Record the number of objects in groups of size 11 and of 12
Resealable plastic bag
Bean sticks Paper
Numeral Cards (photocopied on cardstock)
Ten Frames Activity Sheet
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 (blue 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.
Have the class make a 12-tower. Then hold up one tower and ask how many connecting cubes were used to make it. (11 or 12)
Call on a volunteer to hold up his or her other tower, and to say how many cubes were used to make it. Then compare the two towers. Have students display their tower, compare their towers with a partner, 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.
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 blue 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.
Questions for Students
What numbers did we talk about today? Make a tower with that many cubes.
[11 and 12.]
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.]
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.]
Which tower has more? How can you tell? How many more?
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?
When you count, what number comes after 11? After 10? Before 12?
[12; 11; 11.]
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.]
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.
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.
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?