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Lesson Excerpt:

Counting Ears

This lesson was adapted from a Marilyn Burns activity.

Objective: Second Grade Mathematical Practices:  #2 Reason abstractly and quantitatively, #4 Model with mathematics, #7 Look for and make use of structure.

Explore growing patterns

Theoretical Foundation:  In earlier grades, students have explored and investigated repeating patterns.  Second graders begin to work with simplistic growing patterns which build the foundation for working with functions.

Estimated Time: 40 minutes

Materials:   0-99 chart, Counting Ears t-chart (or have students create their own), one per student and make one large one for display, colored pencils

Description:

1. Ask students: Each person in our class has how many ears?

2. Next, ask students how many ears would be in the room if the room were empty.  On a class t-chart put zero under the “People” column. After students answer, record their response (zero) under the “Ears” column.  Have students record the data on their sheets.

3. Instruct students to shade in the numbers recorded in the “Ears” column on the 0-99 chart.  (This will allow students to see the pattern emerge in two different formats.)

4. Ask students: If only one person were in this room, how many ears would be in the room?  Record a “1” under the “People” column and a “2” under the “Ears” column after students have given response.

5. Repeat this process with the students until you have 4 repetitions on the t-chart and 0-99 chart.  Then have students continue the pattern until they find out how many ears are in the classroom.  Discuss ways to do this. 

6. Once students have found the number of ears in the room, ask them to discuss the pattern and find a rule. Concepts to look for: number of ears is double the number of people, it’s counting by 2s, the number of people is half the number of ears, the ears are always an even number.

7. During the next day’s lesson, have students go through the same procedure using different numbers. Ideas: the number of fingers on one hand, the number of horns on a triceratops, the number of legs on a dog, number of sides on a pentagon, number of eyes on a person, number of eyes on a spider, number of wheels on a tricycle.

Differentiation Suggestions:

1. Allow students to work with a partner.  Have one partner color in a 0-99 chart while the other partner fills in the t-chart.

2. Allow students to work in groups to determine the rule.

Probing Questions:

1.      What patterns do you notice?

2.      How many ears will there be when there are 100 people in the room?

Assessment:

1.      Does the student see the pattern immediately? 

2.      Are students able to see the doubling pattern or do they want to add two every time?

Building Mathematical Thinkers

Second Grade– Counting Ears

Counting Ears

People                 Ears