Multiplication Skip Counting

SKIP COUNTING (Linear Counting)

a. List of Materials

…Board of powers (though it is not named as such at this point)
…Cubes, long chains, squares, short chains
…Two Boxes:
xxx…arrows for short chains, i.e. for 5 we have 1, 2, 3, 4, 5, 10, 15, 20, 25
xxx…arrows for long chains, i.e. for 3 we have 1, 2, 3, 6, 9, 12, 15, 18, 21, 24, 27

b. Initial Presentation:
In the first presentation of the material the nomenclature should be given in a three period lesson, i.e. cube of seven, long chain of seven, short chain of seven, square of seven.

c. Short Chain:
The chain is lain stretched out on the table, and the child identifies it as, i.e. the short chain of 5. The teacher folds it up like a fan, and the child identifies it as a square of 5. This is proven by placing a square on top of the folded chain to see that they are equal. The child is given the arrows to lay face up on the table. Together the teacher and the child put the arrows in their respective places as the beads are counted…1,2,3,4,5…; the counting continues by ones up to 10, and the arrow for 10 is placed there, and likewise counting by ones to 15. From 15, we add five more to reach 20, and place an arrow and add five more to 25, The square of 5 is placed at the end of the chain since the chain is equal to the square.

: same as before
The child lays out the arrows as before. Little by little he works from counting one by one using the arrows face up, to skip counting as he lays the arrows out, and then skip counting with all of the arrows face down.
When the child is able to skip count well with the arrows face down, he may also skip count regressively.

d. Long Chain:
The chain is lain out one the table or floor (if necessary), and the child identifies it as, i.e. the long chain of three. The child lays out the arrows appropriately as he skip counts. At 9, as the square of three is placed, the child is reminded if they do not see it, that this part of the chain makes a square. (It is equal to the short chain.) A square is placed by the chain at 9. The skip counting continues placing a square at 18 and finally at 27. The three squares are stacked up to see that they make a cube of 3, thus this chain is also equal to the cube of three. The cube is placed at the end of the chain.
In successive activities the child works up to counting progressively and regressively with the labels turned over.

e. Games of Comparison

Direct Aim: comparison of quantities sensorially

Indirect Aim: preparation for the powers of numbers (exponential increase)

Materials: same as before

The short chains are arranged as the pipes of the organ. Here the child sees the progression of the quantities which is the same as that seen on the shelves of the frame, in the hanging chains and in the cubes,
The visualization of the difference between the quantities becomes more apparent when the long chains are lain out in the same arrangement. In the long chains, the jump from one quantity to the next is more drastic.

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