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Building Sets of 15 and 16

Number and Operations
Grace M. Burton
Location: unknown

Students explore the numbers 15 and 16. They make and decompose sets of size 15 and size 16, write the numerals 15 and 16, and compare other sets to sets of size 15 and size 16.

To assess students' prior knowledge, prepare trains of 12 to 16 cubes (two models are provided below) in resealable plastic bags. Distribute a train of cubes to each student.

BuildingSetsOf15And16 IMAGE 15,16Train 

Display the numeral cards 12 and 16, one at a time, and ask students to hold up the train that models the numeral.

pdficonNumeral Cards 

Tell the students to use separate their trains into a train of 10 and “ones” (represented by the single cubes). A model is shown below.

BuildingSetsOf15And16 IMAGE 15,16TrainSplit

To begin the lesson, provide students with connecting cubes in two colors and crayons in the same two colors. Request that they make a tower of 10 cubes in one color, and then add 5 cubes in the other color.

Have them trace the tower and label it 15, writing the "1" in the color used for 10 and the "5" in the other color they used for the ones. Repeat with 16. Note that a bigger sheet of paper will be needed if students are tracing using the connecting cubes. If a bigger sheet of paper is not available, have students use graph paper to sketch out their trains.

Ask them to look at the numeral card for 15 and point to the number on the card that means "10." Ask them what the other number signifies. Repeat with 16.

Ask students to break apart the 16-cube tower and divide the cubes into two groups, recording the size of each group. Ask them to divide the cubes in at least four different ways and record the size of each group (example: 8 and 8).

Next, distribute the Ten Frames Activity Sheet.

pdficonTen Frames Activity Sheet 

Check to make certain that students understand the difference between a row and a frame.

Show either the 15 or 16 numeral card. Ask students to show the number on the ten frame by placing one cube in each box of the ten frame. Remind them to start at the smiley face and go in the direction of the arrow.

To help them see the relationship of 15 or 16 to 5, ask guiding questions, such as:

  • How many counters are in the top row? 
  • How many counters are in the second row?
  • How many counters are there in all?
BuildingSetsOf15And16 IMAGE TenFrame16

Go to the Electronic Abacus Tool.

appicon  Electronic Abacus Tool 

Call on a volunteer to use the abacus to show 15 by moving the abacus beads. Tell the student to be sure to use all the beads on the top bar of the abacus before adding beads from the second row. Ask his or her classmates what number is shown.

Call on a volunteer to write the numeral on the board. Repeat with 16, using other volunteers. Repeat with other numbers from 10 to 16. Be sure to clear the abacus each time a number is to be shown.

Ask students to use bean sticks and beans to model the numeral card that you display. Use numeral cards from 11 to 16. Ask them to add pictures of bean sticks modeling 15 and 16 to the recording sheet they started yesterday.


1780 lesson 4 image 4


Burton, Grace M. Towards A Good Beginning: Teaching Early Childhood Mathematics. Menlo Park, CA: Addison-Wesley, 1985.


Assessment Option

Your notes on student progress will help you plan ways to assure that each student will develop a concept of the numbers up to 16. You may wish to note which students are unable to write the numerals even though they understand the quantities they represent. These are different abilities which develop at different times and which require different remediation strategies. The Class Notes recording sheet can be used to document such progress.


Rather than using an extension, it is recommended that you move on to the next lesson in this unit, Building Sets of 17 and 18.

Questions for Students 

1. What new numbers did we talk about today?

[15 and 16.]

2. Show me a tower with 15 connecting cubes. What could you do to make that a tower of 16 cubes?

[Add 1 more cube.]

3. Clap 15 times. Clap 16 times.

[Students should be able to clap the specified number of times.]

4. Show me a group of 15 and a group of 16. Which group has more? How can you tell?

[The group of 16 has 1 more.]

5. How can you change a group of 15 to a group of 16? How can you change a group of 10 to a group of 16?

[Add 1 more; add 6 more.]

6. How did you show 15 on the ten frame? On the abacus? With bean sticks? What is alike between the ways you showed the number? What is different? Repeat with 16.

7. When you show 15 on a ten frame, how many cubes would be in the top frame? In the bottom frame? How many more cubes would you need to add to fill the ten frame?

[10; 5; 5.]

8. What is one way you can divide 16 into two groups? Can you demonstrate this? What is another way?

[Answers may include: 10 and 6, 8 and 8, 9 and 7, and so on.]

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 consistently count out up to 16 objects? What should I do at this time to help them reach this goal?
  • Which students are not yet able to count rationally up to 16? What experiences do they need next?
  • Which students are able to identify the numerals up to 16? Which students can write all of them?
  • Which students are not yet able to write the numerals up to 16? Which numerals are the most difficult for them?
  • Which students are able to compare sets of 15 and 16? Which students are not yet able to do this? What learning activities should I plan for them?
  • Which students are able to decompose sets of 15 and 16? Which students are not yet able to do this? What learning activities should I plan for them?
  • What adjustments will I make the next time I teach this lesson?
Number and Operations

Building Numbers Up to 10

Students construct sets of numbers up to 10, write the numerals up to 10, and count up to 10 rationally. They use ten frames and also make bean sticks.
BuildingSetsOf11And12 ICON
Number and Operations

Building Sets of 11 and 12

Students use bean sticks, connecting cubes, and ten frames to construct sets of 11 and 12, record them, and compare them.
BuildingSetsOf13and14 ICON
Number and Operations

Building Sets of 13 and 14

Students construct and identify sets of size 13 and size 14. They compare sets to sets of size 13 and size 14, and record the number in the sets. They decompose a set of 13 and a set of 14 in several ways.
BuildingSetsOf17And18 ICON
Number and Operations

Building Sets of 17 and 18

Students construct sets up to size 18, write the numerals 17 and 18, and model 17 and 18 with bean sticks, cubes, and ten frames.
BuildingSetsOf19And20 ICON
Number and Operations

Building Sets of 19 and 20

Students explore sets of 19 and 20. They count up to 20, construct and decompose sets up to 20, and record the decomposition.

Learning Objectives

Students will:

  • Construct groups of 15 and 16 objects.
  • Identify and write the numerals to 16.
  • Compare sets of 15 and 16.
  • Record the number of objects in a group of size 15 and size 16.
  • Decompose sets of size 15 and size 16.

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.1
    Count to 100 by ones and by tens.

-Kindergarten, Counting & Cardinality

  • CCSS.Math.Content.K.CC.A.2
    Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

-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, 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.A.1
    Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Common Core State Standards – Practice

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