Connect number words and numerals to the quantities
they represent, using various physical models and representations.
Develop a sense of whole numbers and represent
and use them in flexible ways, including relating, composing, and decomposing numbers.
Count with understanding and recognize "how
many" in sets of objects.
In this
lesson, students make groups of zero to 5 objects, connect number names to the groups, compose and decompose numbers, and
use numerals to record the size of a group. Visual, auditory, and kinesthetic activities are used to help students begin to
acquire a sense of number.
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.
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.
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, and 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, and 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.
Questions for Students
You may wish to use the numeral cards 0 through 5 in
random order for the following questions, asking each question several times.]
What numbers did we talk about today?
[We talked
about the numbers 0, 1, 2, 3, 4, 5.]
Pick a number. Can you show me that many fingers?
Can you count out loud to this number? Show me.
Can you write this number?
Listen as I ring this bell (or tap this drum or hit
this triangle). How many sounds did you hear?
Can you see the number 2 anywhere in the room?
[Possible
answers: On the clock, On the board, On my paper]
Repeat
with the other numbers from 0 through 5.
Assessment Options
Assessment Option 1 is to use the teacher resource
sheet, Class Notes, to document your observations about the students' abilities to do the following:
Construct groups of zero to five objects
Identify and write the numerals 0 through
5
Assessment Option 2 is to use the student activity
sheet “Show
That Number” as a pre- and post-assessment in this lesson.
Re-teaching
Students
having difficulties with this activity may need to be re-taught the lesson. Because counting books are one way to foster rational
counting, the teacher can use them in the classroom for students who have not quite mastered the concept of counting. After
providing the students with these books and practicing with them, the teacher should allow the students to complete this activity
once again. It should be less difficult for the student now.
Teacher Reflection
Which students could count by rote to five?
What experiences are necessary for those who could not?
Which students are able to count rationally
to five?
Which students could identify the numerals
to 5?
Which students were not able to identify how
many times the bell was rung in Questions for Students 4? What instructional experiences do they need next?
What adjustments will I make the next time
that I teach this lesson?
