Before any formal lessons are taught, give students plenty of time to "play" with fraction pieces, base 10 blocks, connecting cubes, and any other manipulatives used to introduce and create fractions. For the purpose of this activity, I prefer to use fraction pieces that are both rectangular and circular. Allow the children to mix and match pieces, divide them into groups, and explore the different sizes and lengths of the fraction pieces.
Activity 1 can last a typical class period 30-45 minutes. Students may work independently or in small groups. As a whole group, ask students to describe the fraction pieces and reflect on how they manipulated the pieces. Student responses are recorded by the teacher on chart paper.
Objectives: Students will be able to name fractions.
Students will be able to create fraction pieces to use as a concrete material (manipulative).
For the purpose of this activity students will create the fractions one whole, two-halves, three-thirds, four-fourths, five-fifths, six-sixths.
Each student will need 6 paper plates. The first paper plate can remain blank or students may color the plate one solid color and on the back write the label one whole. Plate 2 is folded in half and students will color both halves the same color. Students will cut the plate at the fold and label each half 'one-half' on the back of the plate. Plate 3 is divided into thirds by using a ruler to segment each piece. Students will repeat the same process as in plate 2, except one-third is written on the back of each piece. Plates 4-6 are divided into their respective pieces, colored, and labeled (one-fourth, one-fifth, one-sixth). Each plate has its own color and each piece is properly labeled in words, not numbers. Teacher may opt to draw the segment lines for students and have them color and cut the pieces.
Fraction circles can be stored in a large sandwich bag for later use and preservation.
Students are given ample time to manipulate the fraction pieces individually or in small groups.
Teacher will model how to use fraction plates by naming fractions shown with the pieces. Example: teacher will say "this is one-half," and show the fraction plate one-half, "this is three-fourths," and show three-fourths. Teacher will continue calling out fractions and students will demonstrate knowledge by showing and naming the fraction with the fraction plates.
This activity can be extended into math centers with students working together independent of teacher.
Once students feel comfortable with handling and manipulating fraction pieces, students should begin to illustrate fractions they make with the fraction pieces. Begin to introduce only the images of fractions and have students verbally name each fraction. Upon mastery, students can begin to label the fraction by representing the fraction name in words. Activity 2 can last over the course of 2 class periods. Repetition is critical at this stage because students have the opportunity to recall and store information in the long-term memory. For further lessons, students will rely on their schema to progress to the abstract level of solving fraction problems.
Objective: Students will be able to create a math journal and draw fractions.
Students can make math journals using a binder with loose leaf paper, a spiral notebook, composition book, or several pages of copy paper stapled together.
Using the fraction pieces students created in Activity 1 students will transfer fractions made concretely to pictorial representations in their journal. Teacher will repeat activity in Activity 1 by calling out fraction and first have students represent it concretely, then draw the fraction in their journals. Students may label the fraction with words only. Teacher must check each student's journal for accurate pictorial representation.
The Operator Construct
For the purpose of this unit, the operator construct is represented concretely and in pictorial form. Students will continue to use their journals to record their drawings and add fractions.
Teachers will model how to add one-half + one-half. Teacher will demonstrate adding the two fractions by holding up one-half and connecting it to the other half. Teacher will ask students about what they saw. Teacher will illustrate adding the two halves by drawing one circle half + one circle half = one whole. Students will document this example in their journals. Teacher will continue the process with adding simple fractions such as one-third plus one-third, etc. Note: the fractions must be like fractions in order to complete this activity. Students are not expected to add one-third plus two-fifths. This activity is done until students mastered drawing fractions to show the addition operation. This activity can be replaced with subtracting like fractions as well. Multiplication and division are operations introduced in later grades.
In their journal under the pictures, students may write the steps to the operation performed. This can extend into a writing lesson for informational text.