Author: Mathew Needleman

The Great Divide (Fractions Lesson)

Grade/Level: 1-3

Students:
 20 students. 10 boys. 10 girls. 13 ELL students. 1 student mild autism.

Subject Area(s):
 Mathematics
Concept(s):
 Dividing is a way of cutting collections up into parts.

Half is one part of a collection of objects divided into two.
State Academic Content Standard(s):
CA- CCTC: CSTP's (Standards for the Teaching Profession)
• Standard : Standard for Assessing Student Learning
Teachers establish and clearly communicate learning goals for all students. Teachers collect information about student performance from a variety of sources. Teachers involve all students in assessing their own learning. Teachers use information from a variety of ongoing assessments to plan and adjust learning opportunities that promote academic achievement and personal growth for all students. Teachers exchange information about student learning with students, families, and support personnel in ways that improve understanding and encourage further academic progress.
• CSTP Key Element : Collecting and using multiple sources of information to assess student learning.
 Question: "How do I?" or "Why do I?" : select, design, and use assessment tools appropriate to what is being assessed?

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 : Mathematical Reasoning
• Sub-Strand 3.0: Students note connections between one problem and another.
 Standard 3.2: (OUTDATED) Use repeated subtraction, equal sharing, and forming equal groups with remain-ders to do division.
Objective(s):
 After reading "The Great Divide," students will be able to explain the meaning of division as cutting things into equal parts with eighty percent accuracy.
Prerequisite Background Skills/ Knowledge:
 Students need to understand the concepts of equal (as in equal parts) and have had some experience with this when discussing the equal sign. Some review of this will be helpful before beginning.
Vocabulary/Language Skills:
 Addition, divide/division, equal, and one-half.

Students have had some experience with addition and equality. Division and one-half may be entirely new. Meaning will be embedded in the literature read in the lesson and be emphasized with visual representation on the overhead projector.
Materials:
 Overhead projector and manipulatives
Book: The Great Divide by Dayle Ann Dodds
Classroom Management:
 This lesson should be short. Student misbehavior will be minimized if the lesson length is kept to under twenty minutes. Keep it simple. Students are sitting in assigned seats on the carpet but will need to be moved to allow for the overhead projector to be put in place. Discuss appropriate overhead projector behavior before proceeding and have a plan for where to move students sitting in impacted seats.
Models of Instruction:
 Direct Instruction
Procedure
Open:
 Briefly review with students the meaning of addition (bringing groups together). Ask rhetorically, what happens if we a certain number of something (like the Shrek buttons we have in the classroom) and we need to share it? What would we do?
Input:
 Then share the cover of "The Great Divide" by Dayle Ann Dodds with students and explain that dividing is something else we can do with numbers when we need to break it up into equal groups. (Ask what equal means, students should know it means the same).

On the overhead projector, place eighty linking cubes (eight trains of ten). As you read the story, you will break these groups of cubes up in half with student help.
Guided Practice:
 Read the story to the students, pausing at each step of the way, to ask students for estimations (smart guesses) and then break the cubes on the overhead projector apart in half. Split the groups in half yourself the first time to model how to do it and later have students come up to split the groups apart themselves once the numbers get to below 20.
Independent Practice:
 Students will come up to the overhead projector and split the groups in half. More independent practice will be provided in a separate lesson on another day to keep this lesson brief and student interest high.
Close:
 Discuss with students what they have learned, specifically about the meaning of one-half and division. Have students explain what these concepts mean.
Assessment/ Reflection
Assessment:
 Assess student understanding by their ability to break the groups of cubes in half and explain the meaning of division at the end of the lesson. Students should be able to explain the concept of division as breaking objects up into equal groups with eighty percent accuracy.
Reflection:
 This was lesson was successful in teaching the concept of dividing to the majority of my students. I was less successful in teaching the concept of one-half, only because I ended up placing less emphasis on halves and more on dividing. The book was a hit with my students but again, its emphasis was on dividing more so than halves.

I was especially pleased at the terrific student behavior during the lesson. I owe this to the brevity of the lesson and the hands-on nature of the students coming up to the overhead to move the blocks around. I also think my behavior management system is having an effect on student behavior over the long-term.
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