Primer-The Telephone Sequence

Adding and Subtracting Three is as Easy as 147. 

147? I told you it was weird. Hopefully you have done your homework since my last post and studied the telephone dialing pad. The first thing we need to do is rotate it 90° counter-clockwise and then move the zero to the top left next to the 3 key.

Now, let's skip count in 3's starting at 0. Follow along the telephone sequence with your finger: 

3, 6, 9, 12, 15, 18, 21, 24, 27, 30. 

We are back at the beginning of the sequence, 0. Do you see what happened to the tens' place when we changed rows? It incremented. If you commit this sequence to memory, then you can easily add 3 to any number. For example, 34 + 3 = 37 because 7 comes after 4 in the telephone sequence and since it is on the same row, the tens' place value does not change. How about 28 + 3? Since the next number in the telephone sequence is 1 and it appears on the next row, we increment the tens' place value to get 31. 

Let's skip count backwards in 3's starting at 30. Follow along the telephone sequence with your finger:

30, 27, 24, 21, 18, 15,12, 9, 6, 3. 

The sequence is in reverse and we decrement the tens' place value when we change rows. Now we subtract 3 from any value easily. For example, 25 – 3 = 22 since 2 is the previous number in the telephone sequence. The tens' place value did not change, because we did not change rows. How about 31 – 3? Since 8 comes before 1 in the telephone sequence and it is on a different row we decrement the tens' place value to get 28.

Most of you probably have experience with number keypads like those on telephones so memorizing the telephone sequence is not very difficult. Memorizing it pays a tremendous dividend when adding and subtracting 7.

Use the Telephone Sequence for Seven Too.

Why can we use the telephone sequence to add and subtract seven? Since 7 = 10 – 3, we can use the telephone sequence backwards to add and subtract seven. Let's skip count in 7's starting at 7 while following along the telephone sequence backwards with our finger:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77. 

And we've cycled back around to the beginning again. You can see that this time, we always increment the tens' place unless we change rows, in which case we don't. 

Let's skip count backwards in sevens starting at 77. Again, follow along through the sequence with your finger.

77, 70, 63, 56, 49, 42, 35, 28, 21, 14, 7. 

Now we can add and subtract seven easily by navigating the telephone sequence. For example, 65 + 7 = 72 because we didn't change rows and 2 precedes 5 in the telephone sequence. 89 – 7 = 82 because 2 follows 9 in the telephone sequence and we don't change the tens' place because we changed rows. 

Here are some more problems to cut your teeth on.

In the next post, it's all about even and odd numbers. Thanks for reading.
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