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Building Sets of 13 and 14

Number and Operations
Grace M. Burton
Location: unknown

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.

To assess students' prior knowledge, repeat the activity from the previous lesson to determine what numbers (up to 13) students understand sufficiently. Ask them to model the numbers using trains of 10 and ones.

Gather students together. Give them 20 connecting cubes, 10 of two different colors in a resealable plastic bag. Ask students to organize their cubes into one train of 10 and 10 cubes that are separated, as shown below.

 BuildingSetsOf13and14 IMAGE 10TrainPlus10Single 

Display the numeral card 10, and ask each student to show you the number using his or her cubes.

pdficonNumeral Cards 

Look for students who understand that 10 is a unit that can be counted without separating the cubes that compose it. Make note of students who have an emerging understanding of place value and those who do not.

To begin the lesson, show the numeral cards 13 and 14 and ask for a volunteer to say each number. Then choose one card, and tell the students to clap their hands as many times as the number suggests, counting aloud as they do so. Repeat with the other card.

Watch to see which students identify the numeral correctly and can clap the number of times the number suggests.

Give each student a large group of cubes in two colors. Ask them to make towers of 13 and 14 using ten of one color in each tower. Have them record the towers by tracing them on paper and labeling the tracings. You may wish to have them color the towers to show "ten and one more." Ask students to take these sheets home and tell their family how they completed them.

BuildingSetsOf13and14 IMAGE 13,14TrainTrace

Next, distribute the Ten Frames activity sheet.

pdficonTen Frames Activity Sheet 

Show the numeral card for 13 and ask them to put 13 cubes in the frames, one cube per frame, filling the top frame first. Ask for volunteers to explain how they did that.

Ask students to clear the frames. Show the numeral card for 14, and ask them to put 14 cubes in the frames. Then ask them to change the ten frames so that they are showing 13. Call on a volunteer to explain the relationship between 14 and 13.

BuildingSetsOf13and14 IMAGE TenFrame14

Place the students into pairs and ask them to change frames again so that they are showing 14. Ask them to separate the group of 14 into two groups in as many ways as they can, and to record the size of the smaller groups.

They may find this easier to do if they draw circles on paper and place the cubes within the circles.

BuildingSetsOf13and14 IMAGE Splitting14

Now ask the students to use bean sticks and loose beans to represent 13 and 14. Ask them to make an entry for their portfolio by drawing bean sticks for 10, 11, 12, 13, and 14 on a piece of paper. Encourage them to label each model with a numeral.

1774 lesson 3 image 5

They will add to this record during the next lessons, so that at the end of the unit they will have a model for each number from 10 to 20. Be sure to have the students write their names on the paper, and then collect them for use in future lessons.


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

Assessment Option

As you observe students constructing and decomposing sets of 13 and 14, you may wish to make notes on individual understanding and skills on the Class Notes Teacher Resource Sheet. Your observations will help you plan remediation activities for students not yet reaching the lesson goals. This information will also be useful when planning extension activities for students who have mastered the learning objectives.


  1. Pose the following question to students: If you have 10 cubes in the ten frame, how many more will you have to add to make 13? To make 14?
  2. Move on to the next lesson, Building Sets of 15 and 16.

Questions for Students 

1. What new numbers did we talk about today? Get with a partner and show me that many fingers.

[13 and 14.]

2. When you count to 13, what number did you say first? What number did you say just before 13?

[If students start at one, they should say, "1"; 12.]

3. Take 13 connecting cubes. Separate the group into two parts. How many are in each group? Can you do it another way?

[Student responses may include 6 and 7, 5 and 8, and so on.]

4. Show the students a tower of 13 and 14 cubes and ask them to respond to the following questions: Which group has more? How can you tell? How many more? Which group has less? How many less?

[The tower of 14 has more; student explanations may vary; the tower of 14 has 1 more; the tower of 13 has 1 less.]

5. How can you change a group of 13 to a group of 14? How can you change a group of 10 to a group of 13?

[Add one more cube; add three more cubes.]

6. When you count, what number comes after 12? After 13?

[13; 14.]

7. How did you show 13 and 14 with ten frames?

8. How did you model 13 and 14 with bean sticks?

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 model 13 and 14 with cubes, ten frames, and bean sticks? What should I do at this time to help them reach this goal?
  • Which students were able to identify the numerals to 14? Which can write all of them?
  • Which students were not yet able to write the numerals up to 14? What instructional experiences do they need next?
  • Which students are able to explain how to use 10 as a benchmark number as they construct sets of 11, 12, 13, and 14? What learning activities should I plan for those who cannot use 10 as a benchmark?
  • 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.
BuildingSetsOf15And16 ICON
Number and Operations

Building Sets of 15 and 16

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.
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 13 and 14 objects.
  • Identify and write the numerals 13 and 14.
  • Compare sets of 13 and 14 objects.
  • Record the number of objects in a group of size 13 and size 14.
  • Decompose groups of 13 and 14.

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.