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Zero Our Hero

Number and Operations
Grace M. Burton
Location: unknown

Students explore sets of zero items and practice writing the numbers 0 through 5. Students count back from five, identify sets of up to five items, and record "0" on a chart. They also construct sets of up to five items.

Gather the students, and teach them the song "Five Little Ducks," as found on the Nursery Rhymes and Songs resource sheet.

pdficonNursery Rhymes and Songs Resource Sheet 

This song counts backward to zero and uses the word "none." Ask how many ducks came when "none" came home. Then ask what number stands for "none." After the students have heard the song once, have them place five counters in front of them and model the numbers they hear in the song by taking away one counter as they sing each verse. When they have sung the song, show them the numeral cards, and say the name of each numeral as you show it. Show the cards first in sequence, then in random order. You may wish to show the zero card several times if it is new to the students. As you do so, ask the students to use counters to model the number on the numeral cards. Encourage the students to say the number when you show it.

Now display the 0 numeral card and ask students to make a 0 in the air.

pdficonNumeral Cards 

 appicon  Adjustable Spinner 

Go to the Adjustable Spinner applet, and create a six-part spinner by entering the numbers 0 through 5 in the left column. As you enter each number, and to establish the color for each section of the spinner, call on a volunteer to choose a color for the section of the spinner that will hold that number.

Next, activate the spinner by clicking on “Spin.” Ask the students to put out counters on their work space to match the numeral on which the pointer came to rest. (Students who need additional structure may find dropping the counters into the sections of a muffin tin or small cup helpful.) Select different volunteers to activate the spinner each time. Call on other volunteers to write on the board the number that comes up when the spinner stops. This helps students connect the number of objects with the numeral on which the spinner stops.

Next, open the National Library of Virtual Manipulatives Web site, and select "Bar Charts." Then set the number of columns to 6 and the number of rows to 5. (The columns will automatically be numbered 1-6.) When the graph is displayed, click on one box over the numeral 1, two boxes over the numeral 2, and so on. Clear the “Bar Chart” and repeat several times, choosing different students to count by clicking on the boxes and counting as they do.

498 bar graph 

Next, give each student a copy of the Numbers to 5 Activity Sheet and some counters.

pdficonNumbers to 5 Activity Sheet 

Have students make X's in each column to show what size group the numeral represents.

498 numbers 

Next, hold up a copy of the Show How Many Activity Sheet.

pdficonShow How Many Activity Sheet 

Ask the students what they would need to do to complete the "0" column. [Nothing.]

498 boxes 

Assessment Options

  1. The Class Notes observations will help you make short- and long-range plans for your students.
  2. Distribute the Cover Up Activity Sheet to students.
    pdficon  Cover Up Activity Sheet 

    Tell the students that as you show a number, they should cover it on one of the rows on the sheet. [You may wish to provide only one row for students if this is more appropriate for their level of development.] Now ask a volunteer to show the numeral cards in random order while you circulate to see whether the students are able to recognize the numerals and cover with a counter the corresponding numeral on their sheet.



Ask students: Suppose you have four counters and I give you zero more. How many counters will you have then? Suppose you have zero counters and I give you four counters. How many counters will you have then?


Questions for Students 

1. Look at the counters in my hand. (Show five counters.) Say, "Take five counters from my hand. How many counters are left in my hand?" Repeat with other amounts as starting quantities and have a student remove all of them.


2. What new number did we talk about today? Can you show me that many counters? When your hand is empty, how many counters are you holding? Do you know a word that means "zero"?

[Zero; zero; none.]

3. Suppose you have zero counters. Is this more or less than one counter?


4. Can you count to five? Can you show me a group of five? Can you show a group of zero?

5. Make a group of three and a group of zero. Which group has more? Which group has less?

[The group of three has more, and the group of zero has less.]

6. Count out three counters. Now make two groups with those counters. How many are in each group? Can you make two groups with three counters in another way? Repeat with other numbers.

[Possible answers include one group of 2 and one group of 1, or one group of 3 and one group of 0.]

7. How can you change a group of four to a group of five? How can you change a group of one to a group of zero? (Repeat with other numbers.)

[Add one more; take away one.]

8. How did you show zero on your chart? How do you write "0"?

Teacher Reflection 

  • Which students can construct groups for all of the numbers 0 to 5? What are the next appropriate goals for them?
  • Are there students still unable to rote count to 5 objects? What should I do at this time to help them reach this goal?
  • Which students are not yet able to count rationally to 5? What experiences do they need next?
  • Which students were able to identify the numerals 0 to 5? Which students need help on specific numerals?
  • Which students were not yet able to write the numerals 0 to 5? Which numerals are the most difficult for them? What additional experiences shall I plan for them?
  • Which students were able to compare sets 0 to 5? Which students were not yet able to do this? What learning activities should I plan for them?
  • What adjustments will I make the next time I teach this lesson?
Number and Operations

Focus on Two

A nursery rhyme provides a context for using the number 2. Students make groups of two, write the numeral 2, and record a group of two on a personal recording chart.
Number and Operations

Three in a Set

In this lesson, students construct sets of three, compare them with sets of two, and write the numeral 3. They also show a set of three on their recording chart.
Number and Operations

One, Two, Three--Go

After reviewing the numbers 2 and 3, students construct and identify sets of one. They compare sets of one, two, and three objects and record a set of three in chart form.
Number and Operations

Finding Four

Students explore the number 4. They make sets of four, write the numeral 4, and compare sets of four to sets of one, two, and three.
Number and Operations

Here's a Handful

Students construct sets of up to five items, write the numeral 5, identify sets of five, and record "5" on a chart. They also play a game that requires recognizing the numerals to 5. This lesson provides opportunities for connecting mathematics with music.

Learning Objectives

Students will:

  • Construct groups of zero objects.
  • Identify and write the numeral 0.
  • Write the numerals up through five.
  • Construct groups of zero to five objects.

NCTM Standards and Expectations

  • 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.
  • Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.

Common Core State Standards – Mathematics

-Kindergarten, Counting & Cardinality

  • CCSS.Math.Content.K.CC.A.3
    Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

-Kindergarten, Counting & Cardinality

  • CCSS.Math.Content.K.CC.C.6
    Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

-Kindergarten, Counting & Cardinality

  • CCSS.Math.Content.K.CC.C.7
    Compare two numbers between 1 and 10 presented as written numerals.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.3
    Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.4
    For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

-Kindergarten, Number & Operations

  • CCSS.Math.Content.K.NBT.A.1
    Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Grade 1, Number & Operations

  • CCSS.Math.Content.1.NBT.B.3
    Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.A.4
    Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Common Core State Standards – Practice

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