Ask the students whether 1/2 > 1/4 or 1/4  < 1/2 . The expected answer is 1/2 > 1/4 . Now pose this problem:

“Annabelle earns $100 a week, and Maureen earns $400 a week.” Discuss why, in this case, one quarter of Maureen’s weekly pay would be bigger than half of Annabelle’s weekly pay! Record on the board or modelling book, “Half of a small amount can be smaller than a quarter of a larger amount”.

Discuss why, when we are making comparisons between fractions, we need to be careful about what the respective “wholes” are.

Extension Activity

Ask the students to work out in this table whether or not half of Annabelle’s pay is the same as a quarter of Maureen’s pay.

 Discuss the general rule: Half of Annabelle’s pay is the same as a quarter of Maureen’s pay provided Maureen earns exactly twice as much as Annabelle.

Pose similar problems like: “One half of Peter’s pay is the same as one-third of Nicola’s pay.”

“When can this statement be true?” “Come up with some numbers that work.” “Try to find the general rule for this statement.” (They are equal provided Peter earns exactly two-thirds of Nicola’s pay.)