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Building Sets of Seven

Number and Operations
Grace M. Burton
Location: unknown

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.

At this stage of the unit, it is important to determine if students are ready for the next lesson, if they need additional support in learning the content of previous lessons or if they need challenge with mathematical experiences beyond those that are the focus of previous lessons. Use the Show That Number Activity Sheet for students to record responses to questions you ask.

pdficon Show That Number Activity Sheet 

Hold a numeral card and ask students to draw the number of objects to represent that number or provide objects for students to count and record the numeral that represents the set accurately [Examples, place seven cubes on the overhead, placing a stack of four books in front of the class for them to count or ask students to record the number of light fixtures in the classroom.

pdficon Numeral Cards

Show the Numeral Card 7 and tell the students to clap their hands seven times, counting aloud as they do so. Observe which students identify the numeral and can clap seven times. Now give the students a large group of cubes in two colors. Ask them to make trains of seven using one or two colors. Then have them record the trains on the Showing Sets of 7 Activity Sheet.

pdficon Showing Sets of 7 Activity Sheet 

You may wish them to record how many of each color they used for each train of seven by writing the numeral in the appropriate color under the train. Ask the students to take these sheets home and tell their families how they completed them.

1631 image 4.1a
1631 image 4.2a
1631 image 4.3a

Now display the numeral 7, and ask the students to look at it. Turn your back to the students and trace the figure in the air, then encourage them to do it with you. Now spray shaving cream on a plastic work surface and draw the numeral 7 in the cream. Invite the students to do this also.

1631 4.4a

Next give each student a copy of the 10-Frame Activity Sheet and some connecting cubes. Display numerals up through 7, one at a time in random order, and ask the students to put as many connecting cubes, one in each section, as the number indicates.

pdficon 10 Frame Student Activity Sheet 

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

appicon Ten Frame Tool 

After they have finished, give the students their Steps to 10 Activity Sheet.

pdficon Steps to 10 Activity Sheet

Ask them to look for the column with "7" at the top and color seven boxes, starting at the bottom row. Encourage the students to compare the previously colored columns with the column for 7. Then collect the charts or tell the students to put their charts where they will be available for future lessons.


  • 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 seven objects
  • Compare a group of seven objects with groups of other sizes
  • Identify and write the numeral 7
  • Record a group of seven items


 Move on to the last lesson, Building Sets of Eight.

Questions for Students 

1. What new number did we talk about today?

[We talked about the seven.]

2. Can you show me that many fingers?

3. Can you count to seven?

4. Take seven connecting cubes. Separate the group into two parts. How many are in each group? Can you do it another way?

5. Show a train of six cubes and a train of seven cubes. Which group has more?

[The train of seven has more.]

6. How can you tell?

[The train of seven is longer.]

7. How many more does the train of seven have?

[It has 1 more.]

8. How can you change a group of six to a group of seven?

[I can add 1 more cube.]

9. Challenge question: How can you change a group of seven to a group of ten?

[I can add 3 more.]

10. How did you show seven on the "10" Frame? What is different in the way you showed six and the way you recorded seven?

[I had to color one more box to show seven.]

11. Challenge question: If you have five cubes in the "10" Frame, how many more will you have to add to have seven cubes?

[I will have to add 2 more.]

Teacher Reflection 

  • Which students have learned the meaning of each of the numbers studied so far? What are the next appropriate goals for them?
  • Are there students still unable to count out seven objects? What should I do at this time to help them reach this goal?
  • Which students are not yet able to count rationally to seven? What experiences do they need next?
  • Which students were able to identify the numerals to 7? Which students can write all of them?
  • Which students were not yet able to write the numerals to 7? What instructional experiences do they need next?
  • Which students were not yet able to compare a set of six objects with a set of seven objects? Which students were able to compare sets but could not explain how they did that?
  • Which students were able to use five as a benchmark number as they constructed sets of six and seven? What learning activities should I plan for those students who were not able to use five as a benchmark number?
  • 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 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 seven objects.
  • Identify and write the numeral 7.
  • Compare sets of up to seven objects.
  • Record a group of seven 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.