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Simple Math Tricks Using Multiplication Tables
By Joan Whetzel
Addition and multiplication are two of the fundamental math operations. Subtraction and division are their inverse operations, meaning the work in the opposite direction from adding and multiplying. The simple explanation of multiplication is as follows: Rather than presenting individual numbers (addition) in an equation, multiplication represents the "addition" of sets of numbers. In addition, the numbers 3 and 5 are added together (3+5) to find the answer 8, but multiplication takes those same numbers and asks you to "add" 3 sets of 5 (3x5) or 5 sets of 3 (5x3) to produce 15 as the answer. Students begin learning about multiplication and division around the 3rd grade. There are a few tricks that can help them understand these math processes visually, using a multiplication table.
The Multiplication Table
The basic multiplication table used by most schools, lists the numbers from 1 to 12 in a row across the top of the table and again in a column along the left-hand side of the table. The rest of the table is filled in with the products (answers obtained) for each of the multiplication equations.
Multiplying with the Multiplication Table
To use the multiplication table, you need to know the two numbers being multiplied together. Find one number in the top row and follow it down with the index finger on one hand. Find the second number along the left side of the table and follow that row with the other index finger. Where the two fingers meet is the answer to the multiplication equation.
Looking for Sets and Patterns
Using it regularly at first is a great way to train the brain visually when it comes to multiplying numbers together. Here are a few tips to remember how to do this:
· The order of the numbers doesn't matter. To find 3 sets of 5, the equation may read 3x5 or 5x3. So you will need to find the 5 on the top of the table and the 3 on the left-hand side of the table, or find the 3 on top and the 5 along the side. Whichever way you choose to use the table, follow the 5 and the 3 to the box where they meet, and there's your answer: 15. So you see that changing the order of the numbers does not change the answer. It just means that one equation (3x5) has a twin (5x3), that are like mirror images.
· When trying to learn multiplication, practice the table in chunks. This means practicing the 1x_, followed by the 2x_, 3 x_,4 x_, 5 x_, 6 x_, 7 x_, 8 x_, 9x_, 10 x_, 11 x_, and 12 x_. Practice it following the numbers 1 through 12 down the left-hand side of the table and across the top of the table.
· Use the table to count by 1s, 2s, 3s etcetera. Learning to count by 1s, 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s,10s, 11s and12s further reinforces the understanding of sets of numbers. Counting by 2s produces the pattern 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24. Counting by 12s produces the pattern 12 ,24, 36, 48, 60, 72, 84, 96, 108, 120, 132, and 144.
· Remember that "2x" means the same as doubling the number. So 2x2 =4, 2x5= 10, and 2x12 = 24.
· Use a spreadsheet program to create a multiplication table. This is a great exercise for the classroom or for home school math classes. It teaches the students how to use a computer program like Microsoft Office Excel or another spreadsheet program as well as helping them to understand multiplication and division.
· Combine the multiplication table with small manipulatives. The manipulatives can be anything from M&Ms ® to pennies, marbles, grapes, dice, or anything else that can be grouped into sets. The combination reinforces the visual aspect of multiplication.
· Try this trick for remembering the 9s times table. write the numbers 1 through 10 on separate lines on a sheet of notebook paper. Next to each number write "x9" and an equal sign. Then, starting with the 1x9 equation, write the numbers 0 through 9 downward, one number for each equation, so that 1x9 gets a 0 and 10 x 9 gets a 9. Now, starting at the bottom (10x9) do the same thing, beginning with 0 and ending with 9. This time the 10x9 equation gets a 0 and the 9x1 equation gets a 9. You will notice that all the answers have two digits (numbers) and that the first number increases as the second number decreases. Multiplying by 9s is sort of like adding 10 to the previous number and then subtracting 1.
· Learn the "squares" of numbers. The "square" of a number means that the number is multiplied by itself. Since 2x2= 4, that means that 4 is the square of 2, or 2 squared (22) equals 4. This applies to all of the numbers when they are multiplied by themselves, so that 3 squared (32) is the same as 3x3 = 9, and 12 squared (122) is the same as 12x12 which equals 144. Looking at the above table, you will notice a pattern as the squared numbers form a diagonal line that divides the table in two.
Dividing with the Multiplication Table
Yes, multiplication tables can be used to solve division problems. Start with a word problem: "Mom has 35 pennies. She wants to put the same number of pennies in the piggy banks for each of her 5 children. How many pennies does each child receive." Here's how to solve the equation using the multiplication table.
· First find the number of children (5) along the top of the table or along the left-hand side of the table.
· Follow the row or column until you find the total number of pennies (35).
· Then follow that row left or the column upward until you find the quotient, or the number of pennies each child receives (7).
So, the equation 35 ÷ 5 = 7. Each child receives 7 pennies. Another trick here is to notice that for every division problem is a multiplication problem that performs the opposite operation. If
35÷5 = 7, then 7x5 = 35 and 5x7 = 35.
These Websites Provide Additional Multiplication Tables Help:
1. Helping with Math. Printable Tables and Charts for Multiplication. http://www.helpingwithmath.com/by_subject/multiplication/mul_tables_charts.htm
2. Multiplication.com. Teach the Times Tables Videos. http://www.multiplication.com/teach/teach-the-times-tables
Math Is Fun! Learn Your Multiplication Table.
Houghton Mifflin Math. Using a Multiplication Table.
Math A Tube. Multiplication Table Chart.
Simply Teaching. Using a Multiplication Chart to Find Equivalent Fractions.
Investigations in Math, Data, and Space. Math Content by Strand.