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 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.

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

Materials

Connecting cubes
Resealable plastic bag
Crayons
Glue
Bean sticks
Paper
Numeral Cards (photocopied on cardstock)
Ten Frames Activity Sheet
Electronic Abacus Tool

Instructional Plan

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.

Display a Numeral Card and ask the student who has the train that matches the numeral to model the number.

Numeral Cards

Tell the student to use a train of 10 and separate the appropriate number of cubes into “ones” represented by the single cubes.

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.

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.

Next, distribute the Ten Frames activity sheet.

Ten 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, " How many counters are in the top row? How many in the second row?" "How many in all?"

Go to the Electronic Abacus Tool.

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.

Questions for Students

What new numbers did we talk about today?

[15 and 16.]

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

[Add 1 more cube.]

Clap 15 times. Clap 16 times.

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

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.]

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.]

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.

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.]

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.]

Assessment Options

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.

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?

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.
Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
Count with understanding and recognize "how many" in sets of objects.