How to Add Integers Using the Number Line

There are several ways that we can visualize addition of integers. One way is to use the number line. If you can see the pattern in this method, it is easier to see the sign of the sum of two integers. To be able to use this method to add integers, first we should think of integers as movements on the number line. We can think of the positive integers as movement to the right and the negative integers as movement to the left.  Continue reading

Learning Japanese and Mathematics Simultaneously

I studied in Japan in a Teacher Training Program for one and a half years. A 4-month intensive Japanese language course was included in this program, so I was really lucky since I wanted to learn Japanese. Like many of you, I was a fan of Japanese anime since I was a kid.

The Intensive Japanese Language Course

For the first four months in the program, I, together with other international students, studied Japanese 5 hours a day, 5 days a week. We learned grammar, listening, speaking, and writing. As you probably know, writing is the hardest part since Japan uses a different writing system. They use three sets of characters namely, Hiragana, Katakana, Kanji, and they also know our alphabet. After graduating high school, Japanese students should master 46 Hiragana, 46 Katakana, and 2136 Kanji characters.

In our case, after four months of training, we learned around 400 Kanji characters. Although I had the chance to continue our Japanese language studies, I did not. I focused on my research and studied Japanese on my own.  Continue reading

A Different Way to Perform Division

All of us are familiar with the standard division method. The standard algorithm requires us to divide the digits with highest place values and get the largest possible quotient. For example, in dividing 984 by 23, we have to divide 98 by 23 which gives a quotient of 4.

The method that I am going to discuss below does not separate the digits. It lets you repeatedly divide and allows you to choose a more convenient quotient. Below are the steps of this method. We use 984 divided by 23 as example.

1. Write the dividend and the divisor separated by a colon and then draw a line above the numbers as shown.

division 1

2. First, we divide 984 by 23. Well, we don’t have to find the actual quotient. Maybe 30 is easier, so we choose 30. We write 30 above the line aligned to the place values of the dividend.  Continue reading

The Lattice Multiplication Algorithm

Aside from the standard multiplication algorithm we know, and the Line Multiplication which I already discussed, there is another method that we can use to multiply. This is called lattice multiplication. We can do this in multiplying 2-digit by 2-digit numbers but it can be extended to numbers with more digits. The steps of are as follows.

Step 1: Create 2 by 2 grid and place the numbers you want to multiply at the top and at the side as shown in the next figure. In this case, we want to multiply 83 by 42.

lattice multiplication

Step 2: Draw diagonals on each rectangle. This forms two triangles. These triangles will contain the digits of the product of the two given numbers. As shown below, the yellow square will contain the product of 3 and 2.  Continue reading

2015 1st Half in Review – Multimedia Resources

In the previous post, we have reviewed some posts in Math and Multimedia that discusses mathematics content. In this post, let us review some of the multimedia resources that had been posted in the first half of this year. This includes resources software, hardware, and videos. These multimedia resources can be used for teaching and learning mathematics.

2015 Year in Review – 1st Half

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