This is the standard.
K.CC.B.4 – Count to tell the number of objects
4. Understand the relationship between numbers and quantities; connect counting to cardinality.
b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangements or the order in which they are counted.
This was the task.
Six Tiles in All asks students to use six one inch tiles to make different arrangements. Each arrangement has to follow a special rule – each tile has to touch another tile in some way. The teacher showed several arrangements and also had the students identify non-examples. Then several students demonstrated their idea of how the six tiles could be arranged. The students were then challenged to find different arrangements of their own six tiles and to choose one way to record and then share with the class, using paper tiles and one inch grid paper.
On the following day these same paper tile arrangements were used as quick images. Children were encouraged to explain how they remembered the image to reproduce it.This task begins to meet the standard by having the students practice different arrangements of a single number, 6. To meet this element of the standard the students needs to demonstrate their understanding of this same concept with other numbers. They would also need to count the items in each arrangement, understanding that the last number said is the number of objects.
This is the background information.
Six tiles are used for this investigation because six is the number that most kindergartners can count with accuracy. Because it takes two hands to represent six, students naturally work with two numbers to make combinations of six. In addition, six is one of the largest amounts that can be mentally visualized and manipulated and instantly recalled. This is also a number kinders are intimately familiar with because most of them will turn six during the year!
This investigation gets to Piaget’s work with conservation which is a foundational skill in number sense. Conservation of number is the understanding that the quantity of a given number of objects remains the same regardless of how it is spatially arranged. Six is six is six. The child that sees six tiles horizontally as six but then has to recount those same tiles when they take another arrangement would be unable to conserve numbers. But a child that identifies the horizontal as six, and then the same six tiles rearranged to make a rectangle as six, would be able to conserve numbers. The child that has conservation does not need to recount the same tiles as they take different shapes because he knows that the number stays the same.
This investigation also gets at subitizing which is the ability to immediately recognize an arrangement as a single unit. The ability to see the particular arrangements of indentions on a die and know it is 5 without counting would be an example of subitizing. This investigation, like dot cards, ten-frames and rekenreks, provide students with the opportunity to practice subitizing. Quick images help a child practice subitizing and visualizing what the number looks like with different patterns of that same number.
Eren was especially proud of his arrangement which he said looked like a chess board. He liked that the “ends” were touching and that it was a design that no one at his table had imagined.
Nia thought it looked like a zigzag and Alex recognized the checked pattern when he said it looked like a checker board. Tommy said it looked like racing and when Sawyer said he couldn’t see racing, Tommy explained that it looked like the racing start line, the checkered flag! Love the fact that these very young children are beginning to challenge each other in their number talks!