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Building Sets of Ten

Number and Operations
Grace M. Burton
Location: unknown

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.

pdficon Numeral Cards 

Give each student a blank piece of paper. Display a numeral using the numeral cards that are provided. Ask the students to draw the number of objects (such as circles, rectangles, squares, etc.) that matches the displayed numeral and to silently count the number of objects by writing a number on each one. This exercise provides information about the students' number recognition, ability to record the number displayed, and use of one-to-one correspondence to develop rational counting strategies. Use the information gained from this activity to adjust the pace of this lesson and plan experiences that support and challenge learners. Refer to the students' work to measure growth, strengths, and needs.

Display the numeral card for 0 and ask students to make a 0 in the air. Give them a 10-Frame Activity Sheet and connecting cubes in two colors.

pdficon 10-Frame Activity Sheet

Ask them to fill in each section of the "10" Frame with a single cube, counting aloud in unison as they do so.

1649 image 7.1

Now have the students color the sections of the "10" Frame to match the cubes they placed in them. Ask a student to share with the class the way he or she showed 10. [For example, "I used seven green and three blue cubes."] Repeat with several children. Then tell the students to take these sheets home to share with their family.

Go to the Spinner Applet. Create an 11-part spinner by entering the numbers 0 through 10, starting in the left column. As you enter each number, call on a volunteer to choose a color for that section of the spinner. After entering the 11 numbers, activate the spinner. After each spin, ask the students to say the number aloud and make a train with that many connecting cubes, using two colors. Call on a volunteer to tell how many of each color he or she used to make the train. [In the example below, the student might say, "I used four orange and six green cubes to make my train of 10."] Repeat several times, choosing different children to activate the spinner each time.

1649 image 7.2

Next use the "Back" button on the Web site to return to the Number & Operations, preK-2 directory on the National Library of Virtual Manipulatives Web site, and select "Bar Charts." Set the number of columns to 11 and the number of rows to 11. Label the columns with the numbers 0 through 10 on the bottom of each column. Delete the term "label" and enter the values 0 through 10, one number in each column. Then click on one box over "1," seven boxes over "7," and so forth, starting at the bottom of each column and moving up one box at the time until the appropriate number of boxes are highlighted for that column. Remember that the column labeled "0" will have no boxes. Repeat this activity several times, choosing different students to count and click on the boxes.

Now distribute the students' Steps to 10 sheets and ask them to color in the column for "10." Ask the students which numbers they have now shown on the chart [1 through 10]. Ask what they would need to do to complete the "0" column. [Nothing.] Then ask them to compare the online bar chart with the paper chart they have created.

pdficon Steps to 10 Activity Sheet

End the lesson by showing a numeral and asking the students to perform a given action [e. g., stamping a foot, snapping their fingers, turning around] that number of times. Repeat this activity using several different numbers.


  • 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 Option

Use the teacher resource sheet, Class Notes, to document your observations about the students' abilities to do the following:

  • Construct groups of 10 objects
  • Identify and write the numeral 10
  • Write the numerals up through 10
  • Construct and decompose groups of 10 objects
  • Record groups of 10 items


Move on to the next lesson, Wrapping Up the Unit.

Questions for Students 

1. Look at the connecting cubes in my hand. (Show 10 connecting cubes.) Take eight connecting cubes from my hand. How many connecting cubes are left in my hand?

[There are two connecting cubes.]

2. (Repeat, asking the students to take away other amounts from 10.)

3. When your hand is empty, how many connecting cubes are you holding?


4. Do you know a word that means "zero"?


5. Can you count to 10? Can you show me a group of 10?

6. Can you show a way to split the group of 10 into two groups? Can you do it a different way?

7. Make a group of eight and a group of 10. Which group has more? How many more? Which group has less? How many less?

[The group of 10 has two more. The group of 8 has two less.]

8. How can you change a train of nine to a train of 10? How can you change a train of 10 to a train of five?

[I can add five more blocks to make 10 blocks.]

9. ( Repeat using other numbers.)

Teacher Reflection 

  • Which students can construct groups for all the numbers, 0 through 10? What are the next appropriate goals for them?
  • Are there students still unable to count out 10 objects? What should I do at this time to help them reach this goal?
  • Which students are not yet able to count rationally up through 10? What experiences do they need next?
  • Which students are able to identify the numerals 0 through 10? Which students need help on specific numerals?
  • Which students are not yet able to write the numerals 0 to 10? Which numerals are the most difficult for them? What additional experiences should I plan for them?
  • Which students are not able to compare sets of 0 to 10 items? What learning activities should I plan for them?
  • What adjustments will I make the next time that I teach this lesson?
Number and Operations

Building Numbers to Five

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.
Number and Operations

Writing Numerals to Five

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.
BuildingSetsOfSix ICON
Number and Operations

Building Sets of Six

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.
Number and Operations

Building Sets of Seven

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.
Number and Operations

Building Sets of Eight

Students explore the number 8. They make and decompose sets of eight, write the numeral 8, and compare sets of up to eight objects.
Number and Operations

Building Sets of Nine

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.
Number and Operations

Wrapping Up the Unit

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 and record groups of 10 objects.
  • Identify and write the numeral 10.
  • Write the numerals through 10.
  • Construct and decompose groups of 10 objects.

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.