Author: Mathew Needleman  Date Created: 8/5/2003 6:15:30 PM PST
Collections: More and Less
Grade/Level: 1
Students: 20 students. 10 boys. 10 girls. 16 ELL students. 1 student mild autism.
Subject Area(s): Mathematics
Concept(s): The names for numbers refers to a collection of objects of a certain size. More or less than a particular number refers to an increase or decrease in the size of that collection.
State Academic Content Standard(s): CA- CCTC: Aligned CSTP's and TPE's • Standard : CSTP: Standard for Creating and Maintaining Effective Environments for Student Learning TPE: E. Creating and Maintaining Effective Environments for Student Learning CSTP Description: Teachers create physical environments that engage all students in purposeful learning activities and encourage constructive interactions among students. Teachers maintain safe learning environments in which all students are treated fairly and respectfully as they assume responsibility for themselves and one another. Teachers encourage all students to participate in making decisions and in working independently and collaboratively. Expectations for student behavior are established early, clearly understood, and consistently maintained. Teachers make effective use of instructional time as they implement class procedures and routines. • CSTP Key Element : Promoting social development and group responsibility.  Question : help all students accept and respect different experiences, ideas, backgrounds, feelings, and points of view? CA- CCTC: CSTP's (Standards for the Teaching Profession) • Standard : Standard for Engaging and Supporting All Students in Learning Teachers build on students' prior knowledge, life experience, and interests to achieve learning goals for all students. Teachers use a variety of instructional strategies and resources that respond to students' diverse needs. Teachers facilitate challenging learning experiences for all students in environments that promote autonomy, interaction and choice. Teachers actively engage all students in problem solving and critical thinking within and across subject matter areas. Concepts and skills are taught in ways that encourage students to apply them in real-life contexts that make subject matter meaningful. Teachers assist all students to become self-directed learners who are able to demonstrate, articulate, and evaluate what they learn. • CSTP Key Element : Facilitating learning experiences that promote autonomy, interaction, and choice.  Question: "How do I?" or "Why do I?" : support and monitor student collaboration during learning activities? CA- California K-12 Academic Content Standards • Subject : Mathematics • Grade : Grade One By the end of grade one, students understand and use the concept of ones and tens in the place value number system. Students add and subtract small numbers with ease. They measure with simple units and locate objects in space. They describe data and analyze and solve simple problems. • Area : Number Sense • Sub-Strand 1.0: Students understand and use numbers up to 100:  Standard 1.1 (Key Standard): Count, read, and write whole numbers to 100.  Standard 1.2 (Key Standard): Compare and order whole numbers to 100 by using the symbols for less than, equal to, or greater than (<, =, >).
Objective(s): When shown a collection of objects under 10, students will identify the number of objects (and later one more and one less) in under four seconds with ninety percent accuracy.
Prerequisite Background Skills/ Knowledge: Students need to know the names of the numbers and how to write them. Students may know the names of the numbers by rote but may lack an understanding of what the numbers mean e.g. that five is 3 and 2 more. The latter knowledge will hopefully be acquired through this lesson and its follow-ups.
Vocabulary/Language Skills: More and less. Greater than/less than. Also, the names and meanings of all of the numbers. This vocabulary will be taught by looking at real-life collections of objects as well as pictures in the book "More, Less, Fewer" before moving on to more abstract concepts.
Materials: Dot cards, Dot card transparencies, Dominos Collections of objects Book: More, Less, Fewer
Classroom Management: Discuss appropriate behavior for group work...encouraging, positive attitudes, politeness, and sharing before having students work together collaboratively.
Models of Instruction: Direct Instruction
Procedure
Open: Present students with a collection of three Shrek buttons. Ask students how many there are. Students will probably be able to say three without thinking. Present students with a collection of other objects, say three toy cars and two more toy cars. Ask students how many there are. Ask students what there are more of. Explain that we will beginning a unit about collections in which we take a look at things we have collected, sort them, count them, measure them, and examine them in ways we may have never done before.
Input: This lesson will be presented over the course of the two week unit. Early stages: After repeatedly presenting students with different assortments of objects, ask students to think about how they know three objects is three. Think aloud to point out to students that three objects is always three things. Five objects is always five things even if those things are arranged differently. Then, it makes sense that we could see a collection of three objects and know that three objects was three without even counting. Present students with assortments of dots on the overhead and see how quickly they can identify the number of dots, encouraging them not to count but to think about the number they are naming. Mid-stages: After examining the concepts of less and more through the lesson, "More and Less" and examining the book "More, Less, and Fewer," students will now be asked to name the numbers on dot cards and name the number that is one more and one less than that number. Follow Up activities: Students will be asked to name numbers by their parts e.g. 5 is 3 and 2. Or 4 is 2 and 2.
Guided Practice: Teacher will show the students dot cards, pictures from picture file, and various collections of objects and students will name the number. Students will also have repeated opportunity to count out numbers i.e. "Tommy, please count out three baseball cards." Later, students will gather a certain number of objects and hold them up while other students name how many there are.
Independent Practice: Students will work with partners as they quiz each other with the dot cards. Students will also play the game of dominos, first simply lining up the same number with the same number and later playing one more or one less (lining up the number five with number 4, 6 with 5, etc...)
Close: Do a final review of the dot cards as a celebration of how much students have learned. Tell students that that they have figured out the secret of numbers. Ask them to summarize their learning, looking for a statement such as "3 objects is always 3 objects. Or 5 always means 5 objects."
Assessment/ Reflection
Assessment: Teacher will observe pairs of students working and check to see that students are able to identify the number of objects in a group in under four seconds with ninety percent accuracy.
Reflection: I taught this lesson over two plus weeks. I think this was best. The lesson fit seamlessly in with graphing, measuring, sorting, and greater than/less than concepts. It worked best as a ten to fifteen minutes a day lesson. I think this lesson(s) will payoff even more in the long term. I held off on teaching addition until students had a firm concept of what the numbers were that they were dealing with. Time will tell but I suspect that students will have an easier time of addition and subtraction in the long run now that they understand the numbers conceptually. Students without a conceptual understanding are still able to do addition but in my experience, their mathematical ability seems to break down in unfamiliar scenarios e.g. word problems. I hope these students will be better able to face the challenge of new scenarios and situations.