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SAT Mathematics Level 2: Help and Review22 chapters | 224 lessons
Mia has taught math and science and has a Master's Degree in Secondary Teaching.
As a teacher, I have the challenge of teaching to students that have different learning styles and abilities. For this reason, I need to offer them more than one strategy for solving a problem. Some students prefer a systematic process, while others prefer to use visual aids. It is also important for students to understand why the process works, rather than simply to follow the steps that I show them. In this lesson, we will practice three methods to multiply double-digit numbers. They are the box method, distribution method, and column method. You can then decide which one you prefer to use.
While the column method is the most commonly used strategy for multiplication, the box method is useful for understanding why the column method works. For this reason, we will look at the box method first.
The first step in the box method is to write each number in expanded form. Expanded form is a way of writing numbers that shows the value of its digits. For example in the number 34, the three is in the tens place so it is written as three tens, or 30. The four is written in the ones place so it has a value of four ones, or simply 4. Putting the numbers together, 34 is expanded as 30 + 4. In the same manner, the number 12 is expanded as 10 + 2.
Once the numbers are expanded, each number is written in a box, such as the one below. To fill in the boxes, we multiply the numbers that represent the row and column for each box.
30 | 4 | |
10 | 300 | 40 |
2 | 60 | 8 |
The final step is to add the numbers in the boxes together, giving us 408. Therefore, product of 34 and 12 is 408.
The distribution method uses a similar strategy as the box method, but without having to draw the boxes. Instead the numbers are written in expanded form, then placed in parentheses.
Next the distributive property is used to multiply the numbers. The distributive property tells us to multiply each number in the first set of parentheses by each number in the second set of parentheses. Lastly, we add the numbers together to get the final answer.
The column method is the most common method used. Once it is mastered, it is faster and more efficient. To use the column method, the numbers are written one beneath the other, so that the numbers in the ones place line up in a column, as do the numbers in the tens place. Let's see how the column method would have worked for our first example.
We begin by multiplying the first number, 34, times the digit in the ones place of the second number, which is two.
Next, we multiply 34 times the number in the tens place, which is one. Since the one is in the tens place, it has a value of ten. To make sure that this is taken into consideration, we leave a space in the ones place when we multiply the 34 times one.
Just like the box and distribution methods, our last step is to add the numbers together.
In this lesson, we reviewed three methods for multiplying double-digit numbers. All three methods use multiplication and addition to find the final product. The box and distribution methods involve writing each number in expanded form first. The box method organizes the expanded numbers in a table format, while the distributive method uses parentheses. The column method is the most common method and does not require expanding the numbers. Instead, the numbers are arranged so that each ones and tens digits of each number are aligned vertically, so that the digits can be multiplied in a systematic way.
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SAT Mathematics Level 2: Help and Review22 chapters | 224 lessons