STRIP BOARD
a. Introduction and List of Materials
Introduction:
The child first dealt with the concept of subtraction with number
rods. Later he learned the concept with the decimal system material,
and the stamp game. Through memorization the child will master
all of the combinations necessary for his work.
Materials:
...Subtraction Strip Board, which differs from the addition strip
board in that the numerals 19 are in blue,
...followed by a blue line, and 1018
in red.
...Box of 17 neutral strips (to limit the minuend) 9 blue strips
(to function as the subtrahend) and
...9 sectional pink strips (to serve as
the difference)
...Booklet of Combinations (page one deals with 18)
...Box of Subtraction Combinations (same combinations as are
found in the booklet)
...Box of blue tiles for bingo game
...Subtraction Charts I, II, III (for control)
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STRIP BOARD
b. Initial Presentation
To familiarize the child with
the subtraction strip board, the teacher demonstrates. The neutral
strips and the blue strips are lain out in the pipe organ arrangement.
The teacher chooses a neutral strip. This is used to cover the
numerals we don't need
The child then chooses a number to subtract, i.e. 5 The blue
5 strip is placed end to end with the neutral strip. The answer
for 135 is the first number that shows....8. If by chance the
child chooses a subtrahend that would give a difference greater
than nine, the teacher explains that the maximum difference that
can exist is nine, 13  2 for example is not necessary.
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STRIP BOARD
c. Subtraction Booklets
Materials:
...booklets of 18 pages; each page has combinations with a common
minuend the first page deals with 18
...Subtraction Strip Board, strips
...Chart I
Exercise:
The child begins with the first page in his booklet. With 18,
a neutral strip is not needed, it is already the last number
in the row. The combination is 18  9; therefore, the blue strip
for nine is placed over the numbers. The first number to show
is 9. That's the difference, and it is written in the booklet.
18  9 is the only combination possible. The child may try others
to prove this.
Going on to the second page, the minuend is now 17, therefore
the smallest neutral strip is used to cover 18 (the number greater
than 17) The child reads the first combination, takes the blue
strip corresponding to the subtrahend and places it over the
numbers. The answer is read and is written on the form. For the
second combination, we know that the minuend will be the same,
therefore the neutral strip doesn't need to be changed.
After completing the page, the child should notice 17  9 = 8
that while the minuend is fixed, there is 17  8 = 9 a decrease
of one unit in the subtrahend, and, therefore, an increase of
one unit in the difference.
Notes: The blue strip is used
as the subtrahend because the child must realize that he is subtracting
a group. In subtraction, the aim is always to break down the
ten. Since the neutral strips occupy much space, after this exercise
the child may use only the longest, sliding it off the edge to
its correct position.
Observations on the Subtraction
Chart I:
This chart reproduces all of the combinations in the subtraction
booklet. In the first 9 columns the differences are common in
horizontal rows. This indirectly shows the invariable property
of subtraction; if one adds a number to both the subtrahend and
the minuend, the difference is the same, i.e. 1 1 = 0,
2 2 = 0, 3 3 = 09 9 = 0
In the last nine columns, the subtrahend is consistent in each
horizontal row; thus the minuend and the difference increased
by one, i.e. 10 9 = 1, 11 9 = 218 9 = 9
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STRIP BOARD
d. Combination Cards
Materials:
...subtraction strip board, strips (neutral and blue)
...combination cards
...Chart I (for control)
Presentation:
The child fishes for a combination, reads it and writes it on
his paper, 15 7 =. The neutral strip is used to cover all
of the numbers greater than 15 which are not needed. Next to
the neutral strip is placed the blue 7 strip. The difference
is the last number showing; this is recorded.
The exercise continues as long as the child would like, and then
he controls his work with Chart I.
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STRIP BOARD
e. Decomposition of a Number
Materials:
...subtraction strip board, all of the strips
Presentation:
(In this exercise the pink strips are used for the first time
to function as the difference)
Let's see how many ways we can decompose (break down) 9? Nine
will be the minuend, therefore a neutral strip is placed over
the number greater than 9. The teacher writes down the combination
9 1 =___. (Note: decomposition always begins at one, removing
one unit at a time) The subtrahend is one, so a blue 1 strip
is needed. This time it is placed on the first row, under 9.
The child guesses the answer and tries to place the pink strip
for his answer on the row. If it fits he knows that he is correct.
The answer is recorded. The work continues in order until all
of the blue strips are used, and a column of combinations has
been completed9 9 = 0
In this exercise the child may recall his work of this fashion
in addition, which resulted in elimination of some combinations.
In subtraction, all of the combinations are needed and must be
learned.
The child tries to decompose other numbers in the same way: i.e.
14. How many ways can 14 be decomposed? The neutral strip identifies
14 as the minuend. Can I do 14 1? No (the one strip may
be tried, but it will not work because 9 is the maximum difference
we can have) 14 2? 14 4? 14 4? 14 5?
Yes. The decomposition begins here laying out the blue 5 strip
and the pink 9, recording 14 5 = 9, and so on to 14
9 = 5.
Control of Error: Chart I
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STRIP BOARD
f. Decomposition of a Number with Zero as the Subtrahend
Materials:
...subtraction strip board, all of the strips
Presentation:
As before, the teacher presents a number to decompose. The neutral
strip is lain over the number to limit the minuend. On a piece
of paper, the teacher writes, i.e.
7 0 =___. What must be taken away? nothing. In subtraction
also, we see that zero doesn't change anything. On the first
row, then, the pink strip for seven is placed and this difference
is recorded. 7 0 = 7 The child continues7 7 = 0
Control of Error: Chart I
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THE SNAKE GAME
Materials: same materials as for previous snake
games:
...box of colored bead bars 19
...box of ten bars
...box of black and white reminder bars (place holders)
...also box, with 9 compartments, for gray bead bars 19
...(for bars of 69, there is a small
space or color change after the fifth bead to facilitate counting)
Presentation:
As before, a snake is made, though this time we add to these
colored bead bars, some gray bead bars. (Note: before the first
gray bar appears, several colored bead bars should appear to
create a large minuend) As before we begin counting, using the
black and white reminder bead bars. When we come to a gray bar,
we must subtract. The preceding black and white bead bar and
the gray bar are isolated. 8 4 = 4 The 4 black bar is placed
in the box cover with the other original colored beads.
Counting continues as usual. The next two bead bars are isolated:
black 3 and gray 7. This gray bar means I must subtract. 3
7 is impossible; therefore I take one ten bar (from the snake's
new skin) and place it beside the 3 to make 13. 13 7 =
6. The black and white 6 is placed in the snake; the black 3
is placed with the other reminder bars; the ten bar is placed
back in the box with the other ten bars; the gray 7 is placed
in the box cover with the other original colored bead bars.
When the counting is finished, the gold bead bars (and reminder
bar) are counted to find the result.
Control of Error: In the box cover are colored bead
bars and gray bead bars mixed. First, these are separated into
two groups, lain in chronological order. A gray bar is placed
with its equivalent colored bar. Two colored bars may be combined
to match a gray bar, or vice versa. When all of the gray bars
have been matched; the colored bars are paired to be matched
with ten bars as usual . When all of the bars have been matched,
we know the counting was done correctly.
Direct Aim: to memorize subtraction
Indirect Aim: to prepare for algebra: positive
and negative numbers
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SUBTRACTION CHARTS AND COMBINATION
CARD EXERCISES
a. Passage From Chart I to Chart II
Materials:
...Chart II (the numbers in pink function as the minuend; the
blue as the subtrahend)
...combination cards
...Chart I
Exercise:
The child fishes for a combination, i.e. 9 2 =___, reads
it and writes it down on his paper. A finger is placed on 9 on
the pink strip on the chart.; another finger is placed on 2 on
the blue strip. Where the two fingers meet, we find the difference.
This is recorded on the paper. The child continues his work in
this way, and when finished, he controls with Chart I.
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SUBTRACTION CHARTS AND COMBINATION
CARD EXERCISES
b. The Bingo Game of Subtraction (using Chart III)
Materials:
...Chart III and box of corresponding tiles
...combination cards
...Chart I (for control of combinations)
...Chart II (for control of placement of the tiles)
A. Exercise:
The tiles are randomly arranged face up on the table. The child
fishes for a combination, thinks of the answer, and finds the
corresponding tile. After the minuend (pink) and subtrahend (blue)
have been established on the chart, the child is able to find
the place for the tile. He writes the equation on his paper and
continues.
Control of Error: Charts I and II
B. Exercise:
All of the tiles are in the box (or in a sack). The child fishes
for a tile, and thinks, what could this be the remainder of?
He thinks of a combination and writes it down, i.e.
7 = 14 7. He puts the tile in its place. He continues in
this way, then controls his work.
C. Exercise:
The tiles are arranged on the table in common stacks. The child
chooses one stack and thinks of combinations which will yield
this difference. He writes down the combination, finds the place
on the chart, and so on, continuing until he has finished the
stack.
When all of the stacks are arranged in order in a row, what form
do they make? a rectangle or parallelopiped.
Group Games
1. The teacher, or a child functioning as the teacher, fishes
for a combination and reads it. One of the children guess the
difference.
2. The teacher fishes for a
tile and the children offer combinations which give that result,
until all are given.
Aim: (of all of exercises,) to memorize subtraction
combinations
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