Classroom Management: Basic Fractions (3rd or 4th Grade Level)
This lesson is on learning the basics of fractions. Materials used will include:
- Blackboard instruction with colored chalk
- Construction paper, scissors, and glue
A. Direct Instruction
The lesson will consist of an explanation on the board of cutting a circle into pieces—halves, thirds, fourths, fifths, sixths, etc. This will be repeated with other shapes: A triangle into halves, sixths. A square into halves, thirds, quarters, etc. The way of writing each of these will be expressed. Then a group of 12 small circles on the board—how do you break this into thirds, halves, sixths, etc. Comparisons will be drawn to such items as pieces of pizza or pie, or eating part of an apple.
When the concepts seem clear, students will be assigned a section on the blackboard in small groups, and each one will have a figure (square, circle, group). Each will be asked to separate their figure into some simple fraction (halves, thirds, fourths, etc.). They will be asked to indicate ¼ and ¾, for example, and color each in different colors and to correctly label the fractions beside their diagrams. As needed, groups at the board will rotate so every child has a chance to do some of the problems. Furthermore, alternative ways of doing the diagram will be illustrated. For example cutting a square into fourths could be accomplished either with an X or a + type of cut.
a. Goal 1: Basic concepts: Students will understand the concepts of numerator, denominator, and that fractions are pieces of a whole.
b. Goal 2: Applicability: Students will understand that fractions correspond to equal-sized pieces of a single whole, or to multiple elements of a larger group.
c. Goal 3 Expressing Fractions: Students will understand how to construct and write simple fractions.
Students are expected to listen attentively and participate in class discussion and the at-board work in turn.
a. Consequence: If not listening attentively, the student will be moved to the board to participate to give them a chance to move around a little while participating.
b. Reinforcement: Students who do well in their participation will receive an appropriate reward.
B. Cooperative Work
Students will be divided into groups of various sizes and with varying abilities in each group. The groups will be given a colored construction paper sheets. Each student in the group will throw a die (or draw a number or spin a spinner) to determine a number from 3 to 6. (If they throw or spin a 1or 2 they try again.) They will be asked to cut their construction paper sheet into that many pieces in any way they like as long as all pieces are the same size; they will label their pieces with the fraction the piece represents. One piece of paper supplied by the teacher will serve as a trunk. The group will then combine those pieces into a “fractal fraction tree” with each student having one level of branching beyond the trunk. The pieces will be pasted onto the tree appropriately; an example will be shown to demonstrate the idea (Naylor, 2005). Other problems will involve coming up with more than one way to represent fractions such as 2/3 and 4/5. For example, what are two or three different ways to cut a pizza in which 3 people can get equal amounts? The groups will be monitored by the teacher to ensure that it meets criteria of being (1) mathematically correct and (2) universal participation (Ball, Sleep, Boerst, and Bass, 2009).
a. Goal 1 Apply fractions to real-world problems: Students will begin to see that fractions are used in real life.
b. Goal 2 Understand different ways to represent fractions: Students will understand that equivalent fractions mean the same thing, such as 1/3 of a pizza being the same as 2/6 and 4/12.
The students are expected to participate in their group discussions and contribute to their group without dominating the group.
a. Consequence: If one person is dominating the group they will be asked to step down and let others contribute. If one person is not participating they will be asked to lead the group.
b. Reinforcement: The group that creates the most liked fractal fraction tree (as voted on by the class) gets a reward.
Students will be assigned two tasks to do at home. One task is to do a take-home worksheet that provide practice in illustrating fractions. A second task is to determine how to figure simple fractions of fractions—for example, taking 1/3 of 3/4 to get 1/4.
a. Goal 1: To gain practice in working with fractions.
b. Goal 2: To anticipate the following lesson on combining fractions and get the students to think about how fractions might combine.
2. Rule 3
Students will complete their homework assignment.
a. Consequence: Not completing the worksheet or completing it badly will result in a bad score for that assignment. The second part of the worksheet (i.e., the section on figuring fractions of fractions) is not graded since that material has not yet been covered in the class.
b. Reinforcement: Those who complete the worksheet get a good grade on the task. Those who also make an attempt to do the second part of the worksheet get extra credit.