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forces many of these problems and makes it harder to connect oral counting, written numbers, and place value because of the shift from the set of counting numbers to the set of whole numbers. While we start the oral counting pattern at one, we build numbers by building groups of ten and we start that pattern with zero. We have no ones, and add one group of one at a time until we get to nine. When we add one more so we have one group of ten and zero ones. Figure 3 shows that unless we make these two types of number sets explicit when we are using base - 10 blocks, that pattern is not immediately ap parent to students. They will see starting with one block and adding consecutive blocks until they get a group of ten. Once the first block of ten is made, it is easier to talk about having one group of ten and zero ones, but that initial pattern is not intui tive. This causes some problems with skip count ing and rounding that will be discussed later. Another way of looking at it is that when we reach 9, we have used all of the digits in the number pat tern, 0 - 9, in the ones place and we are now out of digits. We have to restart the pattern in the ones place, open a new space for digits (the tens), and move to the next digit in the pattern there, which would be 1 because we previously had 0 groups of ten. I do this pattern with kindergarteners and first graders using two columns of magnetic digits on a cookie sheet (Figure 4). We count from the top to the bottom on the right column and when we get to 9, I will say, “ Oh no, we ’ re out of digits! What are we going to do? ” The students will initially try to Figure 3: Building the first group of ten starting at 0. While 0 is not a counting number, it is inte gral to the building of written numbers and is the starting point in place value. The bracketed blocks show what students see as they build with base - 10 blocks.

Figure 2: Example of a 99s chart. Zero is the start ing number.

2, 3, 4, 5, 6, 7, 8, 9. Every subsequent number uses this pattern. Geeksforgeeks.org explains it this way: A number system can be considered as a mathe matical notation of numbers using a set of digits or symbols. In simpler words the number system is a method of representing numbers. The base - 10 number system which has 10 symbols (sic), these include: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Each position in the decimal system is 10 times more significant than the previous position. That means the numeric value of a decimal number is determined by multiplying each digit of the num ber by the value of the position in which the digit appears and then adding the products (Upadhyay, 2020). Ask an elementary school student what our number pattern is and it is likely they will tell you, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10.” This makes sense because it is how we count. It ’ s how many fingers we have, it is how base - 10 blocks work, and it is what they see on the number charts around them. However, teaching the whole numbers that excludes 0 leads to misconceptions about how our number system works, how numbers are built, with place value that produces an overall poor number sense. I am not saying that all of this stems from using hun dreds charts; but the typical hundreds chart rein

Virginia Mathematics Teacher vol. 47, no. 2

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