Knowing which students understand the number of objects that represent the numerals 1 through 5 before beginning this lesson will allow you to adjust instruction and provide appropriate remediation activities to better meet the needs of each student. Familiarize yourself with the Counting Concepts listed below prior to teaching this lesson.
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Counting Concepts
The following concepts are important to understand when teaching children how to count.
A cardinal number is a number that answers the question, "How many?"
Rote counting is the naming of the number words in the correct sequence. Many students come to school having the ability to count by rote to 10 or higher, and this ability provides an excellent starting point for number work.
In rational counting, one and only one number name is assigned to each object in a group, and the last number name said is understood to name the quantity in the group. When the students show a given number of fingers, they are doing what is called rational counting. Note that a cognitive leap is required to accept that the last number named in counting tells how many are in the whole set. This is radically different than what happens when the names of a group of children are called out. If we call off, "Meg, Tara, Zeke," then "Zeke" does not stand for the whole group, just for the last child named. When we count "one, two, three," three is the answer to, "How many are in the group?"
Although technically what we write is a numeral, not a number, this distinction is not necessary in an early childhood classroom. Writing the numeral is a different skill than either rote or rational counting and may develop at a different rate. Knowing how to reproduce the forms of the numerals will allow the students to record their mathematical investigations.
The "10 Frame" uses the concept of benchmark numbers (namely, 5 and 10) to help the students develop visual images for each number. For example, this device makes it easy to see that 6 is 1 more than 5 and 4 less than 10.
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Distribute the student activity sheet, Show That Number and ask the students to write a different numeral (1, 2, 3, 4, or 5) in each row and draw the number of objects that match the numeral. Collect the papers and review them to determine which students can complete this task correctly and which cannot. Save this work sample for future reference.
Begin the class by inviting the students one by one to count to five as they sit in a circle. [Observe which students can do this and which students cannot yet count fluently.] To help students make connections between in-school mathematics lessons with out-of-school mathematics experiences, ask them whether they have ever heard the expression "high five." To demonstrate its meaning, high-five the student to your right, then ask that child to high-five the student next to him or her, and so on around the circle. Next give each child paper and crayons, and have the students work in pairs to trace one of their hands with the fingers outstretched. This helps students recognize the match between a high-five and the number of fingers on their hand. It also allows students to practice working with a set of five.
Then show the students Numeral Card 4 from the Numeral Cards activity sheet. (In this lesson, the numerals 0 through 5 will be used. To make the numeral cards easier to cut apart and handle, you may want to print them on heavy paper.) Say to students, "Lift your hands in the air. Show this many fingers. How many fingers are you holding up?" Repeat with the other numeral cards for 0 through 5.
Now put out a large set of connecting cubes, show a numeral card [for example "3"], and ask the students to come forward and take out as many connecting cubes as the numeral you are showing. When all the students have returned to their seats, ask them to count aloud the connecting cubes they are holding. Model this counting with the three connecting cubes you are holding by saying, "One, two, three." Then ask, "How many connecting cubes are you holding?" Encourage the students to answer "Three." Now drop your cubes into a metal bowl so they will be heard as they drop. Count "one, two, three" as you do. Then have the students come up one at a time and drop the cubes into the container while counting aloud. [You might invite the class to count along as each child drops his or her connecting cubes into the bowl.] Repeat with other numbers from 0 through 5.
