The question is common on parenting forums:
My daughter is in 4th grade. She has been studying multiplication in school for nearly a year, but she still stumbles over the facts and counts on her fingers. How can I help her?
Many people resort to flashcards and worksheets in such situations, and computer games that flash the math facts are quite popular with parents. I recommend a different approach: Challenge your student to a joint experiment in mental math. Over the next two months, without flashcards or memory drill, how many math facts can the two of you learn together?
We will use the world’s oldest interactive game — conversation — to explore multiplication patterns while memorizing as little as possible.
Make a Monster Times Table
If she is willing to take the challenge, you will need a way to keep track of your progress. Use a manila file folder or tape two pieces of copy paper together, long sides touching. With a ruler, draw a large, blank times table. Take the chart up to 12 × 12, or even higher (and include a column for zero, if you like). One online friend credits his math skills to working out a 30 × 30 times table as a child.
Your daughter has almost certainly seen a chart like this before, but even so, she will probably find it intimidating. Help her fill in the chart for herself by adding or skip counting the numbers in each row and column.
For instance, to write the times-7 facts, she can imagine using the multiplication ray gun’s Replicate setting to copy a row of 7 blocks, over and over again. As she moves from one row to the next, she will write the total number of blocks, adding seven and seven and seven more…
Be patient. If your daughter is afraid of math, it may take several days to fill in the chart, a little bit at a time.
When the chart is finished, hang it on the refrigerator or some other prominent place. Your daughter will be able to find any particular math fact by looking where the appropriate row and column meet. The answer to is found where the 6th row meets the 7th column (or the 7th row and 6th column), because it is like counting up six of the sevens.
At first glance, that chart looks like a real pain: 144 math facts to memorize. But we are not going to memorize hardly anything — we’re just going to look for number patterns.
Our goal in these times table conversations is to build up your child’s mental math skills. Therefore, do not resort to worksheets in an effort to teach the math facts. Instead, take the time — and it does take time — to talk through these patterns and work many, many, many oral math problems together. Discuss the different ways you can find each answer. Notice how the number patterns connect to each other.
When you are practicing each family of rules, be sure to experiment with larger numbers, too. Make it into a game, and take turns quizzing each other for just a few minutes at a time. Students love the chance to stump their parents. Try working mental multiplication puzzles while you are doing dishes, or on the way to soccer practice, or whenever you can find a spare moment of time.
Even the patterns which seem easy are worth spending time to master. For instance, the magic power of one — that it can multiply a number without changing the value — is essential to working with fractions and can simplify a multitude of high school chemistry problems.
The Ones Family
Sit down with your daughter and the chart. Use a highlighter to color in the facts she already knows, making a bright, dynamic statement of how good she is at math. You can mark out the times-1 facts very quickly. Surely your student knows that anything times one is itself, right? With the scale factor set at “1″, the multiplication ray gun won’t change anything.
7 ones = 7
359 1 = 359
Practice with large and small numbers, fractions, and more:
4.6 1 = 4.6
1 897 = 897
Now have your child color in the times-1 row and column with the highlighter.
The Tens Family
Remind your student of how easy the times-10 facts are:
2 tens is 20.
5 tens is 50.
9 tens is 90.
11 tens is eleventy, or 110.
12 tens is twelvety, or 120.
17 tens is 17-ty, or 170.
156 tens is 156-ty, or 1,560.
4,000 tens is 4,000-ty, or 40,000.
Practice the pattern with small numbers, big numbers, and anything in between. Then mark times-10 as mastered, coloring both the row and the column.
More Easy Facts
You can get rid of nearly half the chart in one sweep of the marker. Does your student know — really, truly, thoroughly understand — that is exactly the same as ? Multiplication is commutative, which means you can move the numbers around without changing the answer: 3 rows of 4 blocks have the same total number as 4 rows of 3 blocks.
Spend a day (or a week, or however long your child needs) practicing, to make sure this principle sticks thoroughly in mind:
Q: What is 7 8?
A: The same as 8 7.
Q: What is 115 6?
A: The same as 6 115.
78 49 is the same as 49 78.
is the same as .
192 7 is the same as 7 192.
Then you can mark out all the facts on the lower, left-hand section of the chart that have duplicates on the upper, right-hand section.
Don’t try to do too much at once. So far, you have marked off nearly two-thirds of the chart. Good job! Now would be a great time to take a break and do some fun math — like multiplying a batch of cookies.