Question P6 Repeated identity
Today’s problem — free all day, every step. Every day has one.
There are 3 rows of seats in a classroom, each row with the same number of chairs. A group of students occupied of all the seats. Then, of the students left. The remaining students moved into the first 2 rows. What fraction of the seats in the first 2 rows are now occupied?
Answer
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One length or count, described two ways in the same question.
In this one. The students did not change when they moved — only the seats they are counted against did: 4/5 × 5/8 = 1/2 of all the seats worth of students are now sitting in the 2/3 of the seats that the first two rows make up, and (1/2) ÷ (2/3) = 3/4.
A shape or count is described from two viewpoints in the same question, such as one edge measured as a number of long pieces and again as a number of short pieces.
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
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