Integers Up To Ten Thousand

Information for Teachers

After children learn addition and subtraction of integers on a two-column board (which should be achieved before the end of first grade), they may extend these skills to handle integers up to 1,000, using a three-column board, and up to 10,000, with a four-column board. This extension does not require any more skills than are needed to handle a two-column board, but learning some shortcuts, improving speed, and decreasing the rate of errors is still very important.


The pictures above show the boards used in this lesson. The leftmost board is a two-column board, the center board is a three-column board, and the rightmost board is a four-column board.


1. The first and main goal for children is to master the number names of integers up to 10,000. In bilingual classrooms, all children should learn the names in both languages, because many interesting tasks require that they work together.

Knowing the names of the numbers means that children can correctly read a number represented in base ten (one digit per column) on the board, and that they can read the numbers represented with red counters as negative.


Upon seeing the above board, children should be able to recognize that the board represents the number 42. They should know the name of the number from the board representation.

Upon seeing the above board, children should be able to recognize that the board represents the number -3. Children are expected to understand that a red counter indicates a negative number. They should also know the name of the number from the board representation.


In the case of mixed representations, namely, when one column may hold a number bigger than 9, or both white and red counters are used, children should be able to regroup the counters to get a correct base ten representation, and then to read it.


In the leftmost image, a mixed representation of the number 117 is shown because the tens column holds a number bigger than 9. The correct base ten representation is shown in the rightmost image. Additionally, children should be able to read the number represented on the board.

In the leftmost image, a mixed representation of the number 334 is shown because both red and white counters are used. The correct base ten representation is shown in the rightmost image. Additionally, children should be able to read the number represented on the board.


Children should correctly represent on a board a number that is verbally presented by the teacher or by other children.




When verbally presented a number, children should be able to represent the number on the board. In this example, the number 3891 is verbally presented and represented on the board.


2. The second goal is that children learn to write and read numbers in base ten. This includes correctly writing all digits, and aligning them vertically and horizontally. They need to read correctly not only numbers that are typed, but also numbers that are handwritten by the teacher and by other students.


Typed Number Number Written
By Teacher		 Number Written
By Child

The images above show the number 26 typed, written by a teacher, and written by a child. Students should be able to read both typed and handwritten numbers. As shown in the rightmost image, students should also be able to write numbers.


Achieving these two goals requires considerable class time and should precede the main mathematical tasks that each of these boards are designed for, namely, carrying out multiplication and division of integers.


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