Teaching First Graders to Count to 15 A group of 10 first-grade students who can already count rationally to 10 are now ready to expand their counting prowess to 15. The first step is to make sure they are comfortable with some basic counting principles. The first principle that must be reviewed is one-to one correspondence. Using the numbers with which the students are already familiar (1-10) the students will be given a calendar with all of the days of the week blacked out so there are simply squares arranged numerically. For this portion of the exercise the squares with numbers greater than 10 will be blacked out as well. We will review the calendar starting with “1” and continue to “9”. The students will be asked to point to the square sequentially and count together 1,2,3…9. The students will be asked how many number 1’s, there are, how many 2’s, etc. The teacher will piggy-back on this explaining how each square was counted only once and each had its own number. This will continue until the students’ exhibit through teacher observation an understanding of one-to-one correspondence. The next principle will be the stable order rule. Again the students will count the numbered squares in order. The teacher will count the squares for the students in a random mixed-up order and ask the students if said counting was correct. Of course the students will recognize it’s not at which point the teacher will stress stable order rule of numbers in a fixed order every time. The next principle will require leaving the calendar and moving to colored beads. The students will each be given nine beads of various colors and will be asked to count them one by one and place them on a string. Once all nine are on the string the beads will be removed from the string and mixed up, the re-counted and then again placed on the string. The teacher will stress to the students at this point when we are counting individual objects we can count them in any order as long as each is only counted once. This will teach the order irrelevance rule. The final principle for student recognition is the cardinality rule. Again using the beads and the string we will count out beads one by one and place them on the string. At various points the teacher will stop the students and ask them how many beads they have on the string. The students will answer “x” and the teacher can demonstrate how the last number counted is the number of beads on the string. To advance past counting to 10 the students will be taught about the base of 10 and place values. Using another calendar we will have the squares 1-10 shown with the numbers 11-15 covered with tape. Applying the one-to-one correspondence the students will see each square has only one number and that square 10 shows a 1 and a 0. The teacher will explain that the number 10 has a “1” signifying the number of 10’s and a 0 signifying how many 1’s. At this point the students will be given a bundle of 10 straws to place on the 10 square. Next, the teacher will write the number 10 on the board, give each student one straw, and remove the tape over the 11 square. The teacher will explain that now we have 1 bundle of 10 straws and 1 additional straw, or 11. They will have the visual with the straws and with the calendar square. This will continue with 2 straws at the number 12 on the calendar, all the way to 15. After explaining the concept of places and a base of ten, the teacher and students will practice together counting aloud from 10 to 15, alternating from pointing at the calendar for each number and holding the bundle and number of straws on the next time counting. The students know how to count to ten so we will use the “count on” principle described in the “Helping Children Learn Mathematics” textbook. The students will have 10 beads in front of them on the string and will count as they add 5 more beads one by one; place bead on string “11” place bead on string “12” place bead on string “13” place bead on string “14” place bead on string “15”. The process will then be repeated removing one bead at a time and counting backward from 15 to 10. At some point during the ascending and descending the students will be stopped and asked “without recounting all the beads, how many beads are on the string right now? How do we know?” An assessment to evaluate student mastery of this concept will be an oral assessment with the teacher providing the questions and the students writing their responses on a piece of paper. Example, the teacher will say “the number 12 has how many 10’s? The number 12 has how many ones? We write the number 12 as…” The final portion of the assessment will have the students writing all the numbers in order from 1 to 15. English Language Learners will be asked to say the name of the number in their native tongue then repeat it in English. The assessment will be the conversion of the native version to the English version and in order. The ELL students will be assisted by using the suggestions found in Chapter 3 page 55 of the Helping Children Mathematics textbook assigned as a reference for this class:
“Use teaching strategies and groupings that reduce the anxiety of the students. Look for ways to give English-language learners additional support. Involve as many of their senses as possible. Give students ways to respond besides writing or speaking in English. Allow them to interact with a partner or in a small group, as this is less stressful than having to speak in front of the entire class. Often, working with a peer who speaks the same language can make a student more comfortable.
Assign activities in the classroom that offer students opportunities for active involvement. Using manipulatives and everyday objects can bring meaning to a concept. Some students will be more proficient demonstrating with objects than explaining with words.” Students with learning disabilities will be permitted to count to lower numbers as applicable and provided additional one-on-one time with the teacher. More advanced students will be introduced to the concept of addition and will be shown adding 1 to 11 is 12, 2 to 11 is 13, etc. and will be assessed accordingly.