Illuminations: Let's Count to 20

Let's Count to 20


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 18 objects
  • Identify and write the numerals 17 and 18
  • Compare sets to sets of size 18
  • Record the number of objects in a group of size 17 and size 18

Materials

 
Connecting cubes
Resealable plastic bag
Crayons
Index cards
Glue
Bean sticks
Paper
Numeral Cards (photocopied on cardstock)
Ten Frames Activity Sheet
Virtual Spinner

Instructional Plan

To assess prior knowledge, gather students in a circle. Distribute a Numeral Card with a number between 1 and 18 on it, turned face down, and a resealable plastic bag containing a set of 1 to 18 cubes to each student.

Numeral Cards Numeral Cards

Ask students to compare their numeral card with the cubes in their bag to determine if they match. If the students’ numeral cards do not match the cubes in their bag, have each student display his or her card (taking turns one-by-one) to the other students in the class and ask them to trade their bag for one with the number of cubes that does match the numeral card.

If time permits, you might wish to have students verify that the bag of cubes that is traded does match the numeral card of the student displaying the card.

To begin the lesson, show the numeral 18 and tell students to clap their hands 18 times, counting aloud as they do so. Call on students to name other actions to do 18 times and have the class do them and count each time.

Give each student connecting cubes and the Ten Frames activity sheet.

Ten Frames Activity Sheet

Have each student count out 18 connecting cubes and ask them to show 18 in the ten frame. Then ask how they would model 17 in the ten frames.

 

 

Ask students to divide 18 cubes into two groups in as many ways as they can. Ask them to record the ways. After they have had time to work, encourage them to share how they divided the cubes. Encourage them to make statements, such as "I made a set of 7 and a set of 11 from 18 cubes." Record each decomposition where all the students can see.

Next, open the National Library of Virtual Manipulatives Virtual Spinner. Demonstrate for students how to create and use the spinners.

You may use only one computer for the demonstration or have students work together on multiple computers. You may wish to explore the other tools on this site to determine how they might be useful to you in other lessons.

Create an 11-part spinner by entering the numbers 10 to 20 in the left column. As you enter each number, call on a volunteer to choose a color for that section of the spinner. Then activate the spinner. Ask students to say the resulting number aloud and make a tower with that many connecting cubes, using ten of one color and completing the model with another color. Call on a volunteer to tell how many of each color he or she used to make the tower.

In the example below, the student might say, "I used 10 blue and 8 red cubes to make my tower of 18."

 

 

It may reinforce learning to repeat this activity several times using different numbers and choosing a different child to activate the spinner each time. Ask students to model each number that is selected with bean sticks.

After they have created various numbers and modeled them using two different colored cubes, call on three volunteers to spin the spinner. After each spin, ask all students to model that number with connecting cubes of two different colors (one for tens and one for the ones) and then trace, color, and label the tower. You may wish to ask them to model the number with bean stick pictures. Encourage students to take these sheets home to share with their families.

Ask students to add models of 17 and 18 to their bean stick record sheet, previously started in this unit. Collect these sheets for use in the next lesson.

Questions for Students

 

Show me a group of 18. Repeat with 17.

Make a tower of 17 and a tower of 18. Which tower has more? How can you tell? How many more?

[The tower of 18 has 1 more.]

Count out 18 connecting cubes. Now make two groups with those connecting cubes. How many are in each group? Can you make two groups with 18 connecting cubes in another way? Can you make two groups with 18 in five different ways?

[Answers may include: 10 and 8, 9 and 9, 11 and 7, 12 and 6, and so on.]

What do you need to do to change a group of 18 to a group of 20? What do you need to do to change a group of 18 to a group of 10? Show this using ten frames. Show this using bean sticks. Explain what you did.

[Add 2 more; take away 8.]

What number comes after 18? Before 18?

[19; 17.]

Assessment Options

 
  1. The observations you have recorded throughout the unit will be useful as you discuss student progress with other adults who work with your students. Your observations will also be useful in focusing conversations with parents during conferences. You can record such observations on the Class Notes recording sheet.

Teacher Reflection

 
  • Are there students still unable to count out up to 18 objects? What should I do at this time to help them reach this goal?
  • Which students are able to identify the numerals to 18? Which students are not yet able to count rationally to 18? What experiences do they need next?
  • Which students were not yet able to write the numerals up to 18? Which numerals are the most difficult for them?
  • Which students are able to compare other sets to sets of size 18? 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?

NCTM Standards and Expectations

 
Number & Operations Pre-K-2
  1. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
  2. Connect number words and numerals to the quantities they represent, using various physical models and representations.
  3. Count with understanding and recognize "how many" in sets of objects.

References

 
  • Burton, Grace M. Towards A Good Beginning: Teaching Early Childhood Mathematics. Menlo Park, CA: Addison-Wesley, 1985.
This lesson was developed by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics


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