Grade 3-6 Week 7: Recognizing Multiples of 3 and 9

Teaching Video:

Once again, these are advanced strategies for students who know their number facts securely, and are ready to move on to more advanced topics.

The numbers 3 and 9 have an unusual, perhaps unique characteristic: for each of their multiples, the sum of the digits is also a multiple of 3 or 9. For example:

• Consider the number 78: Since 7 + 8 = 15, which is a multiple of 3, 78 is likewise a multiple of 3. (We could immediately extend this to any other combination of 7 and 8, such as 87, 780, 8070, etc.)
• Think about the number 153: Since 1 + 5 + 3 = 9, 153 is a multiple of 9 (153 = 9 x 17). Again, we could find other numbers with those digits, such as 351, 5013, 13 500, etc.

This feature of multiples of 3 and 9 can be used easily to test any whole number for divisibility by 3 or 9.

N.B. Watch the last few seconds of the video for an inadvertent error. I was embarrassed to see later that I made a mistake in checking 3-digit numbers for divisibility by 9. I hope no-one is too upset.

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