Tuesday, June 13, 2006

Finger Arithmetic Part Three

Continuing finger arithmetic from Part Two. This one is called Part Three. It is the forth part in the series. Five's Complements are introduced. Clear as mud? Let's get started!

The Five's Complement of a number is the number you add to get five. So, the Five's Complement of one is four. That's because one plus four is five. Likewise, the Five's Complement of four is one. The other pair is two and three. The Five's Complement of two is three. Two plus three is five. And the Five's Complement of three is two.

Armed with this new knowledge, we tackle adding slightly bigger numbers. The very first example is 3 + 3. Start with a fist on the right hand. Put up three fingers. You want to add three fingers, but you don't have three fingers that can be added. The idea is to add five, and subtract the Five's Complement of three - which is two. So 3 + 3 = 3 + 5 - 2. However, do it in this order: 3 - 2 + 5. You have three fingers up on your right hand. Subtract two fingers, and add the thumb (five). That leaves you with your thumb (five) and one finger (one), for a total of six. Say six out loud.

The reason that the subtraction should be done first will become apparent in a later lesson. That lesson involves carries from one hand to the other. By performing the steps in this order, you can avoid ever having more than one pending operation. It is less confusing, and more reliable. Handling carries is the single biggest reason for error in traditional pencil and paper arithmetic.

Another example: 4 + 2. Start with a fist and set four fingers. The Five's Complement of two is three. So subtract three fingers. Then add the thumb for five. Read the answer out loud. Six.

Another example: 2 + 3. Start with a fist and set two fingers. The Five's Complement of three is two. Subtract two fingers and add the thumb (five). Read the answer: five. Note that you have no fingers up - just the thumb. You have five (the thumb) plus zero (no fingers). Zero is very important. Zero may mean nothing, but it isn't meaningless.

All of the examples: 1 + 4, 2 + 3, 2 + 4, 3 + 2, 3 + 3, 3 + 4, 4 + 1, 4 + 2, 4 + 3 and 4 + 4. Try them all. Don't forget to read the answer out loud.

When you are done with this lesson, practice some of the examples from previous lessons. Add small numbers. Do some counting. Remember to read the answers out loud. Practice five minutes a day. Five minutes each day for a week is worth more than twenty minutes each day for two days. And, five minutes can be squeezed into just about any schedule.


Anonymous said...

Thanks! I am a novice just exploring mental maths to teach my 6 year old and I found your blog very helpful in understanding basic addition. Well done

Stephen said...

Thanks. I hope to get to mental math in this series. My son does three digit addition and subtraction without using his toes.