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My colleagues and I have long been wondering about whether it is outside the scope of the standards to move multiple place values in 4.NBT.1 and 5.NBT.1.
Thinking for assessment purposes, is asking a student to recognize that 7,000 is 100 times the value of 70 out of the realm of 4.NBT.1? The progressions seem to imply that the standard is really calling for students to only recognize that the place value to the immediate right of a given place value is 10 times that value.
For 5.NBT.1, I certainly feel less clear about whether moving more than one place value is acceptable. For example, if I were to give students a task in which they need to recognize that the 5 in 16.915 is 1/100 the value of the 5 in 182.54, is this going beyond the scope of the standard? 5.NBT.2 seems to imply that students should understand the effect of multiplying or dividing by more than one place value, but some of my colleagues feel that 5.NBT.1 is strictly one place value to the left or right.
Would love others’ thoughts on this.
To me, it looks like 4.NBT.1 is where we start to generalize place value understanding, so it makes sense to start with adjacent digits. Since 5.NBT.1 is still dealing with adjacent digits (although, now both to the left and the right) it seems like your example of 7000 being 100 times the value 70 would not be a typical problem in grade 4.
5.NBT.2, however, seems like the place that we begin to explore multiplying by more than 10 “…multiplying a number by powers of 10,…” So, using your second example, students might explain why when 16.915 is multiplied by 100, the result is 1691.5 and maybe express 1691.5 as 16.915 x 10^2
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