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SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

Instructor:
*Sharon Linde*

Need a way to teach double digit multiplication that will work for some students that aren't quite catching on? This lesson goes over several different methods and shows some examples.

Sheri has been teaching first grade for several years, but recently made the switch to fourth grade. Even though it's the same school, and she already knows most of the students, it's a big change. Lately, she's run into some issues teaching double digit multiplication - something she never had to worry about in the lower grade.

She found teaching the traditional method doesn't work for all of her students and wants to learn additional methods to try with students that are having difficulty. Of course, Sheri also knows that these lessons should only be attempted after the student knows the multiplication tables well, and how to multiply a two digit number by a one digit number.

Sheri discovers several ways to teach the multiplication of 2 two digit numbers. Each of these methods seems to have a number of different names and they're often used interchangeably. The most common names for the alternate methods she found are box method, area method, and lattice method. Let's take a look at these methods. We'll also take a look at the traditional method.

In the **box method** the single complicated multiplication problem is broken up into four easier multiplication problems. The four resulting products are then added to get the final answer.

Multiplying 12 by 35 would look like this:

12x35 | 10 | 2 |

30 | 10 x 30 = 300 | 2 x 30 = 60 |

5 | 10 x 5 = 50 | 2 x 5 = 10 |

300 + 60 + 50 + 10 = 420

After one or two practice problems, most students can skip writing the multiplication steps and the box method would look like this:

12x35 | 10 | 2 |

30 | 300 | 60 |

5 | 50 | 10 |

300 + 60 + 50 + 10 = 420

Sheri notices that the process for the **area method** is almost exactly the same as the box method, but is likely to work very well with visual learners. The method works best with graph paper initially, but it is not necessary. The problem is graphically split up into four areas which correspond exactly to the four numbers from the box method. The areas are added together to get the multiplication product of the two original numbers.

The **lattice method** starts off with a similar concept as the box method but ends up looking very different.

As you can see, the number in each box is obtained by multiplying the number at the top of that column and the number furthest right on that row. The ones digit of the product is written below the diagonal. The tens digit of the product (if any) is written above the diagonal. The resulting numbers are then added along the diagonals.

During her research, Sheri ran across a number of recommendations to continue teaching the traditional method. Although it may be more difficult to learn at first than some of the other methods it also requires less space and is therefore easier to use once students have mastered place value concepts. In fact, most students continue to use this method for the rest of their lives.

There are many different methods of teaching multiplication. While the traditional method is usually the quickest to compute, it is a bit more difficult to conceptualize. The box, area, and lattice methods are designed to be easier to understand, but take more time and room to compute. Most math educators agree that it's best to teach the traditional method only after teaching one or more of the other methods. This allows students both a good understanding of the concepts involved in multi-digit multiplication, and a way to quickly compute these types of problems.

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SAT Mathematics Level 2: Help and Review22 chapters | 225 lessons

- What are the Different Types of Numbers? 6:56
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- How to Find the Prime Factorization of a Number 5:36
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