group of two, three, or four objects. Do not attempt to teach the child to recognize any group composed of more than four objects. Have the children take several objects and separate them into groups of two, three, and four. Teach pupils to measure each number by all numbers within itself. Let them make groups on their slates as follows:
(The four single objects represent the number four.)
(liere the two groups represent the number four.)
(In this the number four is represented by one group of three objects and one single object.)
Then the teacher should make pu])ils see clearly that in each of these three rows there are four caps. In the hrst row there is but one caj) in a place; in the second, two in one place (a group); in the third, three in one place and one in another.
Next lead them to tell what they see in these groups, thus: There are four I’s in four; there are two 2's in four; there is one 3 and 1 more in foui*. Or two caps and two caps are four caps; three caps and one caj) are four caps; four caps less two caps are two caps; four caps less one ca]) are three caps; four caps less three caps is one cap.
Again, hold in your hand two tooth-picks or any objects. Ask, “ How many tooth- picks?” Place two more with the first, keeping the two groups separate. “Now how many?” Pupils say, “Four tooth-picks.” Then lead pupil to say, “two tooth- picks and two tooth-picks are four tooth-picks.” Place four in the hand, asking, “How many?” Pupils say, “ Four tooth-picks. ” Then take away two. “Now how many?” Pupils say “Two tooth-picks. Then lead pupil to say, “Four tooth-picks less two tooth-picks are two tooth-picks.” Holding four, take four away, and as before pupils are led to say, “Four tooth-picks less four tooth-picks are none.” Next let pupil take two tooth-picks one time, then Xwo times, leading him to say, “ If I take two tooth-picks twice, I have four tooth-picks.”
To teach one-half of a number, let the pupil select two others and hand the objects to them alternately, one by one, until all have been distributed; then count the num- ber each has.
In teaching one-third, have the pupil select three persons, in teaching one-fourth, four persons, etc. When he can do this understand ingly, let him imagine the persons and simply lay the sticks in groups. This should be thoroughly mastered before any attempt is made to divide by 2, 3, 4, etc., which is a very different problem.
To divide by 2 is to find how many two-bundles a certain other number of objects contains. In this work the pupil must take away each time a two-bundle, keeping each two-bundle by itself and counting them when the number is exhausted. At first use the expression “How many two-bundles,” but later “How many 2’s.” Rubber bands or strings should be used and the objects actually made into bundles. In dividing by 3, use a three-bundle; by 4, a four-bundle, etc.
The following study of the number /our is given as a suggestive outline that may be used not earlier than the third month:
