Congratulations! You are about to learn about FUNFORMS, the first advance in the general written numbering system in 1000 years, or more.
FUNFORMS© Copyright 2005
My goals today are to teach you enough about FUNFORMS that you will either choose to teach yourself the rest, or contact me for further instructions.
FUNFORMS© Copyright 2005
Eventually, my goal is that certain students will have the opportunity to be enriched by learning FUNFORMS and seeing how it “works”.
FUNFORMS© Copyright 2005
FUNFORMS© Copyright 2005
• You could easily ask, “Well don’t we already teach an alternate numbering system?”
• Yes, we do teach Roman numerals.
Everyone knows what
means, don’t they?
XVI
INTRODUCTION
FUNFORMS© Copyright 2005
• Yes, everyone knows what that means.Yes, everyone knows what that means.
• The problem is Roman Numerals are The problem is Roman Numerals are not easily manipulated. A student not easily manipulated. A student learning them learns little or nothing learning them learns little or nothing about the facts about how numbers about the facts about how numbers work.work.
INTRODUCTION
FUNFORMS© Copyright 2005
• FUNFORMS is a numbering system that is easily manipulated. It is a tally mark place order system, likely the first one.
• All of you recognize what this figure means:
INTRODUCTION
• It means 16, just like the Roman numeral that we just saw
FUNFORMS© Copyright 2005
How about if we wrote “16” like this?
INTRODUCTION
You would still understand that it represented the number value 16, wouldn’t you?
Or this…
FUNFORMS© Copyright 2005
• That brings us to FUNFORMS. In FUNFORMS the glyphs [numerals] are written vertically.
• There are specific positions where a horizontal mark or flag can be written.
• These flags reside on a vertical backbone structure called a staff.
INTRODUCTION
flags
staff
FUNFORMS© Copyright 2005
INTRODUCTION
16
8
4
2
32
64
128
Number values double at each successive position going down the staff.
Not surprisingly, number values halve at each successive position going up the staff.
256
1
FUNFORMS© Copyright 2005
INTRODUCTION
There are a few additional things that you’ll need to know to be able to use FUNFORMS.
Positive ValuesPositive ValuesDrawn to the RIGHT of the staff.
Negative ValuesDrawn to the LEFT of the staff.
positivenegative
FUNFORMS© Copyright 2005
UNITY POINT16
8
4
2
32
64
128
256
11INTRODUCTION
By convention, the first position on the staff, which can be marked by a flag extending to the right, represents the number one. This position is called UNITY POINT
FUNFORMS© Copyright 2005
INTRODUCTION
16
8
4
2
32
64
128
256
1
All potential positions ("points") below unity point have a whole number value that corresponds to a whole number power of 2
24
23
22
21
25
26
27
28
20Unity pointAs you have seen in the
counting that we did earlier, number values double at each successive position going down the staff.
FUNFORMS© Copyright 2005
INTRODUCTION
16
8
4
2
1
All potential positions ("points") above unity point are fractional in nature and represent the value of whole number negative powers of 2.
24
23
22
21
20 Unity Point
1/2 2-1
1/42-2
1/8 2-3
1/16 2-4
Fractional Numbers
Whole Numbers
FUNFORMS© Copyright 2005
COUNTING
COUNTING WITH FUNFORMSCOUNTING WITH FUNFORMS
FUNFORMS© Copyright 2005
COUNTING
COUNTING WITH FUNFORMSCOUNTING WITH FUNFORMS
• Funforms is simple. It is based on the concept of pairs.
• After number one we come to a pair of one's. 2
11
FUNFORMS© Copyright 2005
COUNTING
COUNTING WITH FUNFORMSCOUNTING WITH FUNFORMS
• Then we come to a pair of pairs. 4
2
11
• Funforms is simple. It is based on the concept of pairs.
• After number one we come to a pair of one's.
FUNFORMS© Copyright 2005
COUNTING
COUNTING WITH FUNFORMSCOUNTING WITH FUNFORMS
• Funforms is simple. It is based on the concept of pairs.
• After number one we come to a pair of one's.
• Then we come to a pair of pairs.
• Next is a pair of pairs paired.
• That is what each new position going down the staff stands for.
8
4
2
11
FUNFORMS© Copyright 2005
COUNTING
LETS BEGIN COUNTING!LETS BEGIN COUNTING!LETS BEGIN COUNTING!LETS BEGIN COUNTING!
FUNFORMS© Copyright 2005
COUNTING
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
11 22 33 44 55
FUNFORMS© Copyright 2005
COUNTING
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
66 77 88 99 1010
FUNFORMS© Copyright 2005
COUNTING
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
1111 1212 1313 1414 1515
FUNFORMS© Copyright 2005
COUNTING
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
16
8
4
2
11
1616 1717 1818 1919 2020
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
HERE ARE THE RULES NECESSARY HERE ARE THE RULES NECESSARY TO MANIPULATE FUNFORMSTO MANIPULATE FUNFORMS
You have already learned that numerical values double each time a flag (or a series of flags) moves down one position (or set of positions) on the staff.
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
HERE ARE THE RULES NECESSARY HERE ARE THE RULES NECESSARY TO MANIPULATE FUNFORMSTO MANIPULATE FUNFORMS
Similarly, numerical values halve each time a flag (or a series of flags) moves up one position (or set of positions) on the staff.
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
No more than one flag can be at any one position (except temporarily during manipulation). That is, there is either one flag at any given point (position), or there is no flag there.
flags
FUNFORMS© Copyright 2005
16
8
4
2
11
33 55++
ADDITIONADDITION
MANIPULATING FUNFORMS
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
16
8
4
2
11
33 55++
ADDITIONADDITION
ADDITION is carried out by simply ADDITION is carried out by simply combining (or “coalescing”) whatever combining (or “coalescing”) whatever
number values are to be added from the number values are to be added from the individual figures or glyphs and then individual figures or glyphs and then
simply "clearing" them by following the simply "clearing" them by following the already learned rules.already learned rules.
FUNFORMS© Copyright 2005
16
8
4
2
11
33 55++
ADDITIONADDITION
MANIPULATING FUNFORMS
FUNFORMS© Copyright 2005
CALCULATION/CLEARING CALCULATION/CLEARING PHASEPHASE
16
8
4
2
11
33 55++
ADDITIONADDITION
Remember, no more than one
flag is allowed at any point (EXCEPT
temporarily during calculations).
Remember, Any two flags at one position (point)
are the equivalent of one flag at the
next position down.
MANIPULATING FUNFORMS
88
SUMSUM
FUNFORMS© Copyright 2005
16
8
4
2
11
ADDITIONADDITION
MANIPULATING FUNFORMS
The FUNFORM figure is now in its simplest form and
nothing further needs to be or can
be done.
33 55++ 88
SUMSUM
==
FUNFORMS© Copyright 2005
6565 9191++ADDITIONADDITION
MANIPULATING FUNFORMS
2
11
32
64
4
16
8
128
256
The FUNFORM figure is now in its simplest form and
nothing further needs to be or can
be done.
Simply add the remaining flags for
the answer.
SUMSUM
156156
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
Now, let's shift our attention to negative numbers and subtraction. Converting a number to its negative counterpart simply means drawing it to the left of the staff. Conversely, converting a negative number to its minus equivalent would involve writing it on the right side of the staff.
SUBTRACTIONSUBTRACTION
FUNFORMS© Copyright 2005
CALCULATION/RESOLVING CALCULATION/RESOLVING PHASEPHASE
16
8
4
2
11
1616 11--
SUBTRACTIONSUBTRACTION
negative
Converting a number to its negative counterpart simply means drawing it to the left
of the staff.
MANIPULATING FUNFORMS
Any one flag at one level is the
same as 2 flags at the
preceding level
FUNFORMS© Copyright 2005
16
8
4
2
11
1616 11--
SUBTRACTIONSUBTRACTION
MANIPULATING FUNFORMS
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
16
8
4
2
11
1616 11--
SUBTRACTIONSUBTRACTION
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
16
8
4
2
11
1616 11--
SUBTRACTIONSUBTRACTION
The FUNFORM figure is now in its simplest form and
nothing further needs to be or can
be done.
1515
REMAINDERREMAINDER
==
FUNFORMS© Copyright 2005
225225 4444--SUBTRACTIONSUBTRACTION
MANIPULATING FUNFORMS
2
11
32
64
4
16
8
128
256
FUNFORMS© Copyright 2005
225225 4444--SUBTRACTIONSUBTRACTION
MANIPULATING FUNFORMS
2
11
32
64
4
16
8
128
256
FUNFORMS© Copyright 2005
SUBTRACTIONSUBTRACTION
MANIPULATING FUNFORMS
2
11
32
64
4
16
8
128
256
225225 4444--
FUNFORMS© Copyright 2005
SUBTRACTIONSUBTRACTION
MANIPULATING FUNFORMS
2
11
32
64
4
16
8
128
256
225225 4444--
FUNFORMS© Copyright 2005
225225 4444--SUBTRACTIONSUBTRACTION
MANIPULATING FUNFORMS
2
64
8
11
32
4
16
128
256
181181
The FUNFORM figure is now in its simplest form and
nothing further needs to be or can
be done.
==
FUNFORMS© Copyright 2005
16
8
4
2
11
11--1616
ADDITION AND SUBTRACTIONADDITION AND SUBTRACTION(overview)(overview)
MANIPULATING FUNFORMS
1515Looking back, pay particular attention to 16 – 1, please. Note that whenever there is a long gap between a minus number value (in this case –1) and a positive one (16), exactly what you see here happens. Each intervening point becomes filled with a flag beginning one position up from the first positive flag after the gap.
You should only have to see this operation take place once to be able to apply it each time the situation presents itself. I think of this like unzipping a zipper.
FUNFORMS© Copyright 2005
16
8
4
2
11
ADDITION AND SUBTRACTIONADDITION AND SUBTRACTION (overview)(overview)
MANIPULATING FUNFORMS
11++1515 1616
Similarly, if you added 1 to 15, you would begin with 2 flags at the one position, which would become 1 flag at the two position (where there was already a flag), and the flags would “tumble” down sequentially, leaving just one flag at the sixteen position.
I think of those events mechanically like a zipper closing or like a Jacob’s ladder.
FUNFORMS© Copyright 2005
MULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
Multiplication amounts to serial addition. It is done by writing the multiplicand at each position that a flag exists on the
multiplier (using the formulaic qualities of Funforms), coalescing the intervening glyphs, and then clearing the resultant
figure by the rules already learned.
FUNFORMS© Copyright 2005
66 1010XX
MULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
4
2
11
In the writing processes, it helps to think about the
multiplicand in terms of its spaces and flags beginning at
unity point.
Unity point
For example “10” could be thought of as “space-flag-
space-flag”.
SPACE
FLAG
SPACE
FLAG
32
FUNFORMS© Copyright 2005
66 1010XX
MULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
4
2
11If 10 were to be
multiplied by 6, one would write space-flag-space-flag first at the position of one of the
two flags that make up 6, and then by writing space-flag-space-flag
at the level of the other flag making up 6.
32
New Temporary Unity Point
SPACE
FLAG
SPACE
FLAG
FUNFORMS© Copyright 2005
66 1010XX
MULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
4
2
11
32
New Temporary Unity Point
SPACE
FLAG
SPACE
FLAG
FUNFORMS© Copyright 2005
66 1010XX
MULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
4
2
11
32
FUNFORMS© Copyright 2005
66 1010XX
MULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
2
11
16
8
4
32
6060==
FUNFORMS© Copyright 2005
FUNFORMS
FUNFORMS© Copyright 2005
2222 66xxMULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
4
2
11
32
64
128
256
SPACE
FLAG
FLAG
New Temporary Unity Point
FUNFORMS© Copyright 2005
2222 66xxMULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
4
2
11
32
64
128
256
SPACE
FLAG
FLAG
New Temporary Unity Point
FUNFORMS© Copyright 2005
2222 66xxMULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
4
2
11
32
64
128
256
SPACE
FLAG
FLAG
New Temporary Unity Point
FUNFORMS© Copyright 2005
2222 66xxMULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
4
2
11
32
64
128
256
FUNFORMS© Copyright 2005
2222 66xxMULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
4
2
11
32
64
128
256
FUNFORMS© Copyright 2005
2222 66xxMULTIPLICATIONMULTIPLICATION
MANIPULATING FUNFORMS
16
8
2
11
32
64
4
128
256
132132==
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
16
8
4
2
11
32
64
FRACTIONSFRACTIONS
1/21/2
1/41/4
Consider the following FUNFORM figures.
In the first figures, 24 is repeatedly halved by
moving it up one position at a time.
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
16
8
4
2
11
32
64
FRACTIONSFRACTIONS
1/21/2
1/41/43 of 8
24243 of 4
12123 of 2
663 of 1
333 of 2-1
3/23/2
3 of 2-2
3/43/4
As it passes unity point, it becomes
fractional, at least in part.
Unity Point
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
16
8
4
2
11
32
64
1/21/2
1/41/4
The same is true for "fiveness" written at various positions.
FRACTIONSFRACTIONS
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
16
8
4
2
11
32
64
FRACTIONSFRACTIONS
1/21/2
1/41/45 of 1
555 of 2
10105 of 8
40405 of 2-2
5/45/4
5 of 2-1
5/25/2
Fractional at Unity Point
Unity Point
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
In adding fractions, there is no need to seek
the lowest common
denominator.
ADDING FRACTIONSADDING FRACTIONS
5/85/8 3/43/4++
5/8 (red) + 3/4 (orange) is added exactly like you would add any
Funform figure.
You do not need to know that they have fractional
values to correctly add them.
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
ADDING FRACTIONSADDING FRACTIONS
5/85/8 3/43/4++
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
ADDING FRACTIONSADDING FRACTIONS
5/85/8 3/43/4++ 113/83/8==
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
ADDING FRACTIONSADDING FRACTIONS
7/87/8 ++ 111/21/2
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
ADDING FRACTIONSADDING FRACTIONS
7/87/8 ++ 111/21/2 == 223/83/8
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS
Multiplying fractions is done Multiplying fractions is done just like just like multiplying whole numbersmultiplying whole numbers, attending to , attending to
how the flags on the multiplicand relate to how the flags on the multiplicand relate to unity point. unity point.
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS
To multiply fractions, it is again wise to say to
oneself how the multiplicand looks,
beginning at unity point.
1/21/2 1/21/2xx
Unity Point
½ x ½ is shown. ½ can be thought of as space-flag.
SPACE
FLAG
ACSENDING FROM UNITY POINT
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS
Multiplicand appearance, beginning at unity point.
1/21/2 1/21/2xx
NewTemporaryUnity Point
SPACE
FLAG
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS
1/21/2 1/21/2xx == 1/41/4
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
4
2
1
1/2
1/41/4
8
16
1/81/8
1/161/16
MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS
3/43/4 3/43/4xx
SPACE
FLAG
FLAG
Unity Point
NewTemporaryUnity Point
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
4
2
1
1/2
1/41/4
8
16
1/81/8
1/161/16
MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS
3/43/4 3/43/4xx
SPACE
FLAG
FLAG
NewTemporaryUnity Point
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
4
2
1
1/2
1/41/4
8
16
1/81/8
1/161/16
MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS
3/43/4 3/43/4xx
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
4
2
1
1/2
1/41/4
8
16
1/81/8
1/161/16
MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS
3/43/4 3/43/4xx 9/169/16==
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
DIVISIONDIVISION
DIVISION is just DIVISION is just serial subtractionserial subtraction, while , while keeping score.keeping score.
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
DIVISIONDIVISION
1616 -- 44
1616 44÷÷ == ??I believe that a learner should be asked…
How many times can the divisor be subtracted from the number to be divided?
FUNFORMS© Copyright 2005
12128844001616
MANIPULATING FUNFORMS
-- 44
1616 44÷÷ ??11223344==
DIVISIONDIVISION
How many times can the divisor be
subtracted from the number to be divided?
FUNFORMS© Copyright 2005
3535 77÷÷
DIVISIONDIVISION
MANIPULATING FUNFORMS
16
8
4
2
11
32
Serial Subtraction
Recording Staff
The results of the repeated subtractions are simply recorded
off to one side using a “recording staff” and cleared at the end of
the operation.
Unity Point
FLAG
FLAG
FLAG
FUNFORMS© Copyright 2005
3535 77÷÷
DIVISIONDIVISION
MANIPULATING FUNFORMS
16
8
4
2
11
32
FLAG
FLAG
FLAGNew
TemporaryUnity Point
RECORD FLAG AT NEW UNITY POINT
FUNFORMS© Copyright 2005
3535 77÷÷
DIVISIONDIVISION
MANIPULATING FUNFORMS
16
8
4
2
11
32
FUNFORMS© Copyright 2005
3535 77÷÷
DIVISIONDIVISION
MANIPULATING FUNFORMS
16
8
4
2
11
32
OUR ORIGINAL MATH PROBLEM Serial Subtraction
NOTE: Unity point marker does not change from
original position.
RECORD FLAG AT UNITY POINT
FLAG
FLAG
FLAG
FUNFORMS© Copyright 2005
3535 77÷÷
DIVISIONDIVISION
MANIPULATING FUNFORMS
16
8
2
4
11
32
55==
The final results of our “recording staff” provides us with the
answer.
FUNFORMS© Copyright 2005
6363 99÷÷
DIVISIONDIVISIONMANIPULATING FUNFORMS
16
8
2
4
11
32
64
Serial Subtraction
Recording Staff
Unity Point
FLAG
FLAG
SPACE
SPACE
FUNFORMS© Copyright 2005
6363 99÷÷
DIVISIONDIVISIONMANIPULATING FUNFORMS
16
8
2
4
11
32
64
RECORD FLAG AT UNITY POINT
Unity Point
FLAG
FLAG
SPACE
SPACE
FUNFORMS© Copyright 2005
6363 99÷÷
DIVISIONDIVISIONMANIPULATING FUNFORMS
16
8
2
4
11
32
64
NewTemporaryUnity Point
RECORD FLAG AT NEW UNITY POINT
FUNFORMS© Copyright 2005
6363 99÷÷
DIVISIONDIVISIONMANIPULATING FUNFORMS
16
8
2
4
11
32
64
RECORD FLAG AT NEW UNITY POINT
NewTemporaryUnity Point
FUNFORMS© Copyright 2005
6363 99÷÷
DIVISIONDIVISIONMANIPULATING FUNFORMS
16
8
2
4
11
32
64
== 77
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
551/21/2 221/21/2÷÷
DIVIDING FRACTIONSDIVIDING FRACTIONS
Division for numbers that are Division for numbers that are not wholenot whole powers of two is (again) just serial powers of two is (again) just serial subtraction while keeping score.subtraction while keeping score.
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
551/21/2 221/21/2÷÷
DIVIDING FRACTIONSDIVIDING FRACTIONS
Serial Subtraction
Recording Staff
Unity Point
FLAG
SPACE
FLAG
NewTemporaryUnity Point
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
551/21/2 221/21/2÷÷
DIVIDING FRACTIONSDIVIDING FRACTIONS
DIVISOR
The FUNFORM figure is now a lower value than
our divisor giving us our remainder.
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
1
2
1/21/2
16
32
1/41/4
1/81/8
551/21/2 221/21/2÷÷
DIVIDING FRACTIONSDIVIDING FRACTIONS
22==
REMAINDER
AFTER AFTER PREVIOUS PREVIOUS
SUBTRACTION SUBTRACTION PROCESSPROCESS
1/21/2RRRecording Staff
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
2525 221/21/2÷÷
DIVIDING FRACTIONSDIVIDING FRACTIONS
Serial Subtraction
Recording Staff
Unity Point
New Temporary Unity Point
FLAG
SPACE
FLAG
FLAG
SPACE
FLAG
NewTemporaryUnity Point
FUNFORMS© Copyright 2005
MANIPULATING FUNFORMS
8
4
2
1
1/21/2
16
32
1/41/4
1/81/8
DIVIDING FRACTIONSDIVIDING FRACTIONSRecording Staff
1010==2525 ÷÷ 221/21/2
FUNFORMS© Copyright 2005
FUNFORMS INFORMATION PAGE
FUNFORMS WEBSITEFUNFORMS WEBSITEhttp://www.funforms.comhttp://www.funforms.com
CLICK HERE TO RETURN TO PREVIOUSLY VIEWED SLIDE
PLAY PRESENTATION OVERPLAY PRESENTATION OVER
GLOSSARY PAGEGLOSSARY PAGE
NAVIGATION PAGENAVIGATION PAGE
FUNFORMS© Copyright 2005
GLOSSARY PAGE 1
NAVIGATION PAGENAVIGATION PAGE
FLAGThe horizontal mark used for denoting the presence of that particular numerical value along a staff.
FUNFORMSA new place order, tally mark binary numerical system that uses glyphs and is easily manipulated.
GLYPHA symbol that conveys [numerical in this case] information nonverbally.
RECORDING STAFFA special vertical line used to record the results of repeated subtractions during the division process. These results are later cleared at the end of the operation and used to determine the final answer.
STAFFThe vertical backbone structure used to place flags. Flag values increase in a doubling fashion [arithmetically progressive powers of 2] as they move toward the bottom of the staff and decrease by halving [in whole powers of 2] as they move toward the top of the staff.
UNITY POINTThe first position on the staff, which is marked by a flag extending to the right. It represents the numerical value one.
POSITIVE VALUESAll flag values displayed to the RIGHT of the FUNFORMS staff.
NEGATIVE VALUESAll flag values displayed to the LEFT of the FUNFORMS staff.
CLICK FOR
PAGE 2
FUNFORMS TERMSFUNFORMS TERMS
FUNFORMS© Copyright 2005
GLOSSARY PAGE 2
NAVIGATION PAGENAVIGATION PAGE
DENOMINATORThe divisor of a fraction.
DIVIDENDA number to be divided by another number. E.g. in 10 divided by 2, “10” is the dividend.
DIVISORThe number by which a dividend is divided. E.g. in 10 divided by 2, “2” is the dividend.
EXPONENTA mathematical notation indicating the number of times a quantity is multiplied by itself.
FRACTIONA part of a whole number.
MULTIPLICANDThe number that is multiplied by the multiplier. E.g. in 10 times 2, “2” is the multiplicand.
MULTIPLIERThe number by which a multiplicand is multiplied. E.g. in 10 times 2, “10” is the multiplier.
WHOLE NUMBERAny of the natural numbers (positive or negative) or zero.
CLICK FOR
PAGE 1
MATHEMATICAL TERMSMATHEMATICAL TERMS
FUNFORMS© Copyright 2005
FUNFORMS NAVIGATION PAGE
IntroductionIntroduction
The BasicsThe Basics
Negative and Positive ValuesNegative and Positive Values
Unity PointUnity Point
CountingCounting
ManipulationManipulation
AdditionAddition
SubtractionSubtraction
BACK
MultiplicationMultiplication
FractionsFractions
Adding FractionsAdding Fractions
Multiplying FractionsMultiplying Fractions
DivisionDivision
Dividing FractionsDividing Fractions
GLOSSARY PAGEGLOSSARY PAGE