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put the 0 and 1 in the right column together to make 10. But we talk about needing those digits to make our new numbers and how they need to stay in place so that we can use them over and over again. They learn to take the 1 from the left column and move it down the column of digits on the right to make 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. We then repeat the pattern to create the twenties, thir ties, and so on. This sets them up to be ready to talk about place value.

Many teachers use hundreds charts to help students see skip counting patterns, particularly the patterns of counting by 2s, 5s, and 10s. The pattern that is easiest to see on the hundreds chart and the 99s chart is the pattern of counting by tens. This is most often taught as the 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 pattern, but it can be done at any point in a decade. The biggest misconception that stu dents take away from learning this pattern on the hundreds chart is that numbers that end in 0 come at the end of the decade, rather than the beginning. Each decade begins with a certain number of tens and zero ones. Students often think that the number that ends in zero is the end of a number sequence rather than the beginning. This makes the concept of place value more difficult because there is a dis connect between how they think about counting and what they learn about place value. Again, most students figure out a way around that disconnect, but some do not and continue to struggle. I recall from elementary school where I made a de cision, when skip counting by twos, I would not think about it as ending on the decade. Of course, I didn ’ t have the vocabulary for that, but I reasoned that if I skip counted using numbers that ended in zero as my mental start of the pattern, it was easier to keep track of the pattern because the whole pat tern was contained in a decade.

Figure 4: Example of using columns of digits to build numbers. The 1 is placed next to each digit in the right - hand column to build 11 - 19.

The 99s chart clearly demonstrates and supports learning the pattern of building numbers from 0 - 9. The 99s chart has an entire decade on each line so that students can see how the numbers are made us ing the 0 - 9 digit pattern over and over, compared to the hundreds chart, where each line ends with the beginning of the next decade. Think for a moment about what you are asking a child to do when you tell them to find a number in a decade on a hun dreds chart, for instance 37. There are numbers with a 3 in the tens place on two rows. But on one of those rows there are also numbers with 2s in the tens place, and on the other row, where most of the numbers have a 3 in the tens place, there is a num ber with a 4 in the tens place. Most children figure out how to find specific numbers on the hundreds chart, but they fail to see the pattern by which num bers are constructed.

Figure 5: The difference between skip counting by 2s on a 99s chart (L) and a hundreds chart (R).

For example, if I started at 20, then I just had to think of 2, 4, 6, and 8 with twenty in front of each number (Figure 5). When I made it to 8, in one decade, it was time to move to the next decade. This made it easier for me to keep track of where I was and where I needed to go as I was learning to count by 2s. This is the pattern that is shown using the 99s chart. All of the numbers in the decade are

Virginia Mathematics Teacher vol. 47, no. 2

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