Patterns and Design
This activity (from https://www.ux1.eiu.edu/~cfsjy/mts/math/12-1.htm) is a brief lesson led by the teacher, and is given to children age 4 and up. The teacher cuts an apple in half and asks, "How many apples do I have?" Children will generally respond by saying "two", but the teacher puts the two pieces together and shows that it is one apple. Then the teacher holds up one of the pieces and says "This is one half". The lesson continues when the teacher divides the apple into fourths and then eighths. At the end, the teacher passes out the pieces of apple for the children to eat. (Yen, 1999)
In exercises in Practical Life, the child is shown how to cut up an apple and pass out the pieces to other children.
For learning to take place, the child needs opportunities for mistakes (expectation failure) and course correction. The cost of mistakes must be small enough relative to the rewards of participation in the activity.
In this case, the cost of mistakes is reduced by the selection of children for the lesson. The teacher picks a group in which all or most of the kids are likely to make the same mistake (saying that there are two apples when there are actually two halves).
When the teacher reveals the mistake by showing that she has two halves (instead of two apples), she continues the lesson by dividing the apple into fourths. In this way, she supports course correction.
There is also a nice reward for participation in the activity. The child gets a piece of apple. The teacher's activity of cutting up the apple is rendered meaningful, and the child will likely remember it the next time she cuts up an apple to share with friends.
The activity of cutting up and sharing fruit is common in Montessori classrooms, which further extends the reminding and meaning of this activity.