Digital Dilations and Roots

Digital Dilations: One of the challenges for young mathematicians is being able to write numbers in the appropriate size. Sometimes a number must be written to match another number on a page. When adding numbers vertically, numbers must be written precisely in the same font size lined up by the ones or units column. 

We started the lesson talking about dilations. A dilation is a type of transformation that changes the size of the image. If the dilation of a number is twice the size of the original image or number, we say that it has a scale factor of 2, if it is three times the size, we say it has a scale factor of 3. If the dilation is one half the size of the original image or number, we say that it has a scale factor of 1/2.

I had the children practice creating dilations from a large font to a slightly smaller font and so on until they couldn't even see the number. See the pdf called Digital Dilations.

Digital Roots: We then focused on practicing more digital roots by casting away nines. First, we practiced with two digit numbers, then three, then four up to seven digit numbers. Remember, when casting away nines, you need not add up all of the digits in order to find the root. You first cross out the nines, then two digits that add up to nine, until you are left with only digits that do not add up to nine.

Students are still confused when all of the numbers are cast away. In this case, the digital root is nine. For example, if the number is 189, the 9 and the 1+8 are cast away, leaving 0. But the digital root is not 0. It must be between 1-9. To prove that the digital root here is 9, just add up the three digits and you get 18 which has a digital root of 9.

See the pdf entitled Digital Root 2-7 Digits.

The next post is a little more advanced using digital roots to check the answers to complicated addition problems.