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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 1-9 are in blue,

…followed by a blue line, and 10-18 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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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 13-5 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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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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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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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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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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