Feeding Pets

Using Materials

Ask the students to make the fractions 2/3 and 3/4 with fraction strips. Use the scenario  that the strips represent sections of dog jerky strip (dried meat). Tell them that  two-thirds of a strip leaves Woof, the dog, hungry but three-quarters is too much. Challenge them to find a fraction between 2/3 and 3/4 that could tell you how much of a  strip to feed Woof today.

Discuss their methods, which are likely to include:

(i) Change both fractions to decimals, 2/3 = 0. 666 or 0.67 (2 dp) and 3/4 = 0.75, and find a  decimal fraction between these, e.g., 0.7 or 7/10.

(ii) Change both fractions to equivalent fractions with a common denominator, inthis case 12 because it is the least common multiple of three and four. 2/3 = 8/12 and 3/4 = 9/12, so 8.5/12 will work. This needs to be renamed as 17/24.

“How many different fractions could we find between 2/3 and 3/4 ?” (Answer: An infinite number)

“How could you use your strategy to find others?” (Answer: Any decimal between 0. 666 and 0.75 will work, and any fractional number of between eight-twelfths and nine-twelfths will work.)

Pose other “between” problems such as: “Find three fractions between these pairs of fractions:

1/2 and 3/5, 1/2 and 5/8,  2/3 and 4/5, 6/10 and 3/4, 7/8 and 1

Using Imaging and Number Properties

Pose problems that cannot be modeled easily with the fractions strips and invite students to generalise their strategies. Good problems might be: “Find fractions between these pairs of fractions:

3/4 and 6/7,  2/5 and 5/11, 3/8 and 4/10, 2/3 and 9/13, 1/2 and 51/100

Compare the usefulness of the decimal conversion and equivalent fraction methods.
In what ways are they similar? (Both are equivalent fractions.) When is one method easier to use than the other? (When the fractions are easy to convert to decimals)