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Building Sets of Eight

Number and Operations
Grace M. Burton
Location: unknown

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

Before beginning this lesson, it is important to know the extent of the students' sense of numbers up to eight and to find ways to challenge those students who understand eight and beyond. To determine understanding, give each student a set of 10 connecting cubes. Ask the students to create a set of eight on their work-space and to draw an 8 with "magic chalk” (writing in the air with their finger). A review of the previously covered numbers would also provide formative information. The teacher resource sheet Count to 10 Class Assessment can help you document the level of performance of each student. You may wish to note strengths as well as needs.

pdficon Count to 10 Class Assessment 

Provide the students with the Showing Sets of 8 Activity Sheet, a group of connecting cubes, and crayons in two colors.

pdficon Showing Sets of 8 Activity Sheet 

Encourage students to color each row with the two crayons and to color each row in a different way. Ask them to record the size of each group using the appropriate color crayon. When they have finished, ask them to share one or more ways that they colored the rows. [Their coloring patterns will show the ways that they decomposed eight into two groups. This is a valuable preparation for learning the combinations of eight, such as 4 + 4 and 3 + 5.] Ask them to take their sheets home and share their work with their family.

1638 image 5.1a

Show the students the numeral 8. Describe how it is made and ask them to make large 8s in the air. Then spray some canned shaving cream on a plastic surface and invite them to practice making the numeral in the cream. (This activity can also serve to clean the desk or tabletop.)

appicon Electronic Abacus Applet 

Now, using a computer that all the students can see, go to the Electronic Abacus Applet. Call on a volunteer to use the abacus to show a number from 1 through 8 by moving the abacus beads. (Because this virtual manipulative is designed for other purposes as well, use only the top bar of the abacus.) Then ask the volunteer's classmates what number is shown. Call on another volunteer to write the numeral on the board. Repeat with several other volunteers, clearing the abacus each time.

Next give each student a copy of the 10-Frame Activity Sheet. Ask the students to put eight connecting cubes into the frame, one in each section. Remind them to start at the smiley face and go in the direction of the arrow. To help them see the relationship of eight to five, ask "How many cubes are in the top row? How many are in the second row?"

1638 image 5.2a

pdficon 10-Frame 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.

pdficonSteps to 10 Activity Sheet 

Ask them to look for the column with "8" at the top and to color in eight rows, starting at the bottom row. Circulate as they work. Encourage the students to compare the "8" column with the columns they have colored in previously. Then collect the charts.


  • 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 eight objects
  • Compare a group of eight objects with a group of up to eight objects
  • Identify and write the numeral 8
  • Record a group of eight items


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

Questions for Students 

1. What new number did we talk about today?

[We talked about eight.]

2. Can you show me that many connecting cubes?

3. Can you count to eight? Can you clap eight times?

4. Show me a group of seven and a group of eight. Which group has more?

[The group of eight.]

5. How can you tell?

[The group of seven is shorter.]

6. How can you change a group of eight to a group of seven?

[I can take away one.]

7. How can you change a group of five to a group of eight?

[I can add three more to the group of five.]

8. When you count, what number comes after seven?

[The number 8.]

9. What number comes before eight?

[The number 7.]

10. How did you show eight on your chart? How is that column like the column for 7?

[They both have more than the 6 column. They are not all the way to 10.]

11. How is it different?

[There is one more square colored in column 8.]

12. How can you show eight on a "10" Frame? How many cubes would be in the top row? In the bottom row?

[Five would be on the top.] [Three would be on the bottom.]

13. How many more cubes would you need to add to fill the "10" Frame?

[I need two 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 up to eight objects? What should I do at this time to help them reach this goal?
  • Which students are not yet able to count rationally to eight? What experiences do they need next?
  • Which students are not yet able to write the numerals through 8? Which numerals are the most difficult for them?
  • Which students are able to compare sets of up to eight objects? Which students are not yet able to do this? What learning activities should I plan for them?
  • Are some students reluctant to participate? What experiences might make them more comfortable with participating?
  • 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 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 eight objects.
  • Identify and write the numerals up through 8.
  • Compare sets of eight with sets of up to eight items.
  • Record a group of eight 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.