## MATH GAMES FOR ADULT AND CHILD

A HUNDRED BOTTLES OF BEER ON THE WALL ...

TOPIC AND LEVEL: Counting: Intermediate, Advanced;
PLAY AFTER: THE HUNDREDS BOARD, COUNTING TILL YOU GET THERE, ACTIVITIES IN A BATHTUB
PLAY WITH: THE HUNDREDS BOARD, COUNTING TILL YOU GET THERE, ACTIVITIES IN A BATHTUB
EQUIPMENT: A simple, "four-function," calculator
• The Adult sets up activity on the calculator.
• The calculator provides the prompts for the human child to sing or state the numbers in order.
In order of difficulty:
• Let's count: one, two, three, four, ...
• Let's count backwards to zero from 10.
• Let's count by twos: two, four, six, eight, ...
• Lets's count backwards from twenty.
• Let's count backwards from 100.
• What's 3 plus 3 plus 3 plus 3?
• Let's sing "The Three Times Table."
• What's one and a half, plus one and a half, plus one and a half?
• I have 12. How many bunches of three is that?
• Have the Adult set up the calculator and the Child determine the starting number and constant addend or subtrahend.
• Have the Child set up the calculator and the Adult determine the starting number and constant addend or subtrahend.

 ENABLING CONSTANT FEATURES Method 1: CASIO [Constant addend/subtrahend] [operation] [operation] [Starting number] [=] [=] [=] ... Method 1 Examples: Counting: BY ONES: 1 + + 0 = = ... BY THREES: 3 + + 0 = = ... BACKWARDS FROM 100 BY ONES: 1 - - 100 = = ... Displaying: ODD NUMBERS: 2 + + 1 = = ... EVEN NUMBERS: 2 + + 0 = = ... Method 2: SHARP, TEXAS INSTRUMENTS, STANDARD "FOUR-FUNCTION" [Starting number] [operation] [constant addend/subtrahend] [=] [=] [=] ... Method 2 Examples: Counting: BY ONES: 0 + 1 = = ... BY THREES: 0 + 3 = = ... BACKWARDS FROM 100 BY ONES: 100 - 1 = = ... Displaying: ODD NUMBERS: 1 + 2 = = ... EVEN NUMBERS: 0 + 2 = = ...

We didn't play this game when Michael was a child. It is included here for the following reasons.

1. This activity provides a good means of sequentially printing numbers represented symbolically. The sequence may be used to reinforce, prompt, or verify sequences produced by humans.

2. Elementary teachers love the activity when it is introduced in workshops.

3. Some children are enchanted by calculators.

4. Cell phones have calculators.

This book encourages and demonstrates the presentation of an idea both concretely and abstractly. Throughout the book, numbers are presented in games with objects and with pictures (concretely) and with symbols and the spoken word (abstractly). Written words and symbolic notation (semiabstract or abstract representations) are not however stressed. Here symbolic notation serves as a prompt. This is not an activity for every child. This is not as valuable an activity as others in the book for a child aged two through five or six or even seven.

First, the Adult must set up the calculator to use its constant function capabilities. Constant functions enable the calculator to do the same operation over and over again more quickly. This is really quite easy. The calculator you get with checkbooks probably has the necessary constant features though most adults don't know they exist and don't use them.

To teach the calculator to count by twos, try one of two ways. Either:
[Starting number] + [constant addend] = = = ... or
[Constant addend] + + [Starting number] = = = .

The key sequence  [+]  [=] [=] [=] [=] [=] should show 0 then 2 then 2 then 4 then 6 then 8 then 10.

The key sequence  [+] [+]  [=] [=] [=] [=] [=] should show the numbers 2 then 0 then 2 then 4 then 6 then 8 then 10.

In the game COUNTING BY ..., the Adult softly says the evens and the Child, in a louder or normal voice, says "two, four, six, eight, ten." The calculator simply presents a symbolic representation of the sequence.

When using the calculator, the Adult should at first press the buttons to get the timing of the pressing of the equal button in sinc with the saying of the even number. If the saying comes before the pressing, the symbol verifies what has been said. If the pressing comes before the saying, the symbol prompts the word.

The calculator prompt would be useful for advanced children for difficult sequences. One might count by fives backwards or down from 100 by using the keystrokes:  [-]  [=] [=] [=] ... or  [-] [-]  [=] [=] [=] ...

Constant functions are engaged (and sometimes indicated on the display screen with a "K") in different ways depending on the machine. Above are listed two methods used by common calculators. Though A HUNDRED BOTTLES OF BEER ON THE WALL ... only makes use of addition and subtraction to count forward and backwards, most four-function calculators support other constant functions such as multiplication and division.

 MATH GAMES FOR ADULT AND CHILD© 2010, A² mathnstuff.com/math/games/mg31.htm