Friday, November 4, 2016

Finding Factors of Greater Numbers

To help her student prepare for our upcoming Number of the Day quiz, a parent recently asked me, "Do they need to know all the multipliers of a number or only up to 10?   For instance for 42 – would they need to know 2x21, 3x14, 6x7 ?   Or for 48- 2x24, 3x16, 4x12, 6x8,    He seems to struggle with the double digit multipliers.  I probably would not know those either without a calculator or memorization."

I am sharing my response in case it helps you prepare your student:

In class, we noticed a pattern:  all the numbers we're finding factors of/considering as multiples 2-9 have a one-digit number in the factor pair, so I have been emphasizing testing 1-9 in order using multiplication.  (Since the students only need to be able to work in the range of 1-100, this pattern will be true with every number except 100)  Trying a multiple of 10 as the other factor can help the counting process go faster.  For example with 54:

2 x 20 = 40, so 2 x 21 = 42, 2 x 22 = 44, 2 x 23 = 46, 2 x 24 = 48, 2 x 25 = 50, 2 x 26 = 52 , 2 x 27 = 54 

You could also consider 2 x 30 = 60, which is closer, but past 54 and work backwards: 2 x 29 = 58, 2 x 28 = 56, 2 x 27 = 54

The most efficient strategy will be division (if there is a remainder, then the divisor is not a factor), but since we haven't gotten to division yet in our Math lessons, I am waiting to introduce this (although what the students are doing now with a multiplication equation missing a factor is division).