Folding Fractions

Fold Fourths, Halves, and Eighths. Have students color the first four strips on the Making Fraction Strips page in the Student Activity Book using the colors indicated. These colors also coordinate with the fraction circle pieces used in other lessons in this unit. Instruct students to color the strips lightly since they will write the names of the fractions on the strips during the lesson. After coloring, have students carefully cut out each strip. See TIMS Tip.

The first step in the lesson is to establish that an unfolded strip of paper represents the unit whole. Tell students to label their red strip as one whole and set it aside.

Explain that they will fold each strip to show different fractions. Have students fold their pink strips into two pieces that are exactly the same size. Make sure that they crease their strips carefully, making clean sharp folds. Once the folding is completed ask students to unfold their strips and draw a line with a ruler to show their folds.

Next, ask students how they can fold the yellow strip into four equal pieces. Students may suggest that they can first fold their strips in half and then in half again. When they unfold their strips, they will have four equal pieces. After students have completed their folds, ask them to unfold their strips and use their rulers to draw a line showing each fold. Ask what the denominator will be for each fraction on this strip. Students then label each piece with 1/4 as in Figure 3.

Next, students fold their blue strips into eight equal pieces. Have them suggest a method for doing this. The most efficient method is first to fold the strip in half, then fold the folded strip in half again, and finally fold this in half. When the strip is unfolded it will be in eight equal sections. Ask similar questions to those for halves. Students should mark each fold and label their strips as in Figure 4.

Have students complete Questions 1–4 on the Folding Fractions pages in the Student Guide which review what a fraction is, the definition of the denominator, and the definition of the numerator.

Play Show Me. In this activity, students use their fraction strips to represent different fractions. Students will need all their folded strips and the strip representing one whole. To start this activity, name a fraction that can be represented using the fraction strips, for example, 3/8. To show 3/8, students should use the strip that is divided into eight equal pieces. They fold 5/8 of the strip back and leave 3/8 of the strip showing, as in Figure 5.

Continue this activity by asking students to show you fractions that are less than one, for example, 1/4, 5/8, 1/2, 2/4, and 3/4. Once students are comfortable with these fractions, move on to fractions equivalent to one, such as 2/2 and 4/4. Finally, ask students to show mixed numbers—for example, 11/2. Note: To show 11/2, students will need to use two of their strips, the strip showing one whole and the strip showing halves. Ask students to suggest other mixed numbers the class can show using their fraction strips. Students often have the misconception that fractions are always less than one whole. Eliciting a few examples of mixed numbers from students will help dispel this misconception.

For a variation on this activity, display a fraction using one of the marked fraction strips that you prepared before class. Then, fold it to represent a fraction and ask students to identify the name of that fraction.

Fold Thirds and Sixths. Tell students to lightly color the remaining two strips making one orange and one aqua. Ask students to think about how they can fold their orange strip into three equal parts. Students may suggest first folding the strip into a loose "S" and then carefully matching edges before creasing the folds. Students may also suggest folding the paper like a letter. Both techniques are shown in Figure 6.

Folding strips into thirds is more difficult than the folding done previously, so monitor each student's progress carefully. This process may require some trial and error. See Meeting Individual Needs. Students should use a ruler to draw lines to show each fold then label each piece 1/3.

Ask students how they can fold their aqua strips to make sixths. This can be done by first folding it into thirds and then folding the folded strip in half. Students can also start by folding their strips in half and then folding the halves into thirds. Tell students to use a ruler to draw lines to show their folds then label each part with 1/6.

Play Show Me Thirds and Sixths. Play Show Me a second time naming fractions that can be represented using the thirds and sixths fraction strips. Begin again by asking students to show fractions less than one, then move on to fractions equivalent to one and greater than one. Also ask students to show mixed numbers.

Compare Fractions. Explain that fractions are equivalent if they represent the same part of the whole. See Content Note. Tell students to lay their fraction strips on their desks in the order in which they were made (whole, 1/2, 1/4, 1/8, 1/3, 1/6). Have them line up the left edge of their fraction strips as they do so. See Figure 7. Aligning the strips in this order will help them more easily compare fractions as they complete the questions in the Student Guide. The strips will be glued down in order of size to make a fraction chart at the end of the lesson.

Ask students to show and name fractions equivalent to 1/2 and list their responses on the board: 1/2, 3/6, 2/4, 4/8. Demonstrate for the class how to use the fraction strips to find equivalents or ask a student to explain his or her method.

Ask students to find other pairs of equivalent fractions.

Have students use their fraction strips to complete Questions 5–7 in the Student Guide which explore equivalent fractions.

Next ask students to compare a few fractions and suggest that they use their charts to help them answer.

Then ask them to complete Questions 8–11 which involve comparing fractions.

You can assign the Homework section in the Student Guide after Part 1.

You may want to provide an envelope in which students can store their fraction strips to take home for homework.