Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. 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 nctm.org.

## Building Sets of Nine

Pre-K-2
1

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.

Distribute a set of 10 cubes to each student and a copy of the Show That Number Activity Sheet.

Name a number between 1 and 10, and ask the students to place that number of cubes on their table. Next ask students to draw the specified number of cubes on their recording sheet, label each cube that was drawn with a number, and label the set with the appropriate number. This recording allows you to check for one-to-one correspondence and the students' understanding of the total number of objects in a set. Review the information to determine the pacing of, and the extent of material covered in, this lesson. Keep the student work samples for future reference.

Show the numeral 9 and tell the students to clap their hands nine times, counting aloud as they do. Now call on students to name other actions to do nine times. After each action is suggested, have the students perform this action nine times and count aloud as they do. Then have each student count out nine file cards from a deck of file cards and save them for use later in this lesson.

Give each student a 10-Frame Activity Sheet.

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

Display a numeral card and ask the students to put as many connecting cubes into the sections, one per section, as the number indicates. Encourage them to count aloud in unison as they do so. Then ask them Guiding Question 4. Encourage them to make other similar statements, such as "I would make a set of nine from a set of seven by adding two more cubes."

Then go to the spinner applet at the National Library of Virtual Manipulatives. Choose "Change Spinner," and create nine regions; but, instead of giving them color names, label them 1‑9. As you enter each number, call on a volunteer to choose a color for the section of the spinner that will hold that number. Then choose "Apply" to activate the spinner. Choose "Spin," and ask the students to show the number of connecting cubes that matches the number on which the spinner came to rest. Repeat several times, choosing different students to activate the spinner each time. (For the students needing additional structure, you may wish to provide a 10 Frame in which to put the connecting cubes, one cube in each section.)

Now give the students a large group of connecting cubes in two colors. Ask them to make five different trains of nine cubes using two colors. Then have them record the trains on the Showing Sets of 9 Activity Sheet.

Then ask them to record how many of each color they used for each train of nine cubes. After they have worked for a while, call on volunteers to share how they colored the rows on their sheet. Prompt the students to take these sheets home to share with their family.

Display a numeral 9 and ask the students to make a 9 in the air as you sing the numeral writing song from the lesson Writing Numerals to Five.

Then have one student write "9" on the board. Now return to the online Spinner and call on volunteers to write on the board the number that comes up when the spinner stops. After practicing writing numbers on the board, spin the virtual spinner and ask the students to write the numerals that come up on the spinner, one to a file card until they have all nine of them. Each numeral, 1 through 9, should be written only once.

To provide practice in counting, give each student a Can You Cover All of Them? Activity Sheet and some connecting cubes.

Show the students a numeral card. Tell the students that as you show a number, they should count out that many connecting cubes and put each cube on a different star. [Show cards in random order, and observe which students can count out all the numbers without hesitation and which cannot.] When all the stars are covered, ask the students to clear their sheets. Then place the students in pairs and have them take turns showing numeral cards using their completed file cards and covering the stars on the sheet until the sheet is covered. Encourage the students to take home the Can You Cover All of Them? Activity Sheet and the numeral cards they made so they can play the game with their family.

To end the lesson, have the students complete the "9" column of their Steps to 10 Activity Sheet.

Invite them to compare the columns on the chart by using some of the Questions for Students.

### References

• 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 nine objects
• Compare a group of nine objects with a group of up to nine objects
• Identify and write the numeral 9
• Record a group of nine items

Extension

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

Questions for Students

1. Can you count to nine? Can you show me a group of nine? Can you show what nine means in another way?

[Students might clap their hands nine times or hold up nine fingers.]

2. Make a group of eight and a group of nine. Which group has more?

[The group of nine has more.]

3. How can you tell?

[The group of nine is longer.]

4. How many more does the group of nine have?

[The group of nine has 1 more.]

5. Count out nine connecting cubes. Now make two groups with those connecting cubes. How many are in each group? Can you make two groups with nine connecting cubes in another way?

How can you change a group of nine to a group of 10?

[I can add 1 more to the nine.]

6. How can you change a group of nine to a group of five?

[I can take 4 away from the group of nine.]

7. What number comes after eight? Before eight?

[Nine comes after eight. Seven comes before eight.]

8. How did you show nine on your chart?

[I counted nine boxes and colored them.]

9. How is that column like the column for 8?

[I had to color 8 boxes in both columns.]

10. How is it different?

[I had to color one more box for nine.]

11. (Repeat this activity giving other numerals and then compare the numbers in various columns.)

Teacher Reflection

• Are there students still unable to count out up to nine objects? What should I do at this time to help them reach this goal?
• Which students are able to identify the numerals to 9? Which can write all of them? Which students are not yet able to count rationally to nine? What experiences do they need next?

### Building Numbers to Five

Pre-K-2
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.

### Writing Numerals to Five

Pre-K-2
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.

### Building Sets of Six

Pre-K-2
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.

### Building Sets of Seven

Pre-K-2
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.

### Building Sets of Eight

Pre-K-2
Students explore the number 8. They make and decompose sets of eight, write the numeral 8, and compare sets of up to eight objects.

### Building Sets of Ten

Pre-K-2
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.

### Wrapping Up the Unit

Pre-K-2
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 nine objects.
• Identify and write the numeral 9.
• Compare sets of up to nine items.
• Record a group of nine 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.