Folding fractions

1.

In this lesson, we will fold strips of paper to make fractions, equal parts.

Give each student several strips of the same length (A4 photocopying paper cut lengthwise is good).

• Follow these steps. Fold the strip in half. Now fold it in half again, but don’t open it.
• How many parts have you made? How do you know?
• Are the parts equal? How do you know?
• Did you use all the strip, the whole?

Students should recognise that they created quarters, four equal parts before opening the strip to check.

2.

Ask students to label the parts with the correct symbol, ¼. Cut along the folds to create one-quarter-length strips. If appropriate to the needs of your students, you could introduce te reo Māori kupu for quarter (hauwhā).

Discuss how the denominator (tauraro) matches the creation of equal parts. (Four parts – 4 as the denominator.)

3.

Take another strip and halve it three times.

Look for students to predict that there are eight equal parts.

• What are the parts called? (Eighths − hauwaru).
• Label each part with the correct symbol and cut along the fold lines to create one-eighth-length strips.
• Connect the number of parts with the denominator 8 in the fraction symbol.

4.

Explore other sequences of folds. Ask students to find a way to fold a strip into thirds (hautoru), meaning three equal parts. Looping is the easiest strategy to find fifths.

5.

Investigate these sequences of folds to different fraction length strips:

• Fold the strip into two equal parts, then fold the halves into three equal parts to get sixths.
• Fold the strip into three equal parts, then fold the thirds in half. Why do students get the same number of equal parts as they do when they fold the strip into halves and then fold the halves into three equal parts?
• Halve, then fifth, to produce tenths.
• Third, then third, to produce ninths.
• Halve, then fifth, to produce tenths.

6.

Order the unit fractions by length to reinforce the idea that more partitions produce smaller, equal parts.

7.

Introduce Finding unit fractions CM. In these tasks, the student must locate the places of equal partitioning without the support of folding. They then transfer the idea to locating given unit fractions when the length of one varies. Provide time for students to work in appropriate groupings that encourage scaffolding and extension, and time for students to share their thinking with a range of students.

Look closely at how your students equally partition the length between zero and one.

1.

Ask students to draw number lines and locate non-unit fractions with the same denominators. For example, they might construct a number line for iterations of one seventh.

Encourage students to make generalisations about the meaning of the numerator as a count of equal parts. They might write equations like 4/7 = 1/7 + 1/7 + 1/7 + 1/7.