**The Current Picture**

Being able to count groups by numbers other than 1 is a useful skill for multiplication and division, where, by definition, we are dealing with some number of groups of equal size.

Schools do pay lip service to this idea, but usually only in a limited way. Typically they will give some instruction and sometimes even some practice in counting by 1’s, 2’s, 5’s, and 10’s. Skip counting by other numbers is almost never done. It is often dismissed as dull drill and practice with zero creativity, fun or usefulness, especially in a digital world.

That argument works well unless

- the battery in your calculator or personal assistant device dies,
- or you lose your personal devise,
- or you drop it into a puddle, sink, urinal or overboard
- or God forbid, you enter a wrong digit.

The ultimate price you pay for not having a cortical back-up for these devices, is that you never learn adequate estimation skills. You have little if any idea of approximately what the answer should look like. You are shackled to your calculator and its input errors with no backup.

Besides, teaching and learning skip counting skills is quick and relatively painless and can be achieved in 3-5 minutes of daily self-instruction and practiced while you wait for a bus, stand in a checkout line, or wait for an appointment.

**Using Recursive Number Patterns**

**Â Â Â Â Â Â Â Â Â Â Â **I am continually surprised about how few people have ever been made aware of recursive number patterns. It is an easy way to teach students to do Count âbys or Skip Counting. Take the example from the last blog, where I was teaching college and university graduates to count by 6s as part of a program that teaches multiplication and division.Â When I asked them to count by 6s, they were far from fluent. So I showed them the pattern of recursive numbers for counting by 6s.

6Â Â Â Â Â 12Â Â Â Â 18Â Â Â Â 24Â Â Â Â 30

36Â Â Â Â 42Â Â Â Â 48Â Â Â Â Â Â 54 Â Â Â Â Â 60

66Â Â Â Â 72Â Â Â Â 78Â Â Â Â Â Â 84Â Â Â Â Â 90

When I asked them to **See and Say Counting by 6âs**, they had no trouble reaching 150 counts per minute in a couple of attempts. I then had them **Think and Say Counting by 6’s** (no model, just their memory). They were better but not yet fluent.

The next step was to have them learn a sequence of just 5 numbersÂ Â **6,Â Â 2, Â 8,Â Â 4,Â Â 0. Â Â **Each number in the sequence is the number in the 1’s column for counting by 6’s.Â Once you get to 0, you start back at 6 and say the next number. When you see the pattern and learn the numbers that recur, you see a huge jump in skills. Using these 5 numbers, they were able to skip count by 6’s at 150 counts per minute with 0-2 errors in just a few minutes.

Your child can learn to skip count the same way. Every number has its own pattern, most of which have 5 to 6 numbers from the 1’s column. Try it. Skip counting will make learning multiplication and division much, much easier and faster.