Teacher2Teacher 
Q&A #494 
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From: Gail To: Teacher2Teacher Public Discussion Date: 2000082114:37:20 Subject: learning multiplication tables I have copied the responses to earlier questions that were similar to yours. "Transitioning from manipulatives to use of symbolic concepts/notation is always a problem. You're probably already doing this, but don't forget to have your students record the multiplication sentence whenever they build with manipulatives. Also, have students talk and write about what the manipulative models mean. One successful method we've seen of helping students internalize the multiplication facts is to build arrays (like 2x3 as a 2 by 3 array) using manipulatives (like tiles) as well as recording the arrays on grid paper and recording the multiplication sentence. As you get to facts like 6x8, many students see these as 3x8 doubled because they can visualize the arrays. (This also extends nicely to 1digit and 2digit multiplication.) Playing games which use the multiplication facts (even things like "war") also help students internalize the facts." Jenny, for the Teacher2Teacher service "I have several suggestions for you to look to find your answer. Consider visiting the Internet Math Library, an annotated catalog of mathematics and mathematics education web sites. The Library features a description of each entry, hierarchical categories for browsing, a searcher on each browse page, and selected sites for each category's starting points (look for Math Topics: Arithmetic/Early: Basic Operations: Multiplication) http://mathforum.com/library http://mathforum.com/library/topics/multiplication/ Teach some of the tricks on the Beat the Calculator! page http://mathforum.com/k12/mathtips/beatcalc.html Calculation Tips & Tricks http://mathforum.com/k12/mathtips/multiplication.tips.html Parents, teachers, and students have written to Dr. Math asking for help with learning their multiplication tables. Here are some of the best answers from those archives: Learning Multiplication Facts Dr. Math FAQ http://mathforum.com/dr.math/faq/faq.learn.multiply.html Let us know how this helps you and your students." Roya, for the Teacher2Teacher service "What sorts of strategies have you already tried with her? Have you helped her make a multiplication table? There are many patterns to be found, once the table is constructed. How about using counters to work out the facts, and record them? (i.e. 4x 7 is 4 groups of 7, or 7 groups of 4 depending on how you look at it). You can also build rectangles using graph paper. Make side of the rectangle as long as one of the factors and the other as long as the other factor. Complete the rectangle, and count the number of squares inside the border. This is not really a "trick". Have you had your student look carefully at the products that occur when you are using the one digit factors (1X1 through 9X9)? There are several patterns to be found, and many relationships between the products themselves. For instance, if she knows the twos, the fours and twice as much. The same with the three and sixes, and the fours and eights. If you have not already done this, make a 10 by 10 grid. Above the grid put the numbers 0 through 9, and do the same down the left side. Your student should find a cell (one "square" in the grid), and then multiply the factor at the end of that row with the one at the top of that column. When the grid is finished, have her look for patterns in the grid. She may want to color all the like products the same color, or she may want to shade all the evens, or all the odds. You might want to "help" her notice what happens to the size of the products as you move around in the grid. Are they larger if you move in a certain direction? Is there any way to predict where the largest products will be found? She will find some surprises, and they will help her understand multiplication, and remember the products. I find that some of my elementary students who are having trouble with multiplication facts haven't really internalized the idea that they are rapidly adding, because what they have been shown to do is to memorize a set of facts. There is no understanding behind the facts. It is almost like learning a to sing in a foreign language, but learning phonetically, rather than learning the words themselves. There is no way to construct meaning, and there is no way to use what has been learned in another situation, because it has no meaning. That may be what your son's struggles are stemming from. If so, you could use manipulatives, like counters, washers, or beans, to help him build sets of the facts. For example, Building the sevens family would be making one set of 7, then two sets of 7, then 3, and so on. Having your son look at the size of each successive amount, and noting what that many "looks like" can help a student build a frame of reference for the facts. The same sorts of activities can be done with the other "families". There are also mental math activities that can help your son gain proficiency. For example, if he learns that the fours are twice as large as the twos, (same for sixes and threes, eights and fours, etc.) he can use that knowledge to compute the products that way, too. So 9 X 4 is twice 9 X 2, and 8 X 6 is twice 8 X 3." I hope this is a start for you. Please write back if you would like more suggestions. :) Gail, for the Teacher2Teacher service Visit us again at http://forum.swarthmore.edu/t2t/
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