## Middle School

### Multiplication: 12’s

Many children have trouble memorizing their twelves tables in multiplication. I have found that by exploring patterns in math, children who don’t just automatically memorize their times tables are better apt to learn. What I noticed is that the ones column has a pattern of 0, 2, 4, 6, 8 that continues throughout all the facts. In the first five facts, the tens column keeps the 1, 2, 3, 4.

The first five multiplication facts are:

12 x 0 = 0

12 x 1 = 12 (in the tens column, keep the 1)

12 x 2 = 24 (in the tens column, keep the 2)

12 x 3 = 36 (in the tens column, keep the 3)

12 x 4 = 48 (in the tens column, keep the 4)

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The rule changes every multiple of 5:

We now have 12 x 5 = 60

(the rule changes: in the 10s column, the number will increase by 1)

The ones column keeps the 0, 2, 4, 6, 8 pattern.

12 x 5 = 60 (the five increases by one to 6)

12 x 6 = 72 (the six increases by one to 7)

12 x 7 = 84 (the seven increases by one to 8)

12 x 8 = 96 (the eight increases by one to 9)

12 x 9 = 108 (the nine increases by one to 10)

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We now have our multiple of five: 12 x 10 = 120, which means our rule is changing again.

(the rule changes: the number will increase by 2)

The ones column keeps the 0, 2, 4, 6, 8 pattern.

12 x 10 = 120 (the ten increases by two to 12)

12 x 11 = 132 (the eleven increases by two to 13)

12 x 12 = 144 (the twelve increases by two to 14)

12 x 13 = 156 (the thirteen increases by two to 15)

12 x 14 = 168 (the fourteen increases by two to 16)

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We now have our multiple of five: 12 x 15 = 180, which means our rule is changing again.

(the rule changes: the number will increase by 3)

The ones column keeps the 0, 2, 4, 6, 8 pattern.

12 x 15 = 180 (the fifteen increases by three to 18)

12 x 16 = 192 (the sixteen increases by three to 19)

12 x 17 = 204 (the seventeen increases by three to 20)

12 x 18 = 216 (the eighteen increases by three to 21)

12 x 19 = 228 (the nineteen increases by three to 22)

The pattern continues on and on…

Download the chart: Multiplication 12s

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