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Break down facts into easier parts
Break down facts into easier parts
Multiplication Breakdown gives students a fast way to find accurate answers, unlike through the use of repeated addition. And, it actively reinforces multiplication by continuing to use it, although in easier problems – unlike other strategies like repeated addition.
"A good tool improves the way you work. A great tool improves the way you think."
~ Jeff Duntemann
Begin developing the concept of multiplication, with student discussing models such as 7 x 8 or any fact involving the 12s multiplication by using and discussing arrays to illustrate how Multiplication Breakdown works at a concrete or semi-concrete level.
7 x 8 is not one of the easier math problems. So it's a great one to break down.
Actually, any problem with 7 as a factor is easier to solve through Multiplication Breakdown.
Change the order of the factors so 7 is second. 8 x 7. Why? 7 is the better factor to break down, as should become clear as you read further.
Having the digit that is being broken down in the second place in the equation is less confusing and fewer mistakes.
The third figure shows the problem broken down into 8 rows with 5 in each row, and 8 rows of 2 in each row. In other words, 8 x 5 plus 8 x 2. Note that all of the answers are the same in each array, 56.
Encourage students to solve any multiplication problem that has a 7 in it (for those they don't yet know) by using Multiplication Breakdown. (Of course by now, using the Grasping Math Basics approach to learning multiplication facts, learners know 7 x 10, 7 x 11, 7 x 9, 7 x 5.) As they practice the Multiplication Breakdown technique, eventually they become able to solve it in their head, which is the step just before mastering the fact.
7 can be broken down several ways. Walk students through the pair of options to see which pair would make for a problem where getting the right answer multiplying 7 x each number in the pair would be easy. Eliminate those that are less helpful. That leaves 5 + 2 since the 5s and 2s tables are both easy.
Writing and solving a problem using Multiplication Breakdown:
Writing and solving a problem using Multiplication Breakdown:
Start with 7 as the second number in the problem. Breakdown 7 to 5 + 2.
Multiply 8 x 5 which equals 40. Then multiply 8 x 2 which equals 16. Last add the two partial answers (40 + 16) for the final answer, 56.
Multiplication Breakdown can be used for any multiplication problem. It is especially useful for the 7s and 12s tables, because those tables have super-easy parts to multiply and then add once broken down.
Both factors in 12 x 8 are hard to learn – unless Multiplication Breakdown is used.
The second figure shows changing the order of the factors does not change the answer.
The third figure shows 8 x 12 broken down to 8 x 10 plus 8 x 2. All three figures = 96.
Multiplication Breakdown is the first-choice strategy for working towards mastery of the 12s tables.
Several possibilities for breaking down 12 exist. Two are easy (11 + 1 and 10 + 2), but 10 + 2 is easiest because adding the two smaller products is particularly easy.
Start by ensuring 12 is placed second in the problem. Break down 12 into 10 + 2.
Multiply 8 x 10 which is 80, then 8 x 2 which is 16. Add the partial answers 80 + 16 = 96.
Multiplication Breakdown can be used to solve any times table problem. For instance in 8 x 4, 4 could be broken down to:
12 = 16
+ 2 = + 16
8 x 4 = 32
Practice each table as you learn them using Card Deck Flash Cards. See the process described on the Gamify Multiplication Practice page.
“Play gives children a chance to practice what they are learning.”~ Mr. Rogers
Besides learning by patterns first and Multiplication Breakdown, Factor Arrays are another tool for learning times table facts. [add page link]
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