As children build concept of number, there are several formats that we teach them to record a number at both the picture and symbolic levels. So let's make use of the charts we hang on our walls and include the numeral, the number word, the number's ten-frame picture and the number's tally mark representation all in one place for our kids to refer to as they do work in our classrooms.
Here are tips to think about for each of these four number representations:
1. The Number Word: Notice that the letters are all written in lowercase letters. In order to not confuse children, especially kindergartners, I always refer to this as "the number word." We don't want them to confuse the number of letters in the word with the number. Sometimes this happens at the pre-primer level before children understand the concept of letters and words.
2. The Numeral: Believe it or not, when writing a numeral, I always refer to it as "a numeral." So if I am writing the numeral six, I might say, "I am writing the numeral 6; it stands for 'this' (I hold six fingers or point to a set of six objects) many." I want children to understand that this is a symbol that stands for a set of six.
3. The Ten-Frame: Ten-frames are important tools used in mathematics instruction. In our base ten number system, this structure supports our kids with a visual representation of the numbers 0-10, as they are related to five and ten. The frames are always filled the exact same way for each of the numbers. The top five boxes are always filled first moving from left to right, then moving to the bottom boxes filling from left to right. Looking at the number six ten-frame you can quickly see that six is one more than five and four less than ten, important information we want our kids to know about the numbers from 0 to 10.
4. The Tally Marks: When young kids are solving problems numerically, they often use tally marks to pictorially represents numbers. By modeling a pattern for the tallying process, we give them a tool to use to support precision and fluency (Tip: tools, precision and fluency are all part of the Standards of Mathematical Practice). Notice that a group of five is represented by four vertical tallies and one horizontal tally connecting the set. Two sets of five are placed next to each other and circled to represent a set of 10. Whenever possible, I draw the modified circle in red. This leads to counting by tens, fives and ones.