In this lesson, students use number lines to visualize powers of 10, compare very large numbers, and make sense of orders of magnitude (MP2). They use the structure of a number line that is subdivided into 10 equal intervals to express large numbers as multiples of a power of 10, which naturally leads to the idea of scientific notation, which will be introduced in subsequent lessons (MP7).
In these materials, “multiple of a power of 10” does not necessarily mean an integer multiple of a power of 10. Students explore numbers of the form \(b \boldcdot 10^n\), where \(b\) is some decimal number. Eventually, when students are formally introduced to scientific notation, \(b\) is restricted to values between 1 and 10.
- Compare large numbers using powers of 10, and explain (orally) the solution method.
- Use number lines to represent (orally and in writing) large numbers as multiples of powers of 10.
Let’s visualize large numbers on the number line using powers of 10.
- I can plot a multiple of a power of 10 on such a number line.
- I can subdivide and label a number line between 0 and a power of 10 with a positive exponent into 10 equal intervals.
- I can write a large number as a multiple of a power of 10.