a cup. 4 x 4 = 16. Let's count the tablespoons back out one at a time to prove the equation.
How about putting apples, oranges or potatoes in paper bags?
Try raisins in little piles on the table. 6 raisins in each pile x 7 piles = 42 raisins, let's count them to prove it. Take those 42 raisins in 7 piles and eliminate one pile by distributing the raisins to the other 6. Now we have how many raisins in each pile and how many piles? Do we have a different number of raisins? 6 x 7 and 7 x 6 are the same thing! Now, if we eat one raisin from each pile... Work your way down, eating a raisin from each pile, doing the math, eating raisins. Tomorrow, do it with a different number of piles. Help him realize the value of knowing the tables: counting takes much more time than multiplying.
Try slices of kiwi or apple wedges or orange sections on plates or napkins. This is a great way for the two of you to share a snack while learning the twos. (2 plates, one for Mom and one for child).
STEP #2: Help him make a times table. It should go to 12 each way. Help him set up a neat table before he puts in the numbers. Show him how it works, referring back to learning from Step 1.
STEP #3: Work on the concept using picture language. Start with 1 and 0: If I have 3 bushel baskets and I put 1 apple in each one, how many apples do I have? If I have 7 bushel baskets and I put 1 apple in each one, how many apples do I have? If I have 20 bushel baskets and I put 1 apple in each one, how many apples do I have? If I have 500 bushel baskets and I... keep asking. Do the same thing with putting zero apples in each one. Now, if I have zero (or one) bushel baskets and I... When he gets the right answers, have him look on the table to see that it gives the same answer. Drive home this concept on ones and zeros. Then we can go on to understanding the same questions with bigger numbers, but it's more complicated, so we have to memorize the table. The table has 144 facts to memorize; let's get a jump start by learning some tricks.
STEP #4: Start teaching the multiplication tricks. Make sure he understands the concept before introducing these tricks.
10: All you have to do is put a zero on the end. Practice counting by tens to 100. When he has it, have him practice to 200. Get 100 pennies and have him put them in rows or stacks of 10. Now give him 10 dimes. Talk about the meaning behind the math.
2: Counting by twos is easily learned... do it on stairs, everywhere you go.
5: Once you know 10s, 5s are the same thing with the five stuck in between each one. Also, 5 times any even number is half that number with a zero after it. Practice with coins and bills and an analog clock!
9: Watch this: Take one away from the number and write down the answer (8 - 1 = 7; write down 7) now put down whatever it takes to get 9 by adding (7 + 2 = 9, so write down 2) Now we have 72. Guess what? 8 x 9 = 72! That's called "the rule of nines". Help him try it with the different numbers and check his answer on the table to prove it. (How do you know you have a transposition error in your checkbook? The difference between your balance and the balance per bank is a number whose digits add up to nine.)
STEP #5: Now it's time to memorize. We're going to chant. Will he dance with you? My 8 year old memorized the tables by dancing to them with me. She laughed and she learned faster than we imagined possible. I tried a sort of patty cake thing, but that was still frustrating. You have to try different things... think about your child's learning style... brainstorm. Start with the small numbers to build confidence.
He may like to practice with wrap ups for speed drills. I bought some from Teaching Toys. (Remember to request Teaching Toys' homeschool discount, and to ask for what you don't see because they will order it for you.) You can make your own wrap-ups by cutting a ruler size piece of cardboard and putting 12 notches down each side. Punch a hole on top and tie a piece of string to it. Randomly write numbers 1-12 down one side and put a big 4 (or other number he struggles with) in the middle. Then put the answers (16, 8, 32, 20) down the right hand side. He wraps the string from the 3 on the left to the 12 on the right, from the 7 on the left to the 28 on the right, starting with the top number on the left and working his way down the stick. Do it once for him and mark the back where the strings are. Now when he does it, he can turn the stick over for help if he gets stuck, and when he can do it, he can look on back to see that he did it correctly. Have him use a stopwatch and chart the time it takes him to do the stick each day.
Flash cards: Here's how to use them. Wait until he's learning the tables. Hold up a card, and if he can say "5 x 4 = 20" without much hesitation, then put the card down to the left. If he struggles, help him, then have him repeat the equation after you. Put that card down to the right. When you've gone through the deck, put away the pile on your left. Start over with the "struggle pile" doing the same thing. Work for 20 or 30 minutes each day. When you get down to less than 5 cards, go over them several times, dance to them, chant them going upstairs, look for every opportunity to repeat those equations.
STEP #6: Use your chosen text. The text should continually provide new material coupled with spiral review. Emphasize that he needs to understand each lesson before trying the problems.
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