Goal: Think like a mathematician! Read the problem multiple times.
Alicia, Emma, and Nick dive into an extremely deep pool. Alicia dives to a depth of – 9/4 meters from the surface of the pool. Emma’s depth is twice as far from the surface as Alicia’s dive. Nick’s depth is 2/3 the depth of Alicia’s dive. [What are Emma’s and Nick’s depths, relative to the surface of the pool?]
Source: Ready Common Core Mathematics Grade 7 Lesson 6
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One of the reasons we like this task for the 3 reads is that the problem stem contains two numbers. One of those numbers (-9/4) is the value of a QUANTITY and the other number (2/3) describes a RELATIONSHIP between two quantities. It’s a nice way to sort out the difference between a number, a quantity, and a relationship.
Agreed!!! That’s why I picked this task after my students were continuing to have a hard time identifying relationships within word problems. This was the perfect problem for this and my students definitely left the classroom with a deeper understanding. One thing I noticed that was unexpected was that after the first read, many students stated that the problem was about the depth of a pool! Again, after the second read, there were still students who shared that the problem was asking, “How deep is the pool that Emma and Nick dove into?”. At this phase, other students began responding to this with disagreement and they were all able to determine that the depth of the pool was irrelevant. The students determined that -9/4 was the only quantity and the depth of Nick and Emma’s dives were related to Alicia’s (-9/4). One student stated, “without knowing Alicia’s depth, you can’t find Emma’s or Nick’s depth” and this assisted other students in understanding relationships!