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Building Sets of Six

Number and Operations
Grace M. Burton
Location: unknown

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.

Start the lesson by reviewing the assignment from the end of the previous lesson, asking the students what they found at home that came in sets of two, three, four, and five. Then show the students an egg carton that you have cut in half or a muffin tin with six cups. Call on a volunteer to place one connecting cube in each cup, counting aloud as he or she does so. Then ask the student to tell how many connecting cubes were used. [Six.] Empty the muffin tin and repeat with other volunteers. Now assign the students to pairs, and give each pair one number cube and some connecting cubes. Ask the students to take turns rolling the number cube and making a train with the number of cubes that corresponds to the number on the number cube. (Begin a new train after each roll of the die.)

1626 image 3.1a

After the pairs of students have completed many trains, ask them to take the train they last completed and compare it with someone else's (from another pair) by holding the two trains together and counting to verify if one has more, less or if they are equal. Then ask the students which train has more cubes in it. (If the trains are of equal length, help students understand that neither train has more or less than the other.) Encourage several pairs of students to tell the whole group how their trains compared. Then have them compare a train of five cubes with a train of six cubes.

Now display Numeral Card 6 and ask the students to look at it. Turn your back to the students and trace a "6" in the air, then encourage them to make a large 6 in the air with you. You may wish to put words to the actions you use to make the numeral 6. (See the previous lesson in this unit, Writing Numerals to Five, for how to do this to the tune of "Here We Go Round the Mulberry Bush".) Now have volunteers write "6" in the sand, on the rice tray, or on the board. Remind the students to go to the numeral writing station during the day to practice writing "6."

pdficonNumeral Cards 

Next give the students a copy of the 10 Frame Activity Sheet, and have them place six connecting cubes in it. Ask them to count aloud as they do so.

pdficon10 Frame Activity Sheet 

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Students may also use the Ten Frame Tool to explore numbers up to 10.

appicon Ten Frame Tool 

Give the students their Steps to 10 Activity Sheet, begun in Lesson One. Ask them to find the column headed with "6" and fill in six boxes in that column, starting at the bottom.

pdficonSteps to 10 Activity Sheet 

When the students are done, ask them to show their charts. Collect the charts so they will be available for future lessons.

So that students can record their learning, provide each student with a copy of Showing Sets of 6 and two crayons, each a different color.

pdficonShowing Sets of 6 Activity Sheet 

1626 image 3.4a

Ask them to color exactly six boxes in each row, using two crayons to do so. (If the students need assistance, you may ask them to make trains in the two colors first, then copy the trains on the sheet with crayons.) Then ask the students to write the number of boxes of each color that appears in each row of six boxes. Encourage them to color the boxes a different way each time. (Some students will find this difficult to understand, and you may need to model this for them.) When they have finished, ask them to share what they have done with the class and to take the sheet home to share with their family.

Alternatively, or in addition to the above activities, students can work (either individually or in pairs) to review the numbers 1 through 6 by using the Concentration interactive.

appicon Concentration 

To do so, students should select 1-6 under Levels, and either 1 or 2 players. In this activity, students match the numerals (1-6) with other representations explored in this unit. This is a good "checkpoint" activity which allows students to self-assess before continuing with the other lessons in this unit.


  • 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 six objects
  • Compare groups of up to five objects with a group of six objects
  • Identify and write the numeral 6
  • Record a group of six items


Move on to the next lesson, Building Sets of Seven.

Questions for Students 

1. What number did we talk about today?

[We talked about the number six.]

2. Can you count to six? What number did you say just before six?

[The number five]

3. Show me a train with six cubes. How can you tell that your train and your partner's train have the same number of cubes?

[We can place the trains next to each other to see if they are the same length. We can count the number of cubes in each train.]

4. Show me a train of five cubes and a train of six cubes. Which train has more?

[The train with six cubes has more.]

5. How can you tell?

[The train with six is longer.]

6. How many more? (Encourage the students to line up the trains and match the cubes in them.)

[It has 1 more cube.]

7. Make a "10" Frame for five. How can you change it to show six?

[I can add 1 more block.]

8. How can you change a "10" Frame for six into a "10" Frame for five?

[I can take one cube off.]

9. What was one way you used two colors to color six boxes?

[Possibly: I colored 3 boxes blue and 3 boxes orange.]

10. Did anyone do it a different way?

Teacher Reflection 

  • For students who have not yet demonstrated that could construct sets of six with ease, what experiences do they need next?
  • For students who are not able to compare two sets and explain the relationship between the sets, what additional experiences are necessary?
  • Which students would benefit from additional instruction from adult volunteers?
  • 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.
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

Building Sets of Ten

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.
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 groups of six objects.
  • Identify and write the numeral 6.
  • Compare sets of up to six objects.
  • Record a group of six items.

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.

-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.

Common Core State Standards – Practice

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