Question P6 Repeated identity
Today’s problem — free all day, every step. Every day has one.
A rectangular tank measures 30 cm by 20 cm by 25 cm. It is full of water. All the water is poured into a second rectangular container with a base area of 200 cm². What is the height of the water in the second container?
Answer
45 cm.
One length or count, described two ways in the same question.
In this one. The water is the quantity that does not change when you pour — 9000 cm³ before and after — so the only thing the second container alters is the base area it is spread over, and therefore the depth.
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.
Worked examples of all 33 patterns and skills, in a booklet you can print.