More unit fractions

1.

Challenge your students to model difficult equal divisions using strips of paper.

Find a way to divide your one strip into three equal parts.

• What will the parts be called? (Thirds – note that the word does not indicate three parts)
• How do we write that fraction? (1/3 for one third)

Find a way to divide your one strip into five equal parts.

• What will the parts be called? (Fifths – note that the word does not indicate five parts)
• How do we write that fraction? (1/5 for one fifth)

Continue this process of folding until students have created strips of halves, quarters, thirds, and fifths.

2.

Use unit fraction strips to build up a number line of unit fractions in a predictive way. 
Draw, and have students draw, a number line with ends labelled 0 and 1. Alternatively, you might provide students with a number line. 
Have students use one part of their previously created fraction strips to predict and then confirm the location of their unit fractions on the number line.

• Where do you think the fraction 1/2 will go on the number line? (It will be halfway between 0 and 1)
• Where do you think the fraction 1/4 will go on the number line? (It will be halfway between 0 and 1/2)
• Where do you think the fraction 1/3 will go on the number line? (Greater than 1/4  but less than 1/2)
• Where do you think the fraction 1/5 will go on the number line? (Smaller than 1/4).

You might introduce te reo Māori kupu related to fractions, such as haurua (halves), hautoru (thirds), hauwhā (quarters), and haurima (fifths). Ensure you make links between relevant vocabulary, symbols, and the relative size of different fraction strips as you work.

3.

Extend students’ thinking further by anticipating the location of fraction parts they will not fold, such as one sixth, one eighth, and one tenth. Ask students to justify the location of those fractions in relation to those numbers already on the line. This should involve understanding the role of the denominator, and using processes like halving, thirding, trebling, and doubling.

1.

Increase the level of abstraction by asking students to construct their own number line with iterations of unit fractions (e.g., 2/3, 4/5), and by providing students with number lines of different lengths.

2.

Use equal partitions with small prime numbers, 2, 3 and 5, to create more difficult unit fractions. For example, twelfths can be created by folding quarter then folding the quarters in thirds. That works because 3 x 2 x 2 = 12. Similarly sixths can be created by thirding halves, since 3 x 2 = 6.