Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on

Pin it!
Google Plus

Wrapping Up the Unit

Number and Operations
Grace M. Burton
Location: unknown

Students review this unit by creating, decomposing, and comparing sets of zero to 10 objects and by writing the cardinal number for each set.

Call the students together and choose three volunteers. Have the first student show a Numeral Card selected at random while the second student rings the bell the appropriate number of times and the third student writes the number on the board. Meanwhile, have the rest of the students show with connecting cubes the meaning of the numeral being shown. Repeat with other sets of three volunteers.

pdficon Numeral Card

As the students respond, document their level of understanding on the Count to 10 Class Assessment teacher resource sheet. Determine which students need remediation and which students are ready to move forward. Plan additional experiences for those students who require additional support and extensions for those who need challenges.

pdficon Count to 10 Class Assessment Teacher Resource Sheet

Give each student connecting cubes and a copy of the Fill Up Activity Sheet.

pdficon Fill Up Activity Sheet

Tell the students that as you show a number [using numeral cards or the online Spinner], they should cover the corresponding number on one of the rows on the sheet with a connecting cube. Now ask a volunteer to show the numeral cards one at a time in random order, returning each card to the deck after it is called until all the numerals are covered. (A number may be covered only one time on the card.) Circulate to see which students are able to recognize and cover the corresponding numerals.

1653 image 8.2a

To end the unit, ask a student to make a train of 10 cubes and to show it to the class. Then have the student put it behind his or her back and break it into two pieces. Have the student show one part of the train and ask the other students to make a train as long as the visible part. Then ask them how many cubes they will have to add to make a train 10 cubes long. You may wish to encourage them to use 10 Frames as they do this. Repeat with other students.

Alternatively, or in addition to the above activities, students can work (either individually or in pairs) to review the numbers 1 through 10 by using the Concentration game.

appicon Concentration

To do so, students should select 1-10 under Levels, and either 1 or 2 players. In this activity, students match the numerals (1-10) with other representations explored 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 Options

  1. Use the teacher resource sheet, Class Notes, to document your observations about the students' abilities to do the following:
    • Construct groups of zero objects
    • Identify and write the numeral 0
    • Write the numerals up through 10
    • Construct groups of 0 to 10 objects
    • Record groups of 0 to 10 items
  2. Use the Show That Number Activity Sheet as a post-assessment in this unit.

Questions for Students 

1. Show a train of 10 connecting cubes. Then take five connecting cubes from the train and cover the rest of the train. How many connecting cubes are left?

[Five connecting cubes are left.]

2. (Repeat with taking away other amounts from 10.)

3. Suppose you have 10 connecting cubes. Is this more or less than nine cubes?

[It’s more.]

4. Can you show that?

[Students should place a train of 10 side-by-side with a train of nine to see that 10 is one more than nine.]

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

6. Make two groups. Does one group have more? How many more?

7. How can you change a train of seven to a train of 10?

[Add three connecting cubes.]

8. (Repeat with other numbers.)

Teacher Reflection 

  • Which students met all the objectives of this unit? What extension activities are appropriate for those students?
  • Which students are still having difficulty with the objectives of this unit? What additional instructional experiences do they need?
  • Did all the students display understanding of the relationship between the numerals and the numbers? What is your evidence for this?
  • What were the greatest challenges for the students?
  • How can I help the students extend their understanding to numbers greater than 10?
  • What experiences can I provide so that the students will remember how to write the numerals?
  • What experiences can I plan so that the students will have a genuine need to write the numerals?
  • What learning experiences would help the students not yet comfortable with the concepts of 0 through 10?
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

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 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 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.
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

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 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.

Learning Objectives

Students will:

  • Construct groups of zero to 10 objects.
  • Identify the numerals from 0 through 10.
  • Write the numerals from 0 through 10.
  • Construct and decompose groups of zero to 10 objects.
  • Record groups of zero to 10 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.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.

Grade 4, Num & Ops Base Ten

  • CCSS.Math.Content.4.NBT.A.2
    Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and <. symbols to record the results of comparisons.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP1
    Make sense of problems and persevere in solving them.
  • CCSS.Math.Practice.MP4
    Model with mathematics.