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## Building Sets of 11 and 12

Pre-K-2
1

Students use bean sticks, connecting cubes, and ten frames to construct sets of 11 and 12, record them, and compare them.

To assess prior knowledge, 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.

Display a Numeral Card and ask each student to show you the number using his or her cubes.

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 card for 11. Ask the students to name the numeral and tell them that they will model this numeral in several ways.

Ask the students how many groups of ten and how many ones there are in 11. Students will be able to "hear" the number of tens and ones more clearly in the higher decades such as the 40s. For example, 46 means 4 tens and 6, with the "ty" standing for "tens and." This is less evident in the teens, and even subtler in the numbers in this lesson.

Call on a volunteer to count out ten cubes of one color (red is used in the model) in a tower. Then ask him or her to add one cube in another color onto the tower. Ask the student to count aloud to determine the number of cubes.

Invite the rest of the class to make their own towers of 11, using 10 cubes of one color and one cube of another color. Show the numeral card for 12 and ask the student to make a tower with 12 cubes in the same way.

Then hold up one tower and ask how many connecting cubes were used to make it. [It will be either 11 or 12 cubes.]

Call on a volunteer to hold up one of their towers, and to say how many cubes were used to make it. Then compare the two towers. The one you are holding will either be less than, greater than, or equal to the one the volunteer is holding up.

Have students display one of their towers to the person sitting next to them. Have them compare their towers, and name the number of cubes used to make each tower.

After they have compared the towers, ask students to trace one of the towers and color it to match the cubes they used. Display the numeral 11 or 12. Tell students to make a large 11 or 12 in the air, then write the appropriate number under a tracing of the tower with that many cubes.

Next, distribute the Ten Frames Activity Sheet.

Ask students to place 11 connecting cubes in it with one per section. Ask them to count aloud as they do so.

Be sure that they fill the red frame first. This will help them visualize 11 as "ten and one more."

Repeat making a ten-frame model for 12. Ask students to suggest ways the representations for 11 and 12 are different.

Now ask students to take one bean stick and show how the number 11 might be modeled using a bean stick and a loose bean. Repeat making a model for 12.

### Reference

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

Assessment Options

1. Asking the Questions for Students while students engage in the activities will help students focus on the mathematics in this lesson and will help you make assessment an integral part of the lesson.
2. As you listen to the students' answers, you will be able to determine the students’ level of knowledge and skill. Document progress on the Class Notes recording sheet. What you discover will be useful when discussing student progress toward learning objectives with students, parents, administrators, and colleagues.
Extensions
Rather than an extension, it is recommended, that you move on to the next lesson in this unit, Building Sets of 13 and 14.

Questions for Students

1. What numbers did we talk about today? Make a tower with that many cubes.

[11 and 12.]

2. Count to 11. Count to 12. What number did you say just before 11? Just before 12? How do you write 11? 12?

[10; 11; Students should be able to write these numerals.]

3. Show me a tower with 11 cubes and one with 12 cubes. How can you compare the number of cubes in the two towers?

[Encourage students to line up the towers and match the cubes in them.]

4. Which tower has more? How can you tell? How many more?

[The 12-tower has more because there are 10 red cubes each, but the 12-tower has 2 blue cubes instead of 1. The 12-tower has 1 more.]

5. How would you show 11 using ten frames? How would you show 12? How can you change a ten-frame model for 11 to one for 10?

[Students should be able to demonstrate the removal of one cube to make a ten-frame model for 10.]

6. When you count, what number comes after 11? After 10? Before 12?

[12; 11; 11.]

7. How did you model 11 with your bean sticks and beans? How did you show 12? What was the difference?

[Student models may vary; the difference is 1.]

Teacher Reflection

• Which students demonstrated they could not yet construct sets of size 11 and size 12 with ease? What experiences do they need next?
• Which students were able to physically compare sets of 11 and 12?

Which are able to explain the relationship between the sets? What experiences are necessary for those who could not?

• Which students are able to count rationally to 12?
• Which students were able to identify the numerals 11 and 12? Which could write them? Which students were not yet able to both write and identify the numerals 11 and 12? What instructional experiences do they need next?
• Which students found bean sticks easiest to use? Which preferred ten frames? Which had a preference for using connecting cubes to model the numbers?
• What adjustments will I make the next time I teach this lesson?

### Building Numbers Up to 10

Pre-K-2
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.

### Building Sets of 13 and 14

Pre-K-2
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.

### Building Sets of 15 and 16

Pre-K-2
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.

### Building Sets of 17 and 18

Pre-K-2
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.

### Building Sets of 19 and 20

Pre-K-2
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 11 and 12 objects.
• Identify and write the numerals 11 and 12.
• Compare a set of size 10 to sets of 11 and 12.
• Record the number of objects in groups of size 11 and of 12.

### 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.