Illuminations: Let's Count to 20

Let's Count to 20

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 5

Lesson 6

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 decompositions.

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

Materials

Connecting cubes
Resealable plastic bag
Index cards
Crayons
Glue
Bean sticks
Paper
Ten Frames Activity Sheet
Twenty/Twenty Activity Sheet

Instructional Plan

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.

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.

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. 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.

Questions for Students

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

[20 is 1 more than 19.]

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.]

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.]

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.]

Assessment Options

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.
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.

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.

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?

NCTM Standards and Expectations

Number & Operations Pre-K-2

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.