## Building Numbers to Five

Pre-K-2
1

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, 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.

### References

• Baratta-Lorton, Mary. Mathematics Their Way. Menlo Park, Calif.: Addison-Wesley, 1974.
• Burton, Grace M. Towards a Good Beginning: Teaching Early Childhood Mathematics. Menlo Park, Calif.: Addison-Wesley, 1985.

Assessment Options

1. 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.
Class Notes
2. Use the Show That Number Activity Sheet as a pre- and post-assessment in this lesson.

Extensions

1. Counting books are one way to foster rational counting. Because such books gently pave the way for more formal rational counting experiences, you may want to collect several counting books to display throughout the unit in your class library and ask the students to share with the class any counting books they have at home.
2. Move on to the next lesson, Writing Numerals to Five.

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.
1. What numbers did we talk about today?

[We talked about the numbers 0, 1, 2, 3, 4, 5.]

2. Pick a number. Can you show me that many fingers?

3. Can you count out loud to this number? Show me.

4. Can you write this number?

5. Listen as I ring this bell (or tap this drum or hit this triangle). How many sounds did you hear?

6. Can you see the number 2 anywhere in the room?

[Possible answers: On the clock, On the board, On my paper]

7. Repeat Question #6 with the other numbers from 0 through 5.

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?

### Writing Numerals to Five

Pre-K-2
As students construct groups of a given size, recognize the number in the group, and record that number in numerals, they learn the number words through 5 in order (namely, to rote count), and develop the ability to count rationally.

### Building Sets of Six

Pre-K-2
In this lesson, students construct sets of six, compare them with sets of a size up to six objects, and write the numeral 6. They also show a set of six on a "10" Frame and on a recording chart.

### Building Sets of Seven

Pre-K-2
Students construct and identify sets of seven objects. They compare sets of up to seven items, and record a set of seven in chart form.

### Building Sets of Eight

Pre-K-2
Students explore the number 8. They make and decompose sets of eight, write the numeral 8, and compare sets of up to eight objects.

### Building Sets of Nine

Pre-K-2
Students construct sets of up to nine items, write the numeral 9, and record nine on a chart. They also play a game that requires identifying sets of up to nine objects.

### Building Sets of Ten

Pre-K-2
Students explore sets of up to 10 items and practice writing the numbers 0 through 10. Students count back from 10, identify sets of up to 10 objects, and record 10 on a chart. They also construct and decompose sets of up to 10 items.

### Wrapping Up the Unit

Pre-K-2
Students review this unit by creating, decomposing, and comparing sets of zero to 10 objects and by writing the cardinal number for each set.

### Learning Objectives

Students will:

• Construct groups of zero to five objects.
• Identify the numerals 0 through 5.

### NCTM Standards and Expectations

• Connect number words and numerals to the quantities they represent, using various physical models and representations.
• Count with understanding and recognize "how many" in sets of objects.
• Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

### Common Core State Standards – Mathematics

-Kindergarten, Counting & Cardinality

• CCSS.Math.Content.K.CC.B.5
Count to answer ''how many?'' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.