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Building Sets of 19 and 20

Number and Operations
Grace M. Burton
Location: unknown

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

To assess prior knowledge, provide each student with a blank index card and a resealable plastic bag filled with a set of cubes of two different colors. Ask students to create trains of ten and leave separated any cubes that might be less than or more than ten and to record the number of cubes in their bag on the card provided.

Have each student in turn read the number on his or her card and count the cubes found in the bag to verify the correspondence between the number reported and the cubes.

To begin the lesson, distribute five index cards to each student and ask them to cut each card in half "hamburger" style. Have them write the numerals 11 to 20, one per card.

BuildingSetsOf19And20 IMAGE Activity

Place the students in pairs. Ask one student to show a card at random and the other student to model the number with cubes.

Give the students connecting cubes in two colors and a copy of the Ten Frames Activity Sheet.

pdficon Ten Frames Activity Sheet 

Ask them to model 19 in the Ten Frames, counting aloud in unison as they do so.

Next, ask, "How can we change the ten frames to show 20?" Ask students to model other numbers to 20 using the numbers recorded on their index cards.

Now ask them to model the numbers 19 and 20 with the connecting cubes, 10 in one color and the remainder in another color.

Ask them to break the 20-tower into two parts (ex: 11 and 9). Call on a volunteer to describe how he or she divided the tower, and then record this on the board. Ask if anyone has broken the tower in another way and record these responses on the board. Repeat with several volunteers.

Now distribute bean sticks and beans. Give each student two bean sticks and a collection of at least 20 loose beans.

Ask students to look at a numeral card you are holding and model that number. Use cards from 11 to 20.

This will require that they "trade in" a bean stick for 10 loose beans. By trading loose beans for bean sticks with ten beans glued in place, students develop an understanding of the value of numbers in the 10s place by recognizing that 10 is a unit of beans rather than loose beans used to represent ones.

Count out the required number from the loose beans. This action will set the stage for later work with the addition and subtraction algorithms.

Ask the students to model and label bean sticks showing 19 and 20.


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


Assessment Options 

  1. The observations you have made on the Class Notes Teacher Resource Sheet will help you make short- and long-range plans for your students. You may wish to translate these notes into individual progress reports to share with others who work with your students.
  2. You may wish to use the following game as an assessment activity. As you circulate, see which students are able to recognize and model the number with both materials.

    Give each pair of students a Twenty/Twenty Activity Sheet consisting of two playing fields. Ask students to choose a color of playing field.

    pdficon Twenty/Twenty Activity Sheet 

    To play the game, one student pulls a card from the numeral pack and places on his or her field as many loose beans as that number is greater than 10. For example, if a student pulls a 17 card, he or she will place seven beans on the field. Return the cards to the pack after each turn.

    The next student pulls a card and places the appropriate number of beans on his or her card. Explain that the first player to fill his or her playing field wins the game.

    To make the game more challenging, you might require students to fill their fields exactly. To make it easier, the first student to fill or overfill his or her playing field will be declared the winner.

Give students an opportunity to explore the interactive Ten Frame. This can be played on tablets, interactive whiteboard, or on individual desktops.

Questions for Students 

1. Suppose you have 20 connecting cubes. Is this more or less than 19 cubes? How many more?

[20 is 1 more than 19.]

2. Count to 20. Show me a group of 20. Can you show a way to split a group of 20 into two groups? Can you do it a different way?

[Responses may include 10 and 10, 11 and 9, 12 and 8, and so on.]

3. What change do you need to make a tower of 19 into a tower of 20? What change do you need to make a tower of 20 into a tower of 19? Into a tower of 10? Repeat with other numbers from 11 to 20.

[Add 1 more cube; take away 1 cube; answers may vary.]

4. How did you show 20 with bean sticks? How did you show 20 on the ten frames sheet?

[On the ten frames sheet, two frames would be completely filled in.]

Teacher Reflection 

  • Which students can construct groups for all of the numbers 10 to 20? What are the next appropriate goals for them?
  • Are there students still unable to count out 20 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 20? What experiences do they need next?
  • Which students were able to identify the numerals 10 to 20? Which students need help on specific numerals?
  • Which students were not yet able to write the numerals 10 to 20? Which numerals are the most difficult for them? What additional experiences should I plan for them?
  • Which students were not able to compare sets of size 10 to sets of size 20? What learning activities should I plan for them? 
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.
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.

Learning Objectives

Students will:

  • Construct and decompose groups of 20 objects.
  • Identify and write the numeral 20.
  • Compare other sets to sets of size 20.
  • Record groups up to 20.

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.