Children who enter first grade with under-developed numeracy skills may have difficulty learning new concepts of counting. Young children learn to count by imitating adults and older children, as well as by sound patterns (Reys, Lindquist, Lambdin, & Smith, 2012). Also, young children need an understanding of counting principles that will make sense to them so they can begin to critically think about numbers in a higher order. In this essay I will discuss how I would teach and assess a group of ten first grade students to rationally count to fifteen using four counting principles; one-to-one correspondence, stable order rule, order irrelevance rule, and cardinality rule. For the purpose of this paper it is assumed that these students already possess the skill to rationally count to ten.

A1. One-to-One Correspondence:
Before teaching students a new math skill it is important to ensure that they understand any new terminology that may be used and the main concept of the skill that they will learn. In this case it would be the numbers eleven through fifteen and the concept of one-to-one correspondence. Next, I would write out the words one, two, three, four, five, six, ... , fifteen on the chalkboard with the corresponding number above each word and underline the numbers eleven through fifteen to let students know that those are the new numbers they will be learning. To begin teaching one-to-one correspondence, students must first understand that each object counted has one and only one number name. To do this I would give each student two saucers to place on their desks and then fill one of the saucers with fifteen assorted foam shapes. I would then give myself two saucers, one filled with the fifteen shapes. I would begin modeling the counting process by taking a shape from the filled saucer, holding it up in front of my face, saying “one”, and then placing the shape into the empty saucer. I would then take another shape from the filled saucer, hold it in front of my face, say “two”, and then place it in the saucer that had the one shape. I would ask the students to notice that as I hold up one shape, I am only stating one number name. I would repeat this process until all fifteen were counted. Next I would have the students follow along as I modeled the process again. For added practice I would pair the students up and have them practice the new skill with their partner. Also for added practice, I would have students place ten shapes in one saucer and begin counting one by one from eleven through fifteen, transferring to the saucer with the ten shapes. Before students begin this exercise I would model the procedure for them.
B1. Assessment: One-to-One Correspondence
To assess students’ understanding of one-to-one correspondence, I would give each student a worksheet that listed 15 stars in sequence. Then I would ask each student individually to count the stars on the page using the one-to-one correspondence, pointing to each star as they counted. By observation, I could assess if the students understood the concept if they pointed to one and only one star as they said a number. Even if the student says a number out of sequence, as long as the student is naming one and only one name per star, I will know that they understand the concept of one-to-one correspondence.

A2. Stable Order Rule:
To begin teaching the stable order rule, I would first familiarize students with any new terminology or concepts they may not know, which in this case would be the numbers eleven through fifteen and the concept of the stable order rule. I would explain that this concept requires numbers to be counted in a fixed order every time. Next, I would write out the words one, two, three, four, five, six, ... , fifteen on the chalkboard with the corresponding number above each word and underline the numbers eleven through fifteen to let students know that those are the new numbers they will be learning. I would then